Actual source code: rk.c

  1: /*
  2:   Code for time stepping with the Runge-Kutta method

  4:   Notes:
  5:   The general system is written as

  7:   Udot = F(t,U)

  9: */

 11: #include <petsc/private/tsimpl.h>
 12: #include <petscdm.h>
 13: #include <../src/ts/impls/explicit/rk/rk.h>
 14: #include <../src/ts/impls/explicit/rk/mrk.h>

 16: static TSRKType  TSRKDefault = TSRK3BS;
 17: static PetscBool TSRKRegisterAllCalled;
 18: static PetscBool TSRKPackageInitialized;

 20: static RKTableauLink RKTableauList;

 22: /*MC
 23:      TSRK1FE - First order forward Euler scheme.

 25:      This method has one stage.

 27:      Options Database Key:
 28: .     -ts_rk_type 1fe - use type 1fe

 30:      Level: advanced

 32: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 33: M*/
 34: /*MC
 35:      TSRK2A - Second order RK scheme (Heun's method).

 37:      This method has two stages.

 39:      Options Database Key:
 40: .     -ts_rk_type 2a - use type 2a

 42:      Level: advanced

 44: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 45: M*/
 46: /*MC
 47:      TSRK2B - Second order RK scheme (the midpoint method).

 49:      This method has two stages.

 51:      Options Database Key:
 52: .     -ts_rk_type 2b - use type 2b

 54:      Level: advanced

 56: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 57: M*/
 58: /*MC
 59:      TSRK3 - Third order RK scheme.

 61:      This method has three stages.

 63:      Options Database Key:
 64: .     -ts_rk_type 3 - use type 3

 66:      Level: advanced

 68: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 69: M*/
 70: /*MC
 71:      TSRK3BS - Third order RK scheme of Bogacki-Shampine with 2nd order embedded method.

 73:      This method has four stages with the First Same As Last (FSAL) property.

 75:      Options Database Key:
 76: .     -ts_rk_type 3bs - use type 3bs

 78:      Level: advanced

 80:      References:
 81: . * - https://doi.org/10.1016/0893-9659(89)90079-7

 83: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 84: M*/
 85: /*MC
 86:      TSRK4 - Fourth order RK scheme.

 88:      This is the classical Runge-Kutta method with four stages.

 90:      Options Database Key:
 91: .     -ts_rk_type 4 - use type 4

 93:      Level: advanced

 95: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 96: M*/
 97: /*MC
 98:      TSRK5F - Fifth order Fehlberg RK scheme with a 4th order embedded method.

100:      This method has six stages.

102:      Options Database Key:
103: .     -ts_rk_type 5f - use type 5f

105:      Level: advanced

107: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
108: M*/
109: /*MC
110:      TSRK5DP - Fifth order Dormand-Prince RK scheme with the 4th order embedded method.

112:      This method has seven stages with the First Same As Last (FSAL) property.

114:      Options Database Key:
115: .     -ts_rk_type 5dp - use type 5dp

117:      Level: advanced

119:      References:
120: . * - https://doi.org/10.1016/0771-050X(80)90013-3

122: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
123: M*/
124: /*MC
125:      TSRK5BS - Fifth order Bogacki-Shampine RK scheme with 4th order embedded method.

127:      This method has eight stages with the First Same As Last (FSAL) property.

129:      Options Database Key:
130: .     -ts_rk_type 5bs - use type 5bs

132:      Level: advanced

134:      References:
135: . * - https://doi.org/10.1016/0898-1221(96)00141-1

137: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
138: M*/
139: /*MC
140:      TSRK6VR - Sixth order robust Verner RK scheme with fifth order embedded method.

142:      This method has nine stages with the First Same As Last (FSAL) property.

144:      Options Database Key:
145: .     -ts_rk_type 6vr - use type 6vr

147:      Level: advanced

149:      References:
150: . * - http://people.math.sfu.ca/~jverner/RKV65.IIIXb.Robust.00010102836.081204.CoeffsOnlyRAT

152: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
153: M*/
154: /*MC
155:      TSRK7VR - Seventh order robust Verner RK scheme with sixth order embedded method.

157:      This method has ten stages.

159:      Options Database Key:
160: .     -ts_rk_type 7vr - use type 7vr

162:      Level: advanced

164:      References:
165: . * - http://people.math.sfu.ca/~jverner/RKV76.IIa.Robust.000027015646.081206.CoeffsOnlyRAT

167: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
168: M*/
169: /*MC
170:      TSRK8VR - Eighth order robust Verner RK scheme with seventh order embedded method.

172:      This method has thirteen stages.

174:      Options Database Key:
175: .     -ts_rk_type 8vr - use type 8vr

177:      Level: advanced

179:      References:
180: . * - http://people.math.sfu.ca/~jverner/RKV87.IIa.Robust.00000754677.081208.CoeffsOnlyRATandFLOAT

182: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
183: M*/

185: /*@C
186:   TSRKRegisterAll - Registers all of the Runge-Kutta explicit methods in `TSRK`

188:   Not Collective, but should be called by all processes which will need the schemes to be registered

190:   Level: advanced

192: .seealso: [](ch_ts), `TSRKRegisterDestroy()`, `TSRKRegister()`
193: @*/
194: PetscErrorCode TSRKRegisterAll(void)
195: {
196:   PetscFunctionBegin;
197:   if (TSRKRegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
198:   TSRKRegisterAllCalled = PETSC_TRUE;

