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 <https://doi.org/10.1016/0893-9659(89)90079-7>
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: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
81: M*/
82: /*MC
83: TSRK4 - Fourth order RK scheme.
85: This is the classical Runge-Kutta method with four stages.
87: Options Database Key:
88: . -ts_rk_type 4 - use type 4
90: Level: advanced
92: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
93: M*/
94: /*MC
95: TSRK5F - Fifth order Fehlberg RK scheme with a 4th order embedded method.
97: This method has six stages.
99: Options Database Key:
100: . -ts_rk_type 5f - use type 5f
102: Level: advanced
104: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
105: M*/
106: /*MC
107: TSRK5DP - Fifth order Dormand-Prince RK scheme with the 4th order embedded method <https://doi.org/10.1016/0771-050X(80)90013-3>
109: This method has seven stages with the First Same As Last (FSAL) property.
111: Options Database Key:
112: . -ts_rk_type 5dp - use type 5dp
114: Level: advanced
116: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
117: M*/
118: /*MC
119: TSRK5BS - Fifth order Bogacki-Shampine RK scheme with 4th order embedded method <https://doi.org/10.1016/0898-1221(96)00141-1>
121: This method has eight stages with the First Same As Last (FSAL) property.
123: Options Database Key:
124: . -ts_rk_type 5bs - use type 5bs
126: Level: advanced
128: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
129: M*/
130: /*MC
131: TSRK6VR - Sixth order robust Verner RK scheme with fifth order embedded method.
132: <http://people.math.sfu.ca/~jverner/RKV65.IIIXb.Robust.00010102836.081204.CoeffsOnlyRAT>
134: This method has nine stages with the First Same As Last (FSAL) property.
136: Options Database Key:
137: . -ts_rk_type 6vr - use type 6vr
139: Level: advanced
141: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
142: M*/
143: /*MC
144: TSRK7VR - Seventh order robust Verner RK scheme with sixth order embedded method.
145: <http://people.math.sfu.ca/~jverner/RKV65.IIIXb.Robust.00010102836.081204.CoeffsOnlyRAT>
147: This method has ten stages.
149: Options Database Key:
150: . -ts_rk_type 7vr - use type 7vr
152: Level: advanced
154: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
155: M*/
156: /*MC
157: TSRK8VR - Eighth order robust Verner RK scheme with seventh order embedded method.
158: <http://people.math.sfu.ca/~jverner/RKV87.IIa.Robust.00000754677.081208.CoeffsOnlyRATandFLOAT>
160: This method has thirteen stages.
162: Options Database Key:
163: . -ts_rk_type 8vr - use type 8vr
165: Level: advanced
167: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
168: M*/
170: /*@C
171: TSRKRegisterAll - Registers all of the Runge-Kutta explicit methods in `TSRK`
173: Not Collective, but should be called by all processes which will need the schemes to be registered
175: Level: advanced
177: .seealso: [](ch_ts), `TSRKRegisterDestroy()`, `TSRKRegister()`
178: @*/
179: PetscErrorCode TSRKRegisterAll(void)
180: {
181: PetscFunctionBegin;
182: if (TSRKRegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
183: TSRKRegisterAllCalled = PETSC_TRUE;
185: #define RC PetscRealConstant
186: {
187: const PetscReal A[1][1] = {{0}};
188: const PetscReal b[1] = {RC(1.0)};
189: PetscCall(TSRKRegister(TSRK1FE, 1, 1, &A[0][0], b, NULL, NULL, 0, NULL));
190: }
191: {
192: const PetscReal A[2][2] = {
193: {0, 0},
194: {RC(1.0), 0}
195: };
196: const PetscReal b[2] = {RC(0.5), RC(0.5)};
197: const PetscReal bembed[2] = {RC(1.0), 0};
