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: }