200: #define RC PetscRealConstant
201:   {
202:     const PetscReal A[1][1] = {{0}}, b[1] = {RC(1.0)};
203:     PetscCall(TSRKRegister(TSRK1FE, 1, 1, &A[0][0], b, NULL, NULL, 0, NULL));
204:   }
205:   {
206:     const PetscReal A[2][2] =
207:       {
208:         {0,       0},
209:         {RC(1.0), 0}
210:     },
211:                     b[2] = {RC(0.5), RC(0.5)}, bembed[2] = {RC(1.0), 0};
212:     PetscCall(TSRKRegister(TSRK2A, 2, 2, &A[0][0], b, NULL, bembed, 0, NULL));
213:   }
214:   {
215:     const PetscReal A[2][2] =
216:       {
217:         {0,       0},
218:         {RC(0.5), 0}
219:     },
220:                     b[2] = {0, RC(1.0)};
221:     PetscCall(TSRKRegister(TSRK2B, 2, 2, &A[0][0], b, NULL, NULL, 0, NULL));
222:   }
223:   {
224:     const PetscReal A[3][3] =
225:       {
226:         {0,                  0,       0},
227:         {RC(2.0) / RC(3.0),  0,       0},
228:         {RC(-1.0) / RC(3.0), RC(1.0), 0}
229:     },
230:                     b[3] = {RC(0.25), RC(0.5), RC(0.25)};
231:     PetscCall(TSRKRegister(TSRK3, 3, 3, &A[0][0], b, NULL, NULL, 0, NULL));
232:   }
233:   {
234:     const PetscReal A[4][4] =
235:       {
236:         {0,                 0,                 0,                 0},
237:         {RC(1.0) / RC(2.0), 0,                 0,                 0},
238:         {0,                 RC(3.0) / RC(4.0), 0,                 0},
239:         {RC(2.0) / RC(9.0), RC(1.0) / RC(3.0), RC(4.0) / RC(9.0), 0}
240:     },
241:                     b[4] = {RC(2.0) / RC(9.0), RC(1.0) / RC(3.0), RC(4.0) / RC(9.0), 0}, bembed[4] = {RC(7.0) / RC(24.0), RC(1.0) / RC(4.0), RC(1.0) / RC(3.0), RC(1.0) / RC(8.0)};
242:     PetscCall(TSRKRegister(TSRK3BS, 3, 4, &A[0][0], b, NULL, bembed, 0, NULL));
243:   }
244:   {
245:     const PetscReal A[4][4] =
246:       {
247:         {0,       0,       0,       0},
248:         {RC(0.5), 0,       0,       0},
249:         {0,       RC(0.5), 0,       0},
250:         {0,       0,       RC(1.0), 0}
251:     },
252:                     b[4] = {RC(1.0) / RC(6.0), RC(1.0) / RC(3.0), RC(1.0) / RC(3.0), RC(1.0) / RC(6.0)};
253:     PetscCall(TSRKRegister(TSRK4, 4, 4, &A[0][0], b, NULL, NULL, 0, NULL));
254:   }
255:   {
256:     const PetscReal A[6][6] =
257:       {
258:         {0,                       0,                        0,                        0,                       0,                    0},
259:         {RC(0.25),                0,                        0,                        0,                       0,                    0},
260:         {RC(3.0) / RC(32.0),      RC(9.0) / RC(32.0),       0,                        0,                       0,                    0},
261:         {RC(1932.0) / RC(2197.0), RC(-7200.0) / RC(2197.0), RC(7296.0) / RC(2197.0),  0,                       0,                    0},
262:         {RC(439.0) / RC(216.0),   RC(-8.0),                 RC(3680.0) / RC(513.0),   RC(-845.0) / RC(4104.0), 0,                    0},
263:         {RC(-8.0) / RC(27.0),     RC(2.0),                  RC(-3544.0) / RC(2565.0), RC(1859.0) / RC(4104.0), RC(-11.0) / RC(40.0), 0}
264:     },
265:                     b[6]      = {RC(16.0) / RC(135.0), 0, RC(6656.0) / RC(12825.0), RC(28561.0) / RC(56430.0), RC(-9.0) / RC(50.0), RC(2.0) / RC(55.0)},
266:                     bembed[6] = {RC(25.0) / RC(216.0), 0, RC(1408.0) / RC(2565.0), RC(2197.0) / RC(4104.0), RC(-1.0) / RC(5.0), 0};
267:     PetscCall(TSRKRegister(TSRK5F, 5, 6, &A[0][0], b, NULL, bembed, 0, NULL));
268:   }
269:   {
270:     const PetscReal A[7][7] =
271:       {
272:         {0,                        0,                         0,                        0,                      0,                         0,                   0},
273:         {RC(1.0) / RC(5.0),        0,                         0,                        0,                      0,                         0,                   0},
274:         {RC(3.0) / RC(40.0),       RC(9.0) / RC(40.0),        0,                        0,                      0,                         0,                   0},
275:         {RC(44.0) / RC(45.0),      RC(-56.0) / RC(15.0),      RC(32.0) / RC(9.0),       0,                      0,                         0,                   0},
276:         {RC(19372.0) / RC(6561.0), RC(-25360.0) / RC(2187.0), RC(64448.0) / RC(6561.0), RC(-212.0) / RC(729.0), 0,                         0,                   0},
277:         {RC(9017.0) / RC(3168.0),  RC(-355.0) / RC(33.0),     RC(46732.0) / RC(5247.0), RC(49.0) / RC(176.0),   RC(-5103.0) / RC(18656.0), 0,                   0},
278:         {RC(35.0) / RC(384.0),     0,                         RC(500.0) / RC(1113.0),   RC(125.0) / RC(192.0),  RC(-2187.0) / RC(6784.0),  RC(11.0) / RC(84.0), 0}
279:     },
280:                     b[7] = {RC(35.0) / RC(384.0), 0, RC(500.0) / RC(1113.0), RC(125.0) / RC(192.0), RC(-2187.0) / RC(6784.0), RC(11.0) / RC(84.0), 0},
281:                     bembed[7] = {RC(5179.0) / RC(57600.0), 0, RC(7571.0) / RC(16695.0), RC(393.0) / RC(640.0), RC(-92097.0) / RC(339200.0), RC(187.0) / RC(2100.0), RC(1.0) / RC(40.0)}, binterp[7][5] = {{RC(1.0), RC(-4034104133.0) / RC(1410260304.0), RC(105330401.0) / RC(33982176.0), RC(-13107642775.0) / RC(11282082432.0), RC(6542295.0) / RC(470086768.0)}, {0, 0, 0, 0, 0}, {0, RC(132343189600.0) / RC(32700410799.0), RC(-833316000.0) / RC(131326951.0), RC(91412856700.0) / RC(32700410799.0), RC(-523383600.0) / RC(10900136933.0)}, {0, RC(-115792950.0) / RC(29380423.0), RC(185270875.0) / RC(16991088.0), RC(-12653452475.0) / RC(1880347072.0), RC(98134425.0) / RC(235043384.0)}, {0, RC(70805911779.0) / RC(24914598704.0), RC(-4531260609.0) / RC(600351776.0), RC(988140236175.0) / RC(199316789632.0), RC(-14307999165.0) / RC(24914598704.0)}, {0, RC(-331320693.0) / RC(205662961.0), RC(31361737.0) / RC(7433601.0), RC(-2426908385.0) / RC(822651844.0), RC(97305120.0) / RC(205662961.0)}, {0, RC(44764047.0) / RC(29380423.0), RC(-1532549.0) / RC(353981.0), RC(90730570.0) / RC(29380423.0), RC(-8293050.0) / RC(29380423.0)}};
282:     PetscCall(TSRKRegister(TSRK5DP, 5, 7, &A[0][0], b, NULL, bembed, 5, binterp[0]));
283:   }
284:   {
285:     const PetscReal A[8][8] =
286:       {
287:         {0,                           0,                          0,                              0,                            0,                          0,                           0,                        0},
288:         {RC(1.0) / RC(6.0),           0,                          0,                              0,                            0,                          0,                           0,                        0},
289:         {RC(2.0) / RC(27.0),          RC(4.0) / RC(27.0),         0,                              0,                            0,                          0,                           0,                        0},
290:         {RC(183.0) / RC(1372.0),      RC(-162.0) / RC(343.0),     RC(1053.0) / RC(1372.0),        0,                            0,                          0,                           0,                        0},
291:         {RC(68.0) / RC(297.0),        RC(-4.0) / RC(11.0),        RC(42.0) / RC(143.0),           RC(1960.0) / RC(3861.0),      0,                          0,                           0,                        0},
292:         {RC(597.0) / RC(22528.0),     RC(81.0) / RC(352.0),       RC(63099.0) / RC(585728.0),     RC(58653.0) / RC(366080.0),   RC(4617.0) / RC(20480.0),   0,                           0,                        0},
293:         {RC(174197.0) / RC(959244.0), RC(-30942.0) / RC(79937.0), RC(8152137.0) / RC(19744439.0), RC(666106.0) / RC(1039181.0), RC(-29421.0) / RC(29068.0), RC(482048.0) / RC(414219.0), 0,                        0},
294:         {RC(587.0) / RC(8064.0),      0,                          RC(4440339.0) / RC(15491840.0), RC(24353.0) / RC(124800.0),   RC(387.0) / RC(44800.0),    RC(2152.0) / RC(5985.0),     RC(7267.0) / RC(94080.0), 0}
295:     },
296:                     b[8]      = {RC(587.0) / RC(8064.0), 0, RC(4440339.0) / RC(15491840.0), RC(24353.0) / RC(124800.0), RC(387.0) / RC(44800.0), RC(2152.0) / RC(5985.0), RC(7267.0) / RC(94080.0), 0},
297:                     bembed[8] = {RC(2479.0) / RC(34992.0), 0, RC(123.0) / RC(416.0), RC(612941.0) / RC(3411720.0), RC(43.0) / RC(1440.0), RC(2272.0) / RC(6561.0), RC(79937.0) / RC(1113912.0), RC(3293.0) / RC(556956.0)};
298:     PetscCall(TSRKRegister(TSRK5BS, 5, 8, &A[0][0], b, NULL, bembed, 0, NULL));
299:   }
300:   {
301:     const PetscReal A[9][9] =
302:       {
303:         {0,                                                   0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0},
304:         {RC(1.8000000000000000000000000000000000000000e-01),  0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0},
305:         {RC(8.9506172839506172839506172839506172839506e-02),  RC(7.7160493827160493827160493827160493827160e-02), 0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0},
306:         {RC(6.2500000000000000000000000000000000000000e-02),  0,                                                  RC(1.8750000000000000000000000000000000000000e-01),  0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0},
307:         {RC(3.1651600000000000000000000000000000000000e-01),  0,                                                  RC(-1.0449480000000000000000000000000000000000e+00), RC(1.2584320000000000000000000000000000000000e+00),  0,                                                   0,                                                   0,                                                  0,                                                  0},
308:         {RC(2.7232612736485626257225065566674305502508e-01),  0,                                                  RC(-8.2513360323886639676113360323886639676113e-01), RC(1.0480917678812415654520917678812415654521e+00),  RC(1.0471570799276856873679117969088177628396e-01),  0,                                                   0,                                                  0,                                                  0},
309:         {RC(-1.6699418599716514314329607278961797333198e-01), 0,                                                  RC(6.3170850202429149797570850202429149797571e-01),  RC(1.7461044552773876082146758838488161796432e-01),  RC(-1.0665356459086066122525194734018680677781e+00), RC(1.2272108843537414965986394557823129251701e+00),  0,                                                  0,                                                  0},
310:         {RC(3.6423751686909581646423751686909581646424e-01),  0,                                                  RC(-2.0404858299595141700404858299595141700405e-01), RC(-3.4883737816068643136312309244640071707741e-01), RC(3.2619323032856867443333608747142581729048e+00),  RC(-2.7551020408163265306122448979591836734694e+00), RC(6.8181818181818181818181818181818181818182e-01), 0,                                                  0},
311:         {RC(7.6388888888888888888888888888888888888889e-02),  0,                                                  0,                                                   RC(3.6940836940836940836940836940836940836941e-01),  0,                                                   RC(2.4801587301587301587301587301587301587302e-01),  RC(2.3674242424242424242424242424242424242424e-01), RC(6.9444444444444444444444444444444444444444e-02), 0}
312:     },
313:                     b[9] = {RC(7.6388888888888888888888888888888888888889e-02), 0, 0, RC(3.6940836940836940836940836940836940836941e-01), 0, RC(2.4801587301587301587301587301587301587302e-01), RC(2.3674242424242424242424242424242424242424e-01),
314:                             RC(6.9444444444444444444444444444444444444444e-02), 0},
315:                     bembed[9] = {RC(5.8700209643605870020964360587002096436059e-02), 0, 0, RC(4.8072562358276643990929705215419501133787e-01), RC(-8.5341242076919085578832094861228313083563e-01), RC(1.2046485260770975056689342403628117913832e+00), 0, RC(-5.9242373072160306202859394348756050883710e-02), RC(1.6858043453788134639198468985703028256220e-01)};
316:     PetscCall(TSRKRegister(TSRK6VR, 6, 9, &A[0][0], b, NULL, bembed, 0, NULL));
317:   }
318:   {
319:     const PetscReal A[10][10] =
320:       {
321:         {0,                                                   0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
322:         {RC(5.0000000000000000000000000000000000000000e-03),  0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
323:         {RC(-1.0767901234567901234567901234567901234568e+00), RC(1.1856790123456790123456790123456790123457e+00), 0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
324:         {RC(4.0833333333333333333333333333333333333333e-02),  0,                                                  RC(1.2250000000000000000000000000000000000000e-01),  0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
325:         {RC(6.3607142857142857142857142857142857142857e-01),  0,                                                  RC(-2.4444642857142857142857142857142857142857e+00), RC(2.2633928571428571428571428571428571428571e+00),  0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
326:         {RC(-2.5351211079349245229256383554660215487207e+00), 0,                                                  RC(1.0299374654449267920438514460756024913612e+01),  RC(-7.9513032885990579949493217458266876536482e+00), RC(7.9301148923100592201226014271115261823800e-01),  0,                                                   0,                                                  0,                                                  0, 0},
327:         {RC(1.0018765812524632961969196583094999808207e+00),  0,                                                  RC(-4.1665712824423798331313938005470971453189e+00), RC(3.8343432929128642412552665218251378665197e+00),  RC(-5.0233333560710847547464330228611765612403e-01), RC(6.6768474388416077115385092269857695410259e-01),  0,                                                  0,                                                  0, 0},
328:         {RC(2.7255018354630767130333963819175005717348e+01),  0,                                                  RC(-4.2004617278410638355318645443909295369611e+01), RC(-1.0535713126619489917921081600546526103722e+01), RC(8.0495536711411937147983652158926826634202e+01),  RC(-6.7343882271790513468549075963212975640927e+01), RC(1.3048657610777937463471187029566964762710e+01), 0,                                                  0, 0},
329:         {RC(-3.0397378057114965146943658658755763226883e+00), 0,                                                  RC(1.0138161410329801111857946190709700150441e+01),  RC(-6.4293056748647215721462825629555298064437e+00), RC(-1.5864371483408276587115312853798610579467e+00), RC(1.8921781841968424410864308909131353365021e+00),  RC(1.9699335407608869061292360163336442838006e-02), RC(5.4416989827933235465102724247952572977903e-03), 0, 0},
330:         {RC(-1.4449518916777735137351003179355712360517e+00), 0,                                                  RC(8.0318913859955919224117033223019560435041e+00),  RC(-7.5831741663401346820798883023671588604984e+00), RC(3.5816169353190074211247685442452878696855e+00),  RC(-2.4369722632199529411183809065693752383733e+00), RC(8.5158999992326179339689766032486142173390e-01), 0,                                                  0, 0}
331:     },
332:                     b[10] = {RC(4.7425837833706756083569172717574534698932e-02), 0, 0, RC(2.5622361659370562659961727458274623448160e-01), RC(2.6951376833074206619473817258075952886764e-01), RC(1.2686622409092782845989138364739173247882e-01), RC(2.4887225942060071622046449427647492767292e-01), RC(3.0744837408200631335304388479099184768645e-03), RC(4.8023809989496943308189063347143123323209e-02), 0}, bembed[10] = {RC(4.7485247699299631037531273805727961552268e-02), 0, 0, RC(2.5599412588690633297154918245905393870497e-01), RC(2.7058478081067688722530891099268135732387e-01), RC(1.2505618684425992913638822323746917920448e-01),
333:                                                                                                                                                                                                                                                                                                                                                                                                                                  RC(2.5204468723743860507184043820197442562182e-01), 0, 0, RC(4.8834971521418614557381971303093137592592e-02)};
334:     PetscCall(TSRKRegister(TSRK7VR, 7, 10, &A[0][0], b, NULL, bembed, 0, NULL));
335:   }
336:   {
337:     const PetscReal A[13][13] =
338:       {
339:         {0,                                                   0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
340:         {RC(2.5000000000000000000000000000000000000000e-01),  0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
341:         {RC(8.7400846504915232052686327594877411977046e-02),  RC(2.5487604938654321753087950620345685135815e-02), 0,                                                   0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
342:         {RC(4.2333169291338582677165354330708661417323e-02),  0,                                                  RC(1.2699950787401574803149606299212598425197e-01),  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
343:         {RC(4.2609505888742261494881445237572274090942e-01),  0,                                                  RC(-1.5987952846591523265427733230657181117089e+00), RC(1.5967002257717297115939588706899953707994e+00),  0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
344:         {RC(5.0719337296713929515090618138513639239329e-02),  0,                                                  0,                                                   RC(2.5433377264600407582754714408877778031369e-01),  RC(2.0394689005728199465736223777270858044698e-01),  0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
345:         {RC(-2.9000374717523110970388379285425896124091e-01), 0,                                                  0,                                                   RC(1.3441873910260789889438681109414337003184e+00),  RC(-2.8647779433614427309611103827036562829470e+00), RC(2.6775942995105948517211260646164815438695e+00),  0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
346:         {RC(9.8535011337993546469740402980727014284756e-02),  0,                                                  0,                                                   0,                                                   RC(2.2192680630751384842024036498197387903583e-01),  RC(-1.8140622911806994312690338288073952457474e-01), RC(1.0944411472562548236922614918038631254153e-02),  0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
347:         {RC(3.8711052545731144679444618165166373405645e-01),  0,                                                  0,                                                   RC(-1.4424454974855277571256745553077927767173e+00), RC(2.9053981890699509317691346449233848441744e+00),  RC(-1.8537710696301059290843332675811978025183e+00), RC(1.4003648098728154269497325109771241479223e-01),  RC(5.7273940811495816575746774624447706488753e-01), 0,                                                   0,                                                  0,                                                  0, 0},
348:         {RC(-1.6124403444439308100630016197913480595436e-01), 0,                                                  0,                                                   RC(-1.7339602957358984083578404473962567894901e-01), RC(-1.3012892814065147406016812745172492529744e+00), RC(1.1379503751738617308558792131431003472124e+00),  RC(-3.1747649663966880106923521138043024698980e-02), RC(9.3351293824933666439811064486056884856590e-01), RC(-8.3786318334733852703300855629616433201504e-02), 0,                                                  0,                                                  0, 0},
349:         {RC(-1.9199444881589533281510804651483576073142e-02), 0,                                                  0,                                                   RC(2.7330857265264284907942326254016124275617e-01),  RC(-6.7534973206944372919691611210942380856240e-01), RC(3.4151849813846016071738489974728382711981e-01),  RC(-6.7950064803375772478920516198524629391910e-02), RC(9.6591752247623878884265586491216376509746e-02), RC(1.3253082511182101180721038466545389951226e-01),  RC(3.6854959360386113446906329951531666812946e-01), 0,                                                  0, 0},
350:         {RC(6.0918774036452898676888412111588817784584e-01),  0,                                                  0,                                                   RC(-2.2725690858980016768999800931413088399719e+00), RC(4.7578983426940290068155255881914785497547e+00),  RC(-5.5161067066927584824294689667844248244842e+00), RC(2.9005963696801192709095818565946174378180e-01),  RC(5.6914239633590368229109858454801849145630e-01), RC(7.9267957603321670271339916205893327579951e-01),  RC(1.5473720453288822894126190771849898232047e-01), RC(1.6149708956621816247083215106334544434974e+00), 0, 0},
351:         {RC(8.8735762208534719663211694051981022704884e-01),  0,                                                  0,                                                   RC(-2.9754597821085367558513632804709301581977e+00), RC(5.6007170094881630597990392548350098923829e+00),  RC(-5.9156074505366744680014930189941657351840e+00), RC(2.2029689156134927016879142540807638331238e-01),  RC(1.0155097824462216666143271340902996997549e-01), RC(1.1514345647386055909780397752125850553556e+00),  RC(1.9297101665271239396134361900805843653065e+00), 0,                                                  0, 0}
352:     },
353:                     b[13] = {RC(4.4729564666695714203015840429049382466467e-02), 0, 0, 0, 0, RC(1.5691033527708199813368698010726645409175e-01), RC(1.8460973408151637740702451873526277892035e-01), RC(2.2516380602086991042479419400350721970920e-01), RC(1.4794615651970234687005179885449141753736e-01), RC(7.6055542444955825269798361910336491012732e-02), RC(1.2277290235018619610824346315921437388535e-01), RC(4.1811958638991631583384842800871882376786e-02), 0}, bembed[13] = {RC(4.5847111400495925878664730122010282095875e-02), 0, 0, 0, 0, RC(2.6231891404152387437443356584845803392392e-01), RC(1.9169372337852611904485738635688429008025e-01), RC(2.1709172327902618330978407422906448568196e-01), RC(1.2738189624833706796803169450656737867900e-01), RC(1.1510530385365326258240515750043192148894e-01), 0, 0, RC(4.0561327798437566841823391436583608050053e-02)};
354:     PetscCall(TSRKRegister(TSRK8VR, 8, 13, &A[0][0], b, NULL, bembed, 0, NULL));
355:   }
356: #undef RC
357:   PetscFunctionReturn(PETSC_SUCCESS);
358: }