198: PetscCall(TSRKRegister(TSRK2A, 2, 2, &A[0][0], b, NULL, bembed, 0, NULL));
199: }
200: {
201: const PetscReal A[2][2] = {
202: {0, 0},
203: {RC(0.5), 0}
204: };
205: const PetscReal b[2] = {0, RC(1.0)};
206: PetscCall(TSRKRegister(TSRK2B, 2, 2, &A[0][0], b, NULL, NULL, 0, NULL));
207: }
208: {
209: const PetscReal A[3][3] = {
210: {0, 0, 0},
211: {RC(2.0) / RC(3.0), 0, 0},
212: {RC(-1.0) / RC(3.0), RC(1.0), 0}
213: };
214: const PetscReal b[3] = {RC(0.25), RC(0.5), RC(0.25)};
215: PetscCall(TSRKRegister(TSRK3, 3, 3, &A[0][0], b, NULL, NULL, 0, NULL));
216: }
217: {
218: const PetscReal A[4][4] = {
219: {0, 0, 0, 0},
220: {RC(1.0) / RC(2.0), 0, 0, 0},
221: {0, RC(3.0) / RC(4.0), 0, 0},
222: {RC(2.0) / RC(9.0), RC(1.0) / RC(3.0), RC(4.0) / RC(9.0), 0}
223: };
224: const PetscReal b[4] = {RC(2.0) / RC(9.0), RC(1.0) / RC(3.0), RC(4.0) / RC(9.0), 0};
225: const PetscReal 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)};
226: PetscCall(TSRKRegister(TSRK3BS, 3, 4, &A[0][0], b, NULL, bembed, 0, NULL));
227: }
228: {
229: const PetscReal A[4][4] = {
230: {0, 0, 0, 0},
231: {RC(0.5), 0, 0, 0},
232: {0, RC(0.5), 0, 0},
233: {0, 0, RC(1.0), 0}
234: };
235: const PetscReal 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)};
236: PetscCall(TSRKRegister(TSRK4, 4, 4, &A[0][0], b, NULL, NULL, 0, NULL));
237: }
238: {
239: const PetscReal A[6][6] = {
240: {0, 0, 0, 0, 0, 0},
241: {RC(0.25), 0, 0, 0, 0, 0},
242: {RC(3.0) / RC(32.0), RC(9.0) / RC(32.0), 0, 0, 0, 0},
243: {RC(1932.0) / RC(2197.0), RC(-7200.0) / RC(2197.0), RC(7296.0) / RC(2197.0), 0, 0, 0},
244: {RC(439.0) / RC(216.0), RC(-8.0), RC(3680.0) / RC(513.0), RC(-845.0) / RC(4104.0), 0, 0},
245: {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}
246: };
247: const PetscReal 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)};
248: const PetscReal 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};
249: PetscCall(TSRKRegister(TSRK5F, 5, 6, &A[0][0], b, NULL, bembed, 0, NULL));
250: }
251: {
252: const PetscReal A[7][7] = {
253: {0, 0, 0, 0, 0, 0, 0},
254: {RC(1.0) / RC(5.0), 0, 0, 0, 0, 0, 0},
255: {RC(3.0) / RC(40.0), RC(9.0) / RC(40.0), 0, 0, 0, 0, 0},
256: {RC(44.0) / RC(45.0), RC(-56.0) / RC(15.0), RC(32.0) / RC(9.0), 0, 0, 0, 0},
257: {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},
258: {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},
259: {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}
260: };
261: const PetscReal 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};
262: const PetscReal 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)};
263: const PetscReal binterp[7][5] = {
264: {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) },
265: {0, 0, 0, 0, 0 },
266: {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) },
267: {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) },
268: {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)},
269: {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) },
270: {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) }
271: };
272: PetscCall(TSRKRegister(TSRK5DP, 5, 7, &A[0][0], b, NULL, bembed, 5, binterp[0]));
273: }
274: {
275: const PetscReal A[8][8] = {
276: {0, 0, 0, 0, 0, 0, 0, 0},
277: {RC(1.0) / RC(6.0), 0, 0, 0, 0, 0, 0, 0},
278: {RC(2.0) / RC(27.0), RC(4.0) / RC(27.0), 0, 0, 0, 0, 0, 0},
279: {RC(183.0) / RC(1372.0), RC(-162.0) / RC(343.0), RC(1053.0) / RC(1372.0), 0, 0, 0, 0, 0},
280: {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},
281: {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},