360: /*@C
361:    TSRKRegisterDestroy - Frees the list of schemes that were registered by `TSRKRegister()`.

363:    Not Collective

365:    Level: advanced

367: .seealso: [](ch_ts), `TSRK`, `TSRKRegister()`, `TSRKRegisterAll()`
368: @*/
369: PetscErrorCode TSRKRegisterDestroy(void)
370: {
371:   RKTableauLink link;

373:   PetscFunctionBegin;
374:   while ((link = RKTableauList)) {
375:     RKTableau t   = &link->tab;
376:     RKTableauList = link->next;
377:     PetscCall(PetscFree3(t->A, t->b, t->c));
378:     PetscCall(PetscFree(t->bembed));
379:     PetscCall(PetscFree(t->binterp));
380:     PetscCall(PetscFree(t->name));
381:     PetscCall(PetscFree(link));
382:   }
383:   TSRKRegisterAllCalled = PETSC_FALSE;
384:   PetscFunctionReturn(PETSC_SUCCESS);
385: }

387: /*@C
388:   TSRKInitializePackage - This function initializes everything in the `TSRK` package. It is called
389:   from `TSInitializePackage()`.

391:   Level: developer

393: .seealso: [](ch_ts), `TSInitializePackage()`, `PetscInitialize()`, `TSRKFinalizePackage()`
394: @*/
395: PetscErrorCode TSRKInitializePackage(void)
396: {
397:   PetscFunctionBegin;
398:   if (TSRKPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
399:   TSRKPackageInitialized = PETSC_TRUE;
400:   PetscCall(TSRKRegisterAll());
401:   PetscCall(PetscRegisterFinalize(TSRKFinalizePackage));
402:   PetscFunctionReturn(PETSC_SUCCESS);
403: }

405: /*@C
406:   TSRKFinalizePackage - This function destroys everything in the `TSRK` package. It is
407:   called from `PetscFinalize()`.

409:   Level: developer

411: .seealso: [](ch_ts), `PetscFinalize()`, `TSRKInitializePackage()`
412: @*/
413: PetscErrorCode TSRKFinalizePackage(void)
414: {
415:   PetscFunctionBegin;
416:   TSRKPackageInitialized = PETSC_FALSE;
417:   PetscCall(TSRKRegisterDestroy());
418:   PetscFunctionReturn(PETSC_SUCCESS);
419: }

421: /*@C
422:    TSRKRegister - register an `TSRK` scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation

424:    Not Collective, but the same schemes should be registered on all processes on which they will be used

426:    Input Parameters:
427: +  name - identifier for method
428: .  order - approximation order of method
429: .  s - number of stages, this is the dimension of the matrices below
430: .  A - stage coefficients (dimension s*s, row-major)
431: .  b - step completion table (dimension s; NULL to use last row of A)
432: .  c - abscissa (dimension s; NULL to use row sums of A)
433: .  bembed - completion table for embedded method (dimension s; NULL if not available)
434: .  p - Order of the interpolation scheme, equal to the number of columns of binterp
435: -  binterp - Coefficients of the interpolation formula (dimension s*p; NULL to reuse b with p=1)

437:    Level: advanced

439:    Note:
440:    Several `TSRK` methods are provided, this function is only needed to create new methods.

442: .seealso: [](ch_ts), `TSRK`
443: @*/
444: PetscErrorCode TSRKRegister(TSRKType name, PetscInt order, PetscInt s, const PetscReal A[], const PetscReal b[], const PetscReal c[], const PetscReal bembed[], PetscInt p, const PetscReal binterp[])
445: {
446:   RKTableauLink link;
447:   RKTableau     t;
448:   PetscInt      i, j;

450:   PetscFunctionBegin;

458:   PetscCall(TSRKInitializePackage());
459:   PetscCall(PetscNew(&link));
460:   t = &link->tab;

462:   PetscCall(PetscStrallocpy(name, &t->name));
463:   t->order = order;
464:   t->s     = s;
465:   PetscCall(PetscMalloc3(s * s, &t->A, s, &t->b, s, &t->c));
466:   PetscCall(PetscArraycpy(t->A, A, s * s));
467:   if (b) PetscCall(PetscArraycpy(t->b, b, s));
468:   else
469:     for (i = 0; i < s; i++) t->b[i] = A[(s - 1) * s + i];
470:   if (c) PetscCall(PetscArraycpy(t->c, c, s));
471:   else
472:     for (i = 0; i < s; i++)
473:       for (j = 0, t->c[i] = 0; j < s; j++) t->c[i] += A[i * s + j];
474:   t->FSAL = PETSC_TRUE;
475:   for (i = 0; i < s; i++)
476:     if (t->A[(s - 1) * s + i] != t->b[i]) t->FSAL = PETSC_FALSE;

478:   if (bembed) {
479:     PetscCall(PetscMalloc1(s, &t->bembed));
480:     PetscCall(PetscArraycpy(t->bembed, bembed, s));
481:   }

483:   if (!binterp) {
484:     p       = 1;
485:     binterp = t->b;
486:   }
487:   t->p = p;
488:   PetscCall(PetscMalloc1(s * p, &t->binterp));
489:   PetscCall(PetscArraycpy(t->binterp, binterp, s * p));

491:   link->next    = RKTableauList;
492:   RKTableauList = link;
493:   PetscFunctionReturn(PETSC_SUCCESS);
494: }

496: PetscErrorCode TSRKGetTableau_RK(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed, PetscInt *p, const PetscReal **binterp, PetscBool *FSAL)
497: {
498:   TS_RK    *rk  = (TS_RK *)ts->data;
499:   RKTableau tab = rk->tableau;

501:   PetscFunctionBegin;
502:   if (s) *s = tab->s;
503:   if (A) *A = tab->A;
504:   if (b) *b = tab->b;
505:   if (c) *c = tab->c;
506:   if (bembed) *bembed = tab->bembed;
507:   if (p) *p = tab->p;
508:   if (binterp) *binterp = tab->binterp;
509:   if (FSAL) *FSAL = tab->FSAL;
510:   PetscFunctionReturn(PETSC_SUCCESS);
511: }

513: /*@C
514:    TSRKGetTableau - Get info on the `TSRK` tableau

516:    Not Collective

518:    Input Parameter:
519: .  ts - timestepping context

521:    Output Parameters:
522: +  s - number of stages, this is the dimension of the matrices below
523: .  A - stage coefficients (dimension s*s, row-major)
524: .  b - step completion table (dimension s)
525: .  c - abscissa (dimension s)
526: .  bembed - completion table for embedded method (dimension s; NULL if not available)
527: .  p - Order of the interpolation scheme, equal to the number of columns of binterp
528: .  binterp - Coefficients of the interpolation formula (dimension s*p)
529: -  FSAL - whether or not the scheme has the First Same As Last property

531:    Level: developer

533: .seealso: [](ch_ts), `TSRK`, `TSRKRegister()`, `TSRKSetType()`
534: @*/
535: PetscErrorCode TSRKGetTableau(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed, PetscInt *p, const PetscReal **binterp, PetscBool *FSAL)
536: {
537:   PetscFunctionBegin;
539:   PetscUseMethod(ts, "TSRKGetTableau_C", (TS, PetscInt *, const PetscReal **, const PetscReal **, const PetscReal **, const PetscReal **, PetscInt *, const PetscReal **, PetscBool *), (ts, s, A, b, c, bembed, p, binterp, FSAL));
540:   PetscFunctionReturn(PETSC_SUCCESS);
541: }

543: /*
544:  This is for single-step RK method
545:  The step completion formula is

547:  x1 = x0 + h b^T YdotRHS

549:  This function can be called before or after ts->vec_sol has been updated.
550:  Suppose we have a completion formula (b) and an embedded formula (be) of different order.
551:  We can write

553:  x1e = x0 + h be^T YdotRHS
554:      = x1 - h b^T YdotRHS + h be^T YdotRHS
555:      = x1 + h (be - b)^T YdotRHS

557:  so we can evaluate the method with different order even after the step has been optimistically completed.
558: */
559: static PetscErrorCode TSEvaluateStep_RK(TS ts, PetscInt order, Vec X, PetscBool *done)
560: {
561:   TS_RK       *rk  = (TS_RK *)ts->data;
562:   RKTableau    tab = rk->tableau;
563:   PetscScalar *w   = rk->work;
564:   PetscReal    h;
565:   PetscInt     s = tab->s, j;

567:   PetscFunctionBegin;
568:   switch (rk->status) {
569:   case TS_STEP_INCOMPLETE:
570:   case TS_STEP_PENDING:
571:     h = ts->time_step;
572:     break;
573:   case TS_STEP_COMPLETE:
574:     h = ts->ptime - ts->ptime_prev;
575:     break;
576:   default:
577:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
578:   }
579:   if (order == tab->order) {
580:     if (rk->status == TS_STEP_INCOMPLETE) {
581:       PetscCall(VecCopy(ts->vec_sol, X));
582:       for (j = 0; j < s; j++) w[j] = h * tab->b[j] / rk->dtratio;
583:       PetscCall(VecMAXPY(X, s, w, rk->YdotRHS));
584:     } else PetscCall(VecCopy(ts->vec_sol, X));
585:     PetscFunctionReturn(PETSC_SUCCESS);
586:   } else if (order == tab->order - 1) {
587:     if (!tab->bembed) goto unavailable;
588:     if (rk->status == TS_STEP_INCOMPLETE) { /*Complete with the embedded method (be)*/
589:       PetscCall(VecCopy(ts->vec_sol, X));
590:       for (j = 0; j < s; j++) w[j] = h * tab->bembed[j];
591:       PetscCall(VecMAXPY(X, s, w, rk->YdotRHS));
592:     } else { /*Rollback and re-complete using (be-b) */
593:       PetscCall(VecCopy(ts->vec_sol, X));
594:       for (j = 0; j < s; j++) w[j] = h * (tab->bembed[j] - tab->b[j]);
595:       PetscCall(VecMAXPY(X, s, w, rk->YdotRHS));
596:     }
597:     if (done) *done = PETSC_TRUE;
598:     PetscFunctionReturn(PETSC_SUCCESS);
599:   }
600: unavailable:
601:   if (done) *done = PETSC_FALSE;
602:   else
603:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "RK '%s' of order %" PetscInt_FMT " cannot evaluate step at order %" PetscInt_FMT ". Consider using -ts_adapt_type none or a different method that has an embedded estimate.", tab->name, tab->order, order);
604:   PetscFunctionReturn(PETSC_SUCCESS);
605: }

607: static PetscErrorCode TSForwardCostIntegral_RK(TS ts)
608: {
609:   TS_RK           *rk     = (TS_RK *)ts->data;
610:   TS               quadts = ts->quadraturets;
611:   RKTableau        tab    = rk->tableau;
612:   const PetscInt   s      = tab->s;
613:   const PetscReal *b = tab->b, *c = tab->c;
614:   Vec             *Y = rk->Y;
615:   PetscInt         i;

617:   PetscFunctionBegin;
618:   /* No need to backup quadts->vec_sol since it can be reverted in TSRollBack_RK */
619:   for (i = s - 1; i >= 0; i--) {
620:     /* Evolve quadrature TS solution to compute integrals */
621:     PetscCall(TSComputeRHSFunction(quadts, rk->ptime + rk->time_step * c[i], Y[i], ts->vec_costintegrand));
622:     PetscCall(VecAXPY(quadts->vec_sol, rk->time_step * b[i], ts->vec_costintegrand));
623:   }
624:   PetscFunctionReturn(PETSC_SUCCESS);
625: }

627: static PetscErrorCode TSAdjointCostIntegral_RK(TS ts)
628: {
629:   TS_RK           *rk     = (TS_RK *)ts->data;
630:   RKTableau        tab    = rk->tableau;
631:   TS               quadts = ts->quadraturets;
632:   const PetscInt   s      = tab->s;
633:   const PetscReal *b = tab->b, *c = tab->c;
634:   Vec             *Y = rk->Y;
635:   PetscInt         i;

637:   PetscFunctionBegin;
638:   for (i = s - 1; i >= 0; i--) {
639:     /* Evolve quadrature TS solution to compute integrals */
640:     PetscCall(TSComputeRHSFunction(quadts, ts->ptime + ts->time_step * (1.0 - c[i]), Y[i], ts->vec_costintegrand));
641:     PetscCall(VecAXPY(quadts->vec_sol, -ts->time_step * b[i], ts->vec_costintegrand));
642:   }
643:   PetscFunctionReturn(PETSC_SUCCESS);
644: }

646: static PetscErrorCode TSRollBack_RK(TS ts)
647: {
648:   TS_RK           *rk     = (TS_RK *)ts->data;
649:   TS               quadts = ts->quadraturets;
650:   RKTableau        tab    = rk->tableau;
651:   const PetscInt   s      = tab->s;
652:   const PetscReal *b = tab->b, *c = tab->c;
653:   PetscScalar     *w = rk->work;
654:   Vec             *Y = rk->Y, *YdotRHS = rk->YdotRHS;
655:   PetscInt         j;
656:   PetscReal        h;

658:   PetscFunctionBegin;
659:   switch (rk->status) {
660:   case TS_STEP_INCOMPLETE:
661:   case TS_STEP_PENDING:
662:     h = ts->time_step;
663:     break;
664:   case TS_STEP_COMPLETE:
665:     h = ts->ptime - ts->ptime_prev;
666:     break;
667:   default:
668:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
669:   }
670:   for (j = 0; j < s; j++) w[j] = -h * b[j];
671:   PetscCall(VecMAXPY(ts->vec_sol, s, w, YdotRHS));
672:   if (quadts && ts->costintegralfwd) {
673:     for (j = 0; j < s; j++) {
674:       /* Revert the quadrature TS solution */
675:       PetscCall(TSComputeRHSFunction(quadts, rk->ptime + h * c[j], Y[j], ts->vec_costintegrand));
676:       PetscCall(VecAXPY(quadts->vec_sol, -h * b[j], ts->vec_costintegrand));
677:     }
678:   }
679:   PetscFunctionReturn(PETSC_SUCCESS);
680: }

682: static PetscErrorCode TSForwardStep_RK(TS ts)
683: {
684:   TS_RK           *rk  = (TS_RK *)ts->data;
685:   RKTableau        tab = rk->tableau;
686:   Mat              J, *MatsFwdSensipTemp = rk->MatsFwdSensipTemp;
687:   const PetscInt   s = tab->s;
688:   const PetscReal *A = tab->A, *c = tab->c, *b = tab->b;
689:   Vec             *Y = rk->Y;
690:   PetscInt         i, j;
691:   PetscReal        stage_time, h = ts->time_step;
692:   PetscBool        zero;

694:   PetscFunctionBegin;
695:   PetscCall(MatCopy(ts->mat_sensip, rk->MatFwdSensip0, SAME_NONZERO_PATTERN));
696:   PetscCall(TSGetRHSJacobian(ts, &J, NULL, NULL, NULL));