282: {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},
283: {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}
284: };
285: const PetscReal 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};
286: const PetscReal 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)};
287: PetscCall(TSRKRegister(TSRK5BS, 5, 8, &A[0][0], b, NULL, bembed, 0, NULL));
288: }
289: {
290: const PetscReal A[9][9] = {
291: {0, 0, 0, 0, 0, 0, 0, 0, 0},
292: {RC(1.8000000000000000000000000000000000000000e-01), 0, 0, 0, 0, 0, 0, 0, 0},
293: {RC(8.9506172839506172839506172839506172839506e-02), RC(7.7160493827160493827160493827160493827160e-02), 0, 0, 0, 0, 0, 0, 0},
294: {RC(6.2500000000000000000000000000000000000000e-02), 0, RC(1.8750000000000000000000000000000000000000e-01), 0, 0, 0, 0, 0, 0},
295: {RC(3.1651600000000000000000000000000000000000e-01), 0, RC(-1.0449480000000000000000000000000000000000e+00), RC(1.2584320000000000000000000000000000000000e+00), 0, 0, 0, 0, 0},
296: {RC(2.7232612736485626257225065566674305502508e-01), 0, RC(-8.2513360323886639676113360323886639676113e-01), RC(1.0480917678812415654520917678812415654521e+00), RC(1.0471570799276856873679117969088177628396e-01), 0, 0, 0, 0},
297: {RC(-1.6699418599716514314329607278961797333198e-01), 0, RC(6.3170850202429149797570850202429149797571e-01), RC(1.7461044552773876082146758838488161796432e-01), RC(-1.0665356459086066122525194734018680677781e+00), RC(1.2272108843537414965986394557823129251701e+00), 0, 0, 0},
298: {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},
299: {RC(7.6388888888888888888888888888888888888889e-02), 0, 0, RC(3.6940836940836940836940836940836940836941e-01), 0, RC(2.4801587301587301587301587301587301587302e-01), RC(2.3674242424242424242424242424242424242424e-01), RC(6.9444444444444444444444444444444444444444e-02), 0}
300: };
301: const PetscReal b[9] = {RC(7.6388888888888888888888888888888888888889e-02), 0, 0, RC(3.6940836940836940836940836940836940836941e-01), 0, RC(2.4801587301587301587301587301587301587302e-01), RC(2.3674242424242424242424242424242424242424e-01),
302: RC(6.9444444444444444444444444444444444444444e-02), 0};
303: const PetscReal 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)};
304: PetscCall(TSRKRegister(TSRK6VR, 6, 9, &A[0][0], b, NULL, bembed, 0, NULL));
305: }
306: {
307: const PetscReal A[10][10] = {
308: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
309: {RC(5.0000000000000000000000000000000000000000e-03), 0, 0, 0, 0, 0, 0, 0, 0, 0},
310: {RC(-1.0767901234567901234567901234567901234568e+00), RC(1.1856790123456790123456790123456790123457e+00), 0, 0, 0, 0, 0, 0, 0, 0},
311: {RC(4.0833333333333333333333333333333333333333e-02), 0, RC(1.2250000000000000000000000000000000000000e-01), 0, 0, 0, 0, 0, 0, 0},
312: {RC(6.3607142857142857142857142857142857142857e-01), 0, RC(-2.4444642857142857142857142857142857142857e+00), RC(2.2633928571428571428571428571428571428571e+00), 0, 0, 0, 0, 0, 0},
313: {RC(-2.5351211079349245229256383554660215487207e+00), 0, RC(1.0299374654449267920438514460756024913612e+01), RC(-7.9513032885990579949493217458266876536482e+00), RC(7.9301148923100592201226014271115261823800e-01), 0, 0, 0, 0, 0},
314: {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},
315: {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},
316: {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},
317: {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}
318: };
319: const PetscReal 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};