698:   for (i = 0; i < s; i++) {
699:     stage_time = ts->ptime + h * c[i];
700:     zero       = PETSC_FALSE;
701:     if (b[i] == 0 && i == s - 1) zero = PETSC_TRUE;
702:     /* TLM Stage values */
703:     if (!i) {
704:       PetscCall(MatCopy(ts->mat_sensip, rk->MatsFwdStageSensip[i], SAME_NONZERO_PATTERN));
705:     } else if (!zero) {
706:       PetscCall(MatZeroEntries(rk->MatsFwdStageSensip[i]));
707:       for (j = 0; j < i; j++) PetscCall(MatAXPY(rk->MatsFwdStageSensip[i], h * A[i * s + j], MatsFwdSensipTemp[j], SAME_NONZERO_PATTERN));
708:       PetscCall(MatAXPY(rk->MatsFwdStageSensip[i], 1., ts->mat_sensip, SAME_NONZERO_PATTERN));
709:     } else {
710:       PetscCall(MatZeroEntries(rk->MatsFwdStageSensip[i]));
711:     }

713:     PetscCall(TSComputeRHSJacobian(ts, stage_time, Y[i], J, J));
714:     PetscCall(MatMatMult(J, rk->MatsFwdStageSensip[i], MAT_REUSE_MATRIX, PETSC_DEFAULT, &MatsFwdSensipTemp[i]));
715:     if (ts->Jacprhs) {
716:       PetscCall(TSComputeRHSJacobianP(ts, stage_time, Y[i], ts->Jacprhs)); /* get f_p */
717:       if (ts->vecs_sensi2p) {                                              /* TLM used for 2nd-order adjoint */
718:         PetscScalar *xarr;
719:         PetscCall(MatDenseGetColumn(MatsFwdSensipTemp[i], 0, &xarr));
720:         PetscCall(VecPlaceArray(rk->VecDeltaFwdSensipCol, xarr));
721:         PetscCall(MatMultAdd(ts->Jacprhs, ts->vec_dir, rk->VecDeltaFwdSensipCol, rk->VecDeltaFwdSensipCol));
722:         PetscCall(VecResetArray(rk->VecDeltaFwdSensipCol));
723:         PetscCall(MatDenseRestoreColumn(MatsFwdSensipTemp[i], &xarr));
724:       } else {
725:         PetscCall(MatAXPY(MatsFwdSensipTemp[i], 1., ts->Jacprhs, SUBSET_NONZERO_PATTERN));
726:       }
727:     }
728:   }

730:   for (i = 0; i < s; i++) PetscCall(MatAXPY(ts->mat_sensip, h * b[i], rk->MatsFwdSensipTemp[i], SAME_NONZERO_PATTERN));
731:   rk->status = TS_STEP_COMPLETE;
732:   PetscFunctionReturn(PETSC_SUCCESS);
733: }

735: static PetscErrorCode TSForwardGetStages_RK(TS ts, PetscInt *ns, Mat **stagesensip)
736: {
737:   TS_RK    *rk  = (TS_RK *)ts->data;
738:   RKTableau tab = rk->tableau;

740:   PetscFunctionBegin;
741:   if (ns) *ns = tab->s;
742:   if (stagesensip) *stagesensip = rk->MatsFwdStageSensip;
743:   PetscFunctionReturn(PETSC_SUCCESS);
744: }

746: static PetscErrorCode TSForwardSetUp_RK(TS ts)
747: {
748:   TS_RK    *rk  = (TS_RK *)ts->data;
749:   RKTableau tab = rk->tableau;
750:   PetscInt  i;

752:   PetscFunctionBegin;
753:   /* backup sensitivity results for roll-backs */
754:   PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &rk->MatFwdSensip0));

756:   PetscCall(PetscMalloc1(tab->s, &rk->MatsFwdStageSensip));
757:   PetscCall(PetscMalloc1(tab->s, &rk->MatsFwdSensipTemp));
758:   for (i = 0; i < tab->s; i++) {
759:     PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &rk->MatsFwdStageSensip[i]));
760:     PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &rk->MatsFwdSensipTemp[i]));
761:   }
762:   PetscCall(VecDuplicate(ts->vec_sol, &rk->VecDeltaFwdSensipCol));
763:   PetscFunctionReturn(PETSC_SUCCESS);
764: }

766: static PetscErrorCode TSForwardReset_RK(TS ts)
767: {
768:   TS_RK    *rk  = (TS_RK *)ts->data;
769:   RKTableau tab = rk->tableau;
770:   PetscInt  i;

772:   PetscFunctionBegin;
773:   PetscCall(MatDestroy(&rk->MatFwdSensip0));
774:   if (rk->MatsFwdStageSensip) {
775:     for (i = 0; i < tab->s; i++) PetscCall(MatDestroy(&rk->MatsFwdStageSensip[i]));
776:     PetscCall(PetscFree(rk->MatsFwdStageSensip));
777:   }
778:   if (rk->MatsFwdSensipTemp) {
779:     for (i = 0; i < tab->s; i++) PetscCall(MatDestroy(&rk->MatsFwdSensipTemp[i]));
780:     PetscCall(PetscFree(rk->MatsFwdSensipTemp));
781:   }
782:   PetscCall(VecDestroy(&rk->VecDeltaFwdSensipCol));
783:   PetscFunctionReturn(PETSC_SUCCESS);
784: }

786: static PetscErrorCode TSStep_RK(TS ts)
787: {
788:   TS_RK           *rk  = (TS_RK *)ts->data;
789:   RKTableau        tab = rk->tableau;
790:   const PetscInt   s   = tab->s;
791:   const PetscReal *A = tab->A, *c = tab->c;
792:   PetscScalar     *w = rk->work;
793:   Vec             *Y = rk->Y, *YdotRHS = rk->YdotRHS;
794:   PetscBool        FSAL = tab->FSAL;
795:   TSAdapt          adapt;
796:   PetscInt         i, j;
797:   PetscInt         rejections = 0;
798:   PetscBool        stageok, accept = PETSC_TRUE;
799:   PetscReal        next_time_step = ts->time_step;

801:   PetscFunctionBegin;
802:   if (ts->steprollback || ts->steprestart) FSAL = PETSC_FALSE;
803:   if (FSAL) PetscCall(VecCopy(YdotRHS[s - 1], YdotRHS[0]));

805:   rk->status = TS_STEP_INCOMPLETE;
806:   while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
807:     PetscReal t = ts->ptime;
808:     PetscReal h = ts->time_step;
809:     for (i = 0; i < s; i++) {
810:       rk->stage_time = t + h * c[i];
811:       PetscCall(TSPreStage(ts, rk->stage_time));
812:       PetscCall(VecCopy(ts->vec_sol, Y[i]));
813:       for (j = 0; j < i; j++) w[j] = h * A[i * s + j];
814:       PetscCall(VecMAXPY(Y[i], i, w, YdotRHS));
815:       PetscCall(TSPostStage(ts, rk->stage_time, i, Y));
816:       PetscCall(TSGetAdapt(ts, &adapt));
817:       PetscCall(TSAdaptCheckStage(adapt, ts, rk->stage_time, Y[i], &stageok));
818:       if (!stageok) goto reject_step;
819:       if (FSAL && !i) continue;
820:       PetscCall(TSComputeRHSFunction(ts, t + h * c[i], Y[i], YdotRHS[i]));
821:     }

823:     rk->status = TS_STEP_INCOMPLETE;
824:     PetscCall(TSEvaluateStep(ts, tab->order, ts->vec_sol, NULL));
825:     rk->status = TS_STEP_PENDING;
826:     PetscCall(TSGetAdapt(ts, &adapt));
827:     PetscCall(TSAdaptCandidatesClear(adapt));
828:     PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
829:     PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
830:     rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
831:     if (!accept) { /* Roll back the current step */
832:       PetscCall(TSRollBack_RK(ts));
833:       ts->time_step = next_time_step;
834:       goto reject_step;
835:     }

837:     if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */
838:       rk->ptime     = ts->ptime;
839:       rk->time_step = ts->time_step;
840:     }

842:     ts->ptime += ts->time_step;
843:     ts->time_step = next_time_step;
844:     break;

846:   reject_step:
847:     ts->reject++;
848:     accept = PETSC_FALSE;
849:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
850:       ts->reason = TS_DIVERGED_STEP_REJECTED;
851:       PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
852:     }
853:   }
854:   PetscFunctionReturn(PETSC_SUCCESS);
855: }

857: static PetscErrorCode TSAdjointSetUp_RK(TS ts)
858: {
859:   TS_RK    *rk  = (TS_RK *)ts->data;
860:   RKTableau tab = rk->tableau;
861:   PetscInt  s   = tab->s;

863:   PetscFunctionBegin;
864:   if (ts->adjointsetupcalled++) PetscFunctionReturn(PETSC_SUCCESS);
865:   PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], s * ts->numcost, &rk->VecsDeltaLam));
866:   PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &rk->VecsSensiTemp));
867:   if (ts->vecs_sensip) PetscCall(VecDuplicate(ts->vecs_sensip[0], &rk->VecDeltaMu));
868:   if (ts->vecs_sensi2) {
869:     PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], s * ts->numcost, &rk->VecsDeltaLam2));
870:     PetscCall(VecDuplicateVecs(ts->vecs_sensi2[0], ts->numcost, &rk->VecsSensi2Temp));
871:   }
872:   if (ts->vecs_sensi2p) PetscCall(VecDuplicate(ts->vecs_sensi2p[0], &rk->VecDeltaMu2));
873:   PetscFunctionReturn(PETSC_SUCCESS);
874: }

876: /*
877:   Assumptions:
878:     - TSStep_RK() always evaluates the step with b, not bembed.
879: */
880: static PetscErrorCode TSAdjointStep_RK(TS ts)
881: {
882:   TS_RK           *rk     = (TS_RK *)ts->data;
883:   TS               quadts = ts->quadraturets;
884:   RKTableau        tab    = rk->tableau;
885:   Mat              J, Jpre, Jquad;
886:   const PetscInt   s = tab->s;
887:   const PetscReal *A = tab->A, *b = tab->b, *c = tab->c;
888:   PetscScalar     *w = rk->work, *xarr;
889:   Vec             *Y = rk->Y, *VecsDeltaLam = rk->VecsDeltaLam, VecDeltaMu = rk->VecDeltaMu, *VecsSensiTemp = rk->VecsSensiTemp;
890:   Vec             *VecsDeltaLam2 = rk->VecsDeltaLam2, VecDeltaMu2 = rk->VecDeltaMu2, *VecsSensi2Temp = rk->VecsSensi2Temp;
891:   Vec              VecDRDUTransCol = ts->vec_drdu_col, VecDRDPTransCol = ts->vec_drdp_col;
892:   PetscInt         i, j, nadj;
893:   PetscReal        t = ts->ptime;
894:   PetscReal        h = ts->time_step;

896:   PetscFunctionBegin;
897:   rk->status = TS_STEP_INCOMPLETE;

899:   PetscCall(TSGetRHSJacobian(ts, &J, &Jpre, NULL, NULL));
900:   if (quadts) PetscCall(TSGetRHSJacobian(quadts, &Jquad, NULL, NULL, NULL));
901:   for (i = s - 1; i >= 0; i--) {
902:     if (tab->FSAL && i == s - 1) {
903:       /* VecsDeltaLam[nadj*s+s-1] are initialized with zeros and the values never change.*/
904:       continue;
905:     }
906:     rk->stage_time = t + h * (1.0 - c[i]);
907:     PetscCall(TSComputeSNESJacobian(ts, Y[i], J, Jpre));
908:     if (quadts) { PetscCall(TSComputeRHSJacobian(quadts, rk->stage_time, Y[i], Jquad, Jquad)); /* get r_u^T */ }
909:     if (ts->vecs_sensip) {
910:       PetscCall(TSComputeRHSJacobianP(ts, rk->stage_time, Y[i], ts->Jacprhs)); /* get f_p */
911:       if (quadts) { PetscCall(TSComputeRHSJacobianP(quadts, rk->stage_time, Y[i], quadts->Jacprhs)); /* get f_p for the quadrature */ }
912:     }

914:     if (b[i]) {
915:       for (j = i + 1; j < s; j++) w[j - i - 1] = A[j * s + i] / b[i]; /* coefficients for computing VecsSensiTemp */
916:     } else {
917:       for (j = i + 1; j < s; j++) w[j - i - 1] = A[j * s + i]; /* coefficients for computing VecsSensiTemp */
918:     }

920:     for (nadj = 0; nadj < ts->numcost; nadj++) {
921:       /* Stage values of lambda */
922:       if (b[i]) {
923:         /* lambda_{n+1} + \sum_{j=i+1}^s a_{ji}/b[i]*lambda_{s,j} */
924:         PetscCall(VecCopy(ts->vecs_sensi[nadj], VecsSensiTemp[nadj])); /* VecDeltaLam is an vec array of size s by numcost */
925:         PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
926:         PetscCall(MatMultTranspose(J, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i])); /* VecsSensiTemp will be reused by 2nd-order adjoint */
927:         PetscCall(VecScale(VecsDeltaLam[nadj * s + i], -h * b[i]));
928:         if (quadts) {
929:           PetscCall(MatDenseGetColumn(Jquad, nadj, &xarr));
930:           PetscCall(VecPlaceArray(VecDRDUTransCol, xarr));
931:           PetscCall(VecAXPY(VecsDeltaLam[nadj * s + i], -h * b[i], VecDRDUTransCol));
932:           PetscCall(VecResetArray(VecDRDUTransCol));
933:           PetscCall(MatDenseRestoreColumn(Jquad, &xarr));
934:         }
935:       } else {
936:         /* \sum_{j=i+1}^s a_{ji}*lambda_{s,j} */
937:         PetscCall(VecSet(VecsSensiTemp[nadj], 0));
938:         PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
939:         PetscCall(MatMultTranspose(J, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i]));
940:         PetscCall(VecScale(VecsDeltaLam[nadj * s + i], -h));
941:       }

943:       /* Stage values of mu */
944:       if (ts->vecs_sensip) {
945:         if (b[i]) {
946:           PetscCall(MatMultTranspose(ts->Jacprhs, VecsSensiTemp[nadj], VecDeltaMu));
947:           PetscCall(VecScale(VecDeltaMu, -h * b[i]));
948:           if (quadts) {
949:             PetscCall(MatDenseGetColumn(quadts->Jacprhs, nadj, &xarr));
950:             PetscCall(VecPlaceArray(VecDRDPTransCol, xarr));
951:             PetscCall(VecAXPY(VecDeltaMu, -h * b[i], VecDRDPTransCol));
952:             PetscCall(VecResetArray(VecDRDPTransCol));
953:             PetscCall(MatDenseRestoreColumn(quadts->Jacprhs, &xarr));
954:           }
955:         } else {
956:           PetscCall(VecScale(VecDeltaMu, -h));
957:         }
958:         PetscCall(VecAXPY(ts->vecs_sensip[nadj], 1., VecDeltaMu)); /* update sensip for each stage */
959:       }
960:     }

962:     if (ts->vecs_sensi2 && ts->forward_solve) { /* 2nd-order adjoint, TLM mode has to be turned on */
963:       /* Get w1 at t_{n+1} from TLM matrix */
964:       PetscCall(MatDenseGetColumn(rk->MatsFwdStageSensip[i], 0, &xarr));
965:       PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
966:       /* lambda_s^T F_UU w_1 */
967:       PetscCall(TSComputeRHSHessianProductFunctionUU(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_sensip_col, ts->vecs_guu));
968:       if (quadts) {
969:         /* R_UU w_1 */
970:         PetscCall(TSComputeRHSHessianProductFunctionUU(quadts, rk->stage_time, Y[i], NULL, ts->vec_sensip_col, ts->vecs_guu));
971:       }
972:       if (ts->vecs_sensip) {
973:         /* lambda_s^T F_UP w_2 */
974:         PetscCall(TSComputeRHSHessianProductFunctionUP(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_dir, ts->vecs_gup));
975:         if (quadts) {
976:           /* R_UP w_2 */
977:           PetscCall(TSComputeRHSHessianProductFunctionUP(quadts, rk->stage_time, Y[i], NULL, ts->vec_sensip_col, ts->vecs_gup));
978:         }
979:       }
980:       if (ts->vecs_sensi2p) {
981:         /* lambda_s^T F_PU w_1 */
982:         PetscCall(TSComputeRHSHessianProductFunctionPU(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_sensip_col, ts->vecs_gpu));
983:         /* lambda_s^T F_PP w_2 */
984:         PetscCall(TSComputeRHSHessianProductFunctionPP(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_dir, ts->vecs_gpp));
985:         if (b[i] && quadts) {
986:           /* R_PU w_1 */
987:           PetscCall(TSComputeRHSHessianProductFunctionPU(quadts, rk->stage_time, Y[i], NULL, ts->vec_sensip_col, ts->vecs_gpu));
988:           /* R_PP w_2 */
989:           PetscCall(TSComputeRHSHessianProductFunctionPP(quadts, rk->stage_time, Y[i], NULL, ts->vec_dir, ts->vecs_gpp));
990:         }
991:       }
992:       PetscCall(VecResetArray(ts->vec_sensip_col));
993:       PetscCall(MatDenseRestoreColumn(rk->MatsFwdStageSensip[i], &xarr));

995:       for (nadj = 0; nadj < ts->numcost; nadj++) {
996:         /* Stage values of lambda */
997:         if (b[i]) {
998:           /* J_i^T*(Lambda_{n+1}+\sum_{j=i+1}^s a_{ji}/b_i*Lambda_{s,j} */
999:           PetscCall(VecCopy(ts->vecs_sensi2[nadj], VecsSensi2Temp[nadj]));
1000:           PetscCall(VecMAXPY(VecsSensi2Temp[nadj], s - i - 1, w, &VecsDeltaLam2[nadj * s + i + 1]));
1001:           PetscCall(MatMultTranspose(J, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj * s + i]));
1002:           PetscCall(VecScale(VecsDeltaLam2[nadj * s + i], -h * b[i]));
1003:           PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h * b[i], ts->vecs_guu[nadj]));
1004:           if (ts->vecs_sensip) PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h * b[i], ts->vecs_gup[nadj]));
1005:         } else {
1006:           /* \sum_{j=i+1}^s a_{ji}*Lambda_{s,j} */
1007:           PetscCall(VecSet(VecsDeltaLam2[nadj * s + i], 0));
1008:           PetscCall(VecMAXPY(VecsSensi2Temp[nadj], s - i - 1, w, &VecsDeltaLam2[nadj * s + i + 1]));
1009:           PetscCall(MatMultTranspose(J, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj * s + i]));
1010:           PetscCall(VecScale(VecsDeltaLam2[nadj * s + i], -h));
1011:           PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h, ts->vecs_guu[nadj]));
1012:           if (ts->vecs_sensip) PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h, ts->vecs_gup[nadj]));
1013:         }
1014:         if (ts->vecs_sensi2p) { /* 2nd-order adjoint for parameters */
1015:           PetscCall(MatMultTranspose(ts->Jacprhs, VecsSensi2Temp[nadj], VecDeltaMu2));
1016:           if (b[i]) {
1017:             PetscCall(VecScale(VecDeltaMu2, -h * b[i]));
1018:             PetscCall(VecAXPY(VecDeltaMu2, -h * b[i], ts->vecs_gpu[nadj]));
1019:             PetscCall(VecAXPY(VecDeltaMu2, -h * b[i], ts->vecs_gpp[nadj]));
1020:           } else {
1021:             PetscCall(VecScale(VecDeltaMu2, -h));
1022:             PetscCall(VecAXPY(VecDeltaMu2, -h, ts->vecs_gpu[nadj]));
1023:             PetscCall(VecAXPY(VecDeltaMu2, -h, ts->vecs_gpp[nadj]));
1024:           }
1025:           PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], 1, VecDeltaMu2)); /* update sensi2p for each stage */
1026:         }
1027:       }
1028:     }
1029:   }

1031:   for (j = 0; j < s; j++) w[j] = 1.0;
1032:   for (nadj = 0; nadj < ts->numcost; nadj++) { /* no need to do this for mu's */
1033:     PetscCall(VecMAXPY(ts->vecs_sensi[nadj], s, w, &VecsDeltaLam[nadj * s]));
1034:     if (ts->vecs_sensi2) PetscCall(VecMAXPY(ts->vecs_sensi2[nadj], s, w, &VecsDeltaLam2[nadj * s]));
1035:   }
1036:   rk->status = TS_STEP_COMPLETE;
1037:   PetscFunctionReturn(PETSC_SUCCESS);
1038: }

1040: static PetscErrorCode TSAdjointReset_RK(TS ts)
1041: {
1042:   TS_RK    *rk  = (TS_RK *)ts->data;
1043:   RKTableau tab = rk->tableau;

1045:   PetscFunctionBegin;
1046:   PetscCall(VecDestroyVecs(tab->s * ts->numcost, &rk->VecsDeltaLam));
1047:   PetscCall(VecDestroyVecs(ts->numcost, &rk->VecsSensiTemp));
1048:   PetscCall(VecDestroy(&rk->VecDeltaMu));
1049:   PetscCall(VecDestroyVecs(tab->s * ts->numcost, &rk->VecsDeltaLam2));
1050:   PetscCall(VecDestroy(&rk->VecDeltaMu2));
1051:   PetscCall(VecDestroyVecs(ts->numcost, &rk->VecsSensi2Temp));
1052:   PetscFunctionReturn(PETSC_SUCCESS);
1053: }