320: const PetscReal bembed[10] = {RC(4.7485247699299631037531273805727961552268e-02), 0, 0, RC(2.5599412588690633297154918245905393870497e-01), RC(2.7058478081067688722530891099268135732387e-01), RC(1.2505618684425992913638822323746917920448e-01),
321: RC(2.5204468723743860507184043820197442562182e-01), 0, 0, RC(4.8834971521418614557381971303093137592592e-02)};
322: PetscCall(TSRKRegister(TSRK7VR, 7, 10, &A[0][0], b, NULL, bembed, 0, NULL));
323: }
324: {
325: const PetscReal A[13][13] = {
326: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
327: {RC(2.5000000000000000000000000000000000000000e-01), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
328: {RC(8.7400846504915232052686327594877411977046e-02), RC(2.5487604938654321753087950620345685135815e-02), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
329: {RC(4.2333169291338582677165354330708661417323e-02), 0, RC(1.2699950787401574803149606299212598425197e-01), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
330: {RC(4.2609505888742261494881445237572274090942e-01), 0, RC(-1.5987952846591523265427733230657181117089e+00), RC(1.5967002257717297115939588706899953707994e+00), 0, 0, 0, 0, 0, 0, 0, 0, 0},
331: {RC(5.0719337296713929515090618138513639239329e-02), 0, 0, RC(2.5433377264600407582754714408877778031369e-01), RC(2.0394689005728199465736223777270858044698e-01), 0, 0, 0, 0, 0, 0, 0, 0},
332: {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},
333: {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},
334: {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},
335: {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},
336: {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},
337: {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},
338: {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}
339: };
340: const PetscReal 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};
341: const PetscReal 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)};
342: PetscCall(TSRKRegister(TSRK8VR, 8, 13, &A[0][0], b, NULL, bembed, 0, NULL));
343: }
344: #undef RC
345: PetscFunctionReturn(PETSC_SUCCESS);
346: }
348: /*@C
349: TSRKRegisterDestroy - Frees the list of schemes that were registered by `TSRKRegister()`.
351: Not Collective
353: Level: advanced
355: .seealso: [](ch_ts), `TSRK`, `TSRKRegister()`, `TSRKRegisterAll()`
356: @*/
357: PetscErrorCode TSRKRegisterDestroy(void)
358: {
359: RKTableauLink link;
361: PetscFunctionBegin;
362: while ((link = RKTableauList)) {
363: RKTableau t = &link->tab;
364: RKTableauList = link->next;
365: PetscCall(PetscFree3(t->A, t->b, t->c));
366: PetscCall(PetscFree(t->bembed));
367: PetscCall(PetscFree(t->binterp));
368: PetscCall(PetscFree(t->name));
369: PetscCall(PetscFree(link));
370: }
371: TSRKRegisterAllCalled = PETSC_FALSE;
372: PetscFunctionReturn(PETSC_SUCCESS);
373: }
375: /*@C
376: TSRKInitializePackage - This function initializes everything in the `TSRK` package. It is called
377: from `TSInitializePackage()`.
379: Level: developer
381: .seealso: [](ch_ts), `TSInitializePackage()`, `PetscInitialize()`, `TSRKFinalizePackage()`
382: @*/
383: PetscErrorCode TSRKInitializePackage(void)
384: {
385: PetscFunctionBegin;
386: if (TSRKPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
387: TSRKPackageInitialized = PETSC_TRUE;
388: PetscCall(TSRKRegisterAll());
389: PetscCall(PetscRegisterFinalize(TSRKFinalizePackage));
390: PetscFunctionReturn(PETSC_SUCCESS);
391: }
393: /*@C
394: TSRKFinalizePackage - This function destroys everything in the `TSRK` package. It is
395: called from `PetscFinalize()`.
397: Level: developer
399: .seealso: [](ch_ts), `PetscFinalize()`, `TSRKInitializePackage()`
400: @*/
401: PetscErrorCode TSRKFinalizePackage(void)
402: {
403: PetscFunctionBegin;
404: TSRKPackageInitialized = PETSC_FALSE;
405: PetscCall(TSRKRegisterDestroy());
406: PetscFunctionReturn(PETSC_SUCCESS);
407: }
409: /*@C
410: TSRKRegister - register an `TSRK` scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation
412: Not Collective, but the same schemes should be registered on all processes on which they will be used
414: Input Parameters:
415: + name - identifier for method
416: . order - approximation order of method
417: . s - number of stages, this is the dimension of the matrices below
418: . A - stage coefficients (dimension s*s, row-major)
419: . b - step completion table (dimension s; NULL to use last row of A)
420: . c - abscissa (dimension s; NULL to use row sums of A)
421: . bembed - completion table for embedded method (dimension s; NULL if not available)
422: . p - Order of the interpolation scheme, equal to the number of columns of binterp
423: - binterp - Coefficients of the interpolation formula (dimension s*p; NULL to reuse b with p=1)
425: Level: advanced
427: Note:
428: Several `TSRK` methods are provided, this function is only needed to create new methods.
430: .seealso: [](ch_ts), `TSRK`
431: @*/
432: 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[])
433: {
434: RKTableauLink link;
435: RKTableau t;
436: PetscInt i, j;
438: PetscFunctionBegin;
439: PetscAssertPointer(name, 1);
440: PetscAssertPointer(A, 4);
441: if (b) PetscAssertPointer(b, 5);
442: if (c) PetscAssertPointer(c, 6);
443: if (bembed) PetscAssertPointer(bembed, 7);
444: if (binterp || p > 1) PetscAssertPointer(binterp, 9);
445: PetscCheck(s >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expected number of stages s %" PetscInt_FMT " >= 0", s);
447: PetscCall(TSRKInitializePackage());
448: PetscCall(PetscNew(&link));
449: t = &link->tab;
451: PetscCall(PetscStrallocpy(name, &t->name));
452: t->order = order;
453: t->s = s;
454: PetscCall(PetscMalloc3(s * s, &t->A, s, &t->b, s, &t->c));
455: PetscCall(PetscArraycpy(t->A, A, s * s));
456: if (b) PetscCall(PetscArraycpy(t->b, b, s));
457: else
458: for (i = 0; i < s; i++) t->b[i] = A[(s - 1) * s + i];
459: if (c) PetscCall(PetscArraycpy(t->c, c, s));
460: else
461: for (i = 0; i < s; i++)
462: for (j = 0, t->c[i] = 0; j < s; j++) t->c[i] += A[i * s + j];
463: t->FSAL = PETSC_TRUE;
464: for (i = 0; i < s; i++)
465: if (t->A[(s - 1) * s + i] != t->b[i]) t->FSAL = PETSC_FALSE;
467: if (bembed) {
468: PetscCall(PetscMalloc1(s, &t->bembed));
469: PetscCall(PetscArraycpy(t->bembed, bembed, s));
470: }
472: if (!binterp) {
473: p = 1;
474: binterp = t->b;
475: }
476: t->p = p;
477: PetscCall(PetscMalloc1(s * p, &t->binterp));
478: PetscCall(PetscArraycpy(t->binterp, binterp, s * p));
480: link->next = RKTableauList;
481: RKTableauList = link;
482: PetscFunctionReturn(PETSC_SUCCESS);
483: }
485: static 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)
486: {
487: TS_RK *rk = (TS_RK *)ts->data;
488: RKTableau tab = rk->tableau;
490: PetscFunctionBegin;
491: if (s) *s = tab->s;
492: if (A) *A = tab->A;
493: if (b) *b = tab->b;
494: if (c) *c = tab->c;
495: if (bembed) *bembed = tab->bembed;