1055: static PetscErrorCode TSInterpolate_RK(TS ts, PetscReal itime, Vec X)
1056: {
1057:   TS_RK           *rk = (TS_RK *)ts->data;
1058:   PetscInt         s = rk->tableau->s, p = rk->tableau->p, i, j;
1059:   PetscReal        h;
1060:   PetscReal        tt, t;
1061:   PetscScalar     *b;
1062:   const PetscReal *B = rk->tableau->binterp;

1064:   PetscFunctionBegin;
1065:   PetscCheck(B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSRK %s does not have an interpolation formula", rk->tableau->name);

1067:   switch (rk->status) {
1068:   case TS_STEP_INCOMPLETE:
1069:   case TS_STEP_PENDING:
1070:     h = ts->time_step;
1071:     t = (itime - ts->ptime) / h;
1072:     break;
1073:   case TS_STEP_COMPLETE:
1074:     h = ts->ptime - ts->ptime_prev;
1075:     t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
1076:     break;
1077:   default:
1078:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1079:   }
1080:   PetscCall(PetscMalloc1(s, &b));
1081:   for (i = 0; i < s; i++) b[i] = 0;
1082:   for (j = 0, tt = t; j < p; j++, tt *= t) {
1083:     for (i = 0; i < s; i++) b[i] += h * B[i * p + j] * tt;
1084:   }
1085:   PetscCall(VecCopy(rk->Y[0], X));
1086:   PetscCall(VecMAXPY(X, s, b, rk->YdotRHS));
1087:   PetscCall(PetscFree(b));
1088:   PetscFunctionReturn(PETSC_SUCCESS);
1089: }

1091: /*------------------------------------------------------------*/

1093: static PetscErrorCode TSRKTableauReset(TS ts)
1094: {
1095:   TS_RK    *rk  = (TS_RK *)ts->data;
1096:   RKTableau tab = rk->tableau;

1098:   PetscFunctionBegin;
1099:   if (!tab) PetscFunctionReturn(PETSC_SUCCESS);
1100:   PetscCall(PetscFree(rk->work));
1101:   PetscCall(VecDestroyVecs(tab->s, &rk->Y));
1102:   PetscCall(VecDestroyVecs(tab->s, &rk->YdotRHS));
1103:   PetscFunctionReturn(PETSC_SUCCESS);
1104: }

1106: static PetscErrorCode TSReset_RK(TS ts)
1107: {
1108:   PetscFunctionBegin;
1109:   PetscCall(TSRKTableauReset(ts));
1110:   if (ts->use_splitrhsfunction) {
1111:     PetscTryMethod(ts, "TSReset_RK_MultirateSplit_C", (TS), (ts));
1112:   } else {
1113:     PetscTryMethod(ts, "TSReset_RK_MultirateNonsplit_C", (TS), (ts));
1114:   }
1115:   PetscFunctionReturn(PETSC_SUCCESS);
1116: }

1118: static PetscErrorCode DMCoarsenHook_TSRK(DM fine, DM coarse, void *ctx)
1119: {
1120:   PetscFunctionBegin;
1121:   PetscFunctionReturn(PETSC_SUCCESS);
1122: }

1124: static PetscErrorCode DMRestrictHook_TSRK(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
1125: {
1126:   PetscFunctionBegin;
1127:   PetscFunctionReturn(PETSC_SUCCESS);
1128: }

1130: static PetscErrorCode DMSubDomainHook_TSRK(DM dm, DM subdm, void *ctx)
1131: {
1132:   PetscFunctionBegin;
1133:   PetscFunctionReturn(PETSC_SUCCESS);
1134: }

1136: static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
1137: {
1138:   PetscFunctionBegin;
1139:   PetscFunctionReturn(PETSC_SUCCESS);
1140: }

1142: static PetscErrorCode TSRKTableauSetUp(TS ts)
1143: {
1144:   TS_RK    *rk  = (TS_RK *)ts->data;
1145:   RKTableau tab = rk->tableau;

1147:   PetscFunctionBegin;
1148:   PetscCall(PetscMalloc1(tab->s, &rk->work));
1149:   PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &rk->Y));
1150:   PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &rk->YdotRHS));
1151:   PetscFunctionReturn(PETSC_SUCCESS);
1152: }

1154: static PetscErrorCode TSSetUp_RK(TS ts)
1155: {
1156:   TS quadts = ts->quadraturets;
1157:   DM dm;

1159:   PetscFunctionBegin;
1160:   PetscCall(TSCheckImplicitTerm(ts));
1161:   PetscCall(TSRKTableauSetUp(ts));
1162:   if (quadts && ts->costintegralfwd) {
1163:     Mat Jquad;
1164:     PetscCall(TSGetRHSJacobian(quadts, &Jquad, NULL, NULL, NULL));
1165:   }
1166:   PetscCall(TSGetDM(ts, &dm));
1167:   PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSRK, DMRestrictHook_TSRK, ts));
1168:   PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSRK, DMSubDomainRestrictHook_TSRK, ts));
1169:   if (ts->use_splitrhsfunction) {
1170:     PetscTryMethod(ts, "TSSetUp_RK_MultirateSplit_C", (TS), (ts));
1171:   } else {
1172:     PetscTryMethod(ts, "TSSetUp_RK_MultirateNonsplit_C", (TS), (ts));
1173:   }
1174:   PetscFunctionReturn(PETSC_SUCCESS);
1175: }

1177: static PetscErrorCode TSSetFromOptions_RK(TS ts, PetscOptionItems *PetscOptionsObject)
1178: {
1179:   TS_RK *rk = (TS_RK *)ts->data;

1181:   PetscFunctionBegin;
1182:   PetscOptionsHeadBegin(PetscOptionsObject, "RK ODE solver options");
1183:   {
1184:     RKTableauLink link;
1185:     PetscInt      count, choice;
1186:     PetscBool     flg, use_multirate = PETSC_FALSE;
1187:     const char  **namelist;

1189:     for (link = RKTableauList, count = 0; link; link = link->next, count++)
1190:       ;
1191:     PetscCall(PetscMalloc1(count, (char ***)&namelist));
1192:     for (link = RKTableauList, count = 0; link; link = link->next, count++) namelist[count] = link->tab.name;
1193:     PetscCall(PetscOptionsBool("-ts_rk_multirate", "Use interpolation-based multirate RK method", "TSRKSetMultirate", rk->use_multirate, &use_multirate, &flg));
1194:     if (flg) PetscCall(TSRKSetMultirate(ts, use_multirate));
1195:     PetscCall(PetscOptionsEList("-ts_rk_type", "Family of RK method", "TSRKSetType", (const char *const *)namelist, count, rk->tableau->name, &choice, &flg));
1196:     if (flg) PetscCall(TSRKSetType(ts, namelist[choice]));
1197:     PetscCall(PetscFree(namelist));
1198:   }
1199:   PetscOptionsHeadEnd();
1200:   PetscOptionsBegin(PetscObjectComm((PetscObject)ts), NULL, "Multirate methods options", "");
1201:   PetscCall(PetscOptionsInt("-ts_rk_dtratio", "time step ratio between slow and fast", "", rk->dtratio, &rk->dtratio, NULL));
1202:   PetscOptionsEnd();
1203:   PetscFunctionReturn(PETSC_SUCCESS);
1204: }

1206: static PetscErrorCode TSView_RK(TS ts, PetscViewer viewer)
1207: {
1208:   TS_RK    *rk = (TS_RK *)ts->data;
1209:   PetscBool iascii;

1211:   PetscFunctionBegin;
1212:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1213:   if (iascii) {
1214:     RKTableau        tab = rk->tableau;
1215:     TSRKType         rktype;
1216:     const PetscReal *c;
1217:     PetscInt         s;
1218:     char             buf[512];
1219:     PetscBool        FSAL;

1221:     PetscCall(TSRKGetType(ts, &rktype));
1222:     PetscCall(TSRKGetTableau(ts, &s, NULL, NULL, &c, NULL, NULL, NULL, &FSAL));
1223:     PetscCall(PetscViewerASCIIPrintf(viewer, "  RK type %s\n", rktype));
1224:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Order: %" PetscInt_FMT "\n", tab->order));
1225:     PetscCall(PetscViewerASCIIPrintf(viewer, "  FSAL property: %s\n", FSAL ? "yes" : "no"));
1226:     PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", s, c));
1227:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Abscissa c = %s\n", buf));
1228:   }
1229:   PetscFunctionReturn(PETSC_SUCCESS);
1230: }

1232: static PetscErrorCode TSLoad_RK(TS ts, PetscViewer viewer)
1233: {
1234:   TSAdapt adapt;

1236:   PetscFunctionBegin;
1237:   PetscCall(TSGetAdapt(ts, &adapt));
1238:   PetscCall(TSAdaptLoad(adapt, viewer));
1239:   PetscFunctionReturn(PETSC_SUCCESS);
1240: }

1242: /*@
1243:   TSRKGetOrder - Get the order of the `TSRK` scheme

1245:   Not Collective

1247:   Input Parameter:
1248: .  ts - timestepping context

1250:   Output Parameter:
1251: .  order - order of `TSRK` scheme

1253:   Level: intermediate

1255: .seealso: [](ch_ts), `TSRK`, `TSRKGetType()`
1256: @*/
1257: PetscErrorCode TSRKGetOrder(TS ts, PetscInt *order)
1258: {
1259:   PetscFunctionBegin;
1262:   PetscUseMethod(ts, "TSRKGetOrder_C", (TS, PetscInt *), (ts, order));
1263:   PetscFunctionReturn(PETSC_SUCCESS);
1264: }

1266: /*@C
1267:   TSRKSetType - Set the type of the `TSRK` scheme

1269:   Logically Collective

1271:   Input Parameters:
1272: +  ts - timestepping context
1273: -  rktype - type of `TSRK` scheme

1275:   Options Database Key:
1276: .   -ts_rk_type - <1fe,2a,3,3bs,4,5f,5dp,5bs>

1278:   Level: intermediate

1280: .seealso: [](ch_ts), `TSRKGetType()`, `TSRK`, `TSRKType`, `TSRK1FE`, `TSRK2A`, `TSRK2B`, `TSRK3`, `TSRK3BS`, `TSRK4`, `TSRK5F`, `TSRK5DP`, `TSRK5BS`, `TSRK6VR`, `TSRK7VR`, `TSRK8VR`
1281: @*/
1282: PetscErrorCode TSRKSetType(TS ts, TSRKType rktype)
1283: {
1284:   PetscFunctionBegin;
1287:   PetscTryMethod(ts, "TSRKSetType_C", (TS, TSRKType), (ts, rktype));
1288:   PetscFunctionReturn(PETSC_SUCCESS);
1289: }

1291: /*@C
1292:   TSRKGetType - Get the type of `TSRK` scheme

1294:   Not Collective

1296:   Input Parameter:
1297: .  ts - timestepping context

1299:   Output Parameter:
1300: .  rktype - type of `TSRK`-scheme

1302:   Level: intermediate

1304: .seealso: [](ch_ts), `TSRKSetType()`
1305: @*/
1306: PetscErrorCode TSRKGetType(TS ts, TSRKType *rktype)
1307: {
1308:   PetscFunctionBegin;
1310:   PetscUseMethod(ts, "TSRKGetType_C", (TS, TSRKType *), (ts, rktype));
1311:   PetscFunctionReturn(PETSC_SUCCESS);
1312: }

1314: static PetscErrorCode TSRKGetOrder_RK(TS ts, PetscInt *order)
1315: {
1316:   TS_RK *rk = (TS_RK *)ts->data;

1318:   PetscFunctionBegin;
1319:   *order = rk->tableau->order;
1320:   PetscFunctionReturn(PETSC_SUCCESS);
1321: }

1323: static PetscErrorCode TSRKGetType_RK(TS ts, TSRKType *rktype)
1324: {
1325:   TS_RK *rk = (TS_RK *)ts->data;

1327:   PetscFunctionBegin;
1328:   *rktype = rk->tableau->name;
1329:   PetscFunctionReturn(PETSC_SUCCESS);
1330: }

1332: static PetscErrorCode TSRKSetType_RK(TS ts, TSRKType rktype)
1333: {
1334:   TS_RK        *rk = (TS_RK *)ts->data;
1335:   PetscBool     match;
1336:   RKTableauLink link;

1338:   PetscFunctionBegin;
1339:   if (rk->tableau) {
1340:     PetscCall(PetscStrcmp(rk->tableau->name, rktype, &match));
1341:     if (match) PetscFunctionReturn(PETSC_SUCCESS);
1342:   }
1343:   for (link = RKTableauList; link; link = link->next) {
1344:     PetscCall(PetscStrcmp(link->tab.name, rktype, &match));
1345:     if (match) {
1346:       if (ts->setupcalled) PetscCall(TSRKTableauReset(ts));
1347:       rk->tableau = &link->tab;
1348:       if (ts->setupcalled) PetscCall(TSRKTableauSetUp(ts));
1349:       ts->default_adapt_type = rk->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1350:       PetscFunctionReturn(PETSC_SUCCESS);
1351:     }
1352:   }
1353:   SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", rktype);
1354: }

1356: static PetscErrorCode TSGetStages_RK(TS ts, PetscInt *ns, Vec **Y)
1357: {
1358:   TS_RK *rk = (TS_RK *)ts->data;

1360:   PetscFunctionBegin;
1361:   if (ns) *ns = rk->tableau->s;
1362:   if (Y) *Y = rk->Y;
1363:   PetscFunctionReturn(PETSC_SUCCESS);
1364: }

1366: static PetscErrorCode TSDestroy_RK(TS ts)
1367: {
1368:   PetscFunctionBegin;
1369:   PetscCall(TSReset_RK(ts));
1370:   if (ts->dm) {
1371:     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSRK, DMRestrictHook_TSRK, ts));
1372:     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSRK, DMSubDomainRestrictHook_TSRK, ts));
1373:   }
1374:   PetscCall(PetscFree(ts->data));
1375:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetOrder_C", NULL));
1376:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetType_C", NULL));
1377:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetType_C", NULL));
1378:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetTableau_C", NULL));
1379:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetMultirate_C", NULL));
1380:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetMultirate_C", NULL));
1381:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateSplit_C", NULL));
1382:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateSplit_C", NULL));
1383:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateNonsplit_C", NULL));
1384:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateNonsplit_C", NULL));
1385:   PetscFunctionReturn(PETSC_SUCCESS);
1386: }

1388: /*
1389:   This defines the nonlinear equation that is to be solved with SNES
1390:   We do not need to solve the equation; we just use SNES to approximate the Jacobian
1391: */
1392: static PetscErrorCode SNESTSFormFunction_RK(SNES snes, Vec x, Vec y, TS ts)
1393: {
1394:   TS_RK *rk = (TS_RK *)ts->data;
1395:   DM     dm, dmsave;

1397:   PetscFunctionBegin;
1398:   PetscCall(SNESGetDM(snes, &dm));
1399:   /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
1400:   dmsave = ts->dm;
1401:   ts->dm = dm;
1402:   PetscCall(TSComputeRHSFunction(ts, rk->stage_time, x, y));
1403:   ts->dm = dmsave;
1404:   PetscFunctionReturn(PETSC_SUCCESS);
1405: }

1407: static PetscErrorCode SNESTSFormJacobian_RK(SNES snes, Vec x, Mat A, Mat B, TS ts)
1408: {
1409:   TS_RK *rk = (TS_RK *)ts->data;
1410:   DM     dm, dmsave;

1412:   PetscFunctionBegin;
1413:   PetscCall(SNESGetDM(snes, &dm));
1414:   dmsave = ts->dm;
1415:   ts->dm = dm;
1416:   PetscCall(TSComputeRHSJacobian(ts, rk->stage_time, x, A, B));
1417:   ts->dm = dmsave;
1418:   PetscFunctionReturn(PETSC_SUCCESS);
1419: }

1421: /*@C
1422:   TSRKSetMultirate - Use the interpolation-based multirate `TSRK` method

1424:   Logically Collective

1426:   Input Parameters:
1427: +  ts - timestepping context
1428: -  use_multirate - `PETSC_TRUE` enables the multirate `TSRK` method, sets the basic method to be RK2A and sets the ratio between slow stepsize and fast stepsize to be 2

1430:   Options Database Key:
1431: .   -ts_rk_multirate - <true,false>

1433:   Level: intermediate

1435:   Note:
1436:   The multirate method requires interpolation. The default interpolation works for 1st- and 2nd- order RK, but not for high-order RKs except `TSRK5DP` which comes with the interpolation coefficients (binterp).

1438: .seealso: [](ch_ts), `TSRK`, `TSRKGetMultirate()`
1439: @*/
1440: PetscErrorCode TSRKSetMultirate(TS ts, PetscBool use_multirate)
1441: {
1442:   PetscFunctionBegin;
1443:   PetscTryMethod(ts, "TSRKSetMultirate_C", (TS, PetscBool), (ts, use_multirate));
1444:   PetscFunctionReturn(PETSC_SUCCESS);
1445: }

1447: /*@C
1448:   TSRKGetMultirate - Gets whether to use the interpolation-based multirate `TSRK` method

1450:   Not Collective

1452:   Input Parameter:
1453: .  ts - timestepping context

1455:   Output Parameter:
1456: .  use_multirate - `PETSC_TRUE` if the multirate RK method is enabled, `PETSC_FALSE` otherwise

1458:   Level: intermediate

1460: .seealso: [](ch_ts), `TSRK`, `TSRKSetMultirate()`
1461: @*/
1462: PetscErrorCode TSRKGetMultirate(TS ts, PetscBool *use_multirate)
1463: {
1464:   PetscFunctionBegin;
1465:   PetscUseMethod(ts, "TSRKGetMultirate_C", (TS, PetscBool *), (ts, use_multirate));
1466:   PetscFunctionReturn(PETSC_SUCCESS);
1467: }

1469: /*MC
1470:       TSRK - ODE and DAE solver using Runge-Kutta schemes

1472:   The user should provide the right hand side of the equation
1473:   using `TSSetRHSFunction()`.

1475:   Level: beginner

1477:   Notes:
1478:   The default is `TSRK3BS`, it can be changed with `TSRKSetType()` or -ts_rk_type

1480: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSRK`, `TSSetType()`, `TSRKSetType()`, `TSRKGetType()`, `TSRK2D`, `TSRK2E`, `TSRK3`,
1481:           `TSRK4`, `TSRK5`, `TSRKPRSSP2`, `TSRKBPR3`, `TSRKType`, `TSRKRegister()`, `TSRKSetMultirate()`, `TSRKGetMultirate()`, `TSType`
1482: M*/
1483: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
1484: {
1485:   TS_RK *rk;

1487:   PetscFunctionBegin;
1488:   PetscCall(TSRKInitializePackage());

1490:   ts->ops->reset          = TSReset_RK;
1491:   ts->ops->destroy        = TSDestroy_RK;
1492:   ts->ops->view           = TSView_RK;
1493:   ts->ops->load           = TSLoad_RK;
1494:   ts->ops->setup          = TSSetUp_RK;
1495:   ts->ops->interpolate    = TSInterpolate_RK;
1496:   ts->ops->step           = TSStep_RK;
1497:   ts->ops->evaluatestep   = TSEvaluateStep_RK;
1498:   ts->ops->rollback       = TSRollBack_RK;
1499:   ts->ops->setfromoptions = TSSetFromOptions_RK;
1500:   ts->ops->getstages      = TSGetStages_RK;

1502:   ts->ops->snesfunction    = SNESTSFormFunction_RK;
1503:   ts->ops->snesjacobian    = SNESTSFormJacobian_RK;
1504:   ts->ops->adjointintegral = TSAdjointCostIntegral_RK;
1505:   ts->ops->adjointsetup    = TSAdjointSetUp_RK;
1506:   ts->ops->adjointstep     = TSAdjointStep_RK;
1507:   ts->ops->adjointreset    = TSAdjointReset_RK;

1509:   ts->ops->forwardintegral  = TSForwardCostIntegral_RK;
1510:   ts->ops->forwardsetup     = TSForwardSetUp_RK;
1511:   ts->ops->forwardreset     = TSForwardReset_RK;
1512:   ts->ops->forwardstep      = TSForwardStep_RK;
1513:   ts->ops->forwardgetstages = TSForwardGetStages_RK;

1515:   PetscCall(PetscNew(&rk));
1516:   ts->data = (void *)rk;

1518:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetOrder_C", TSRKGetOrder_RK));
1519:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetType_C", TSRKGetType_RK));
1520:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetType_C", TSRKSetType_RK));
1521:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetTableau_C", TSRKGetTableau_RK));
1522:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetMultirate_C", TSRKSetMultirate_RK));
1523:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetMultirate_C", TSRKGetMultirate_RK));

1525:   PetscCall(TSRKSetType(ts, TSRKDefault));
1526:   rk->dtratio = 1;
1527:   PetscFunctionReturn(PETSC_SUCCESS);
1528: }