496: if (p) *p = tab->p;
497: if (binterp) *binterp = tab->binterp;
498: if (FSAL) *FSAL = tab->FSAL;
499: PetscFunctionReturn(PETSC_SUCCESS);
500: }
502: /*@C
503: TSRKGetTableau - Get info on the `TSRK` tableau
505: Not Collective
507: Input Parameter:
508: . ts - timestepping context
510: Output Parameters:
511: + s - number of stages, this is the dimension of the matrices below
512: . A - stage coefficients (dimension s*s, row-major)
513: . b - step completion table (dimension s)
514: . c - abscissa (dimension s)
515: . bembed - completion table for embedded method (dimension s; NULL if not available)
516: . p - Order of the interpolation scheme, equal to the number of columns of binterp
517: . binterp - Coefficients of the interpolation formula (dimension s*p)
518: - FSAL - whether or not the scheme has the First Same As Last property
520: Level: developer
522: .seealso: [](ch_ts), `TSRK`, `TSRKRegister()`, `TSRKSetType()`
523: @*/
524: 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)
525: {
526: PetscFunctionBegin;
528: 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));
529: PetscFunctionReturn(PETSC_SUCCESS);
530: }
532: /*
533: This is for single-step RK method
534: The step completion formula is
536: x1 = x0 + h b^T YdotRHS
538: This function can be called before or after ts->vec_sol has been updated.
539: Suppose we have a completion formula (b) and an embedded formula (be) of different order.
540: We can write
542: x1e = x0 + h be^T YdotRHS
543: = x1 - h b^T YdotRHS + h be^T YdotRHS
544: = x1 + h (be - b)^T YdotRHS
546: so we can evaluate the method with different order even after the step has been optimistically completed.
547: */
548: static PetscErrorCode TSEvaluateStep_RK(TS ts, PetscInt order, Vec X, PetscBool *done)
549: {
550: TS_RK *rk = (TS_RK *)ts->data;
551: RKTableau tab = rk->tableau;
552: PetscScalar *w = rk->work;
553: PetscReal h;
554: PetscInt s = tab->s, j;
556: PetscFunctionBegin;
557: switch (rk->status) {
558: case TS_STEP_INCOMPLETE:
559: case TS_STEP_PENDING:
560: h = ts->time_step;
561: break;
562: case TS_STEP_COMPLETE:
563: h = ts->ptime - ts->ptime_prev;
564: break;
565: default:
566: SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
567: }
568: if (order == tab->order) {
569: if (rk->status == TS_STEP_INCOMPLETE) {
570: PetscCall(VecCopy(ts->vec_sol, X));
571: for (j = 0; j < s; j++) w[j] = h * tab->b[j] / rk->dtratio;
572: PetscCall(VecMAXPY(X, s, w, rk->YdotRHS));
573: } else PetscCall(VecCopy(ts->vec_sol, X));
574: PetscFunctionReturn(PETSC_SUCCESS);
575: } else if (order == tab->order - 1) {
576: if (!tab->bembed) goto unavailable;
577: if (rk->status == TS_STEP_INCOMPLETE) { /*Complete with the embedded method (be)*/
578: PetscCall(VecCopy(ts->vec_sol, X));
579: for (j = 0; j < s; j++) w[j] = h * tab->bembed[j];
580: PetscCall(VecMAXPY(X, s, w, rk->YdotRHS));
581: } else { /*Rollback and re-complete using (be-b) */
582: PetscCall(VecCopy(ts->vec_sol, X));
583: for (j = 0; j < s; j++) w[j] = h * (tab->bembed[j] - tab->b[j]);
584: PetscCall(VecMAXPY(X, s, w, rk->YdotRHS));
585: }
586: if (done) *done = PETSC_TRUE;
587: PetscFunctionReturn(PETSC_SUCCESS);
588: }
589: unavailable:
590: if (done) *done = PETSC_FALSE;
591: else
592: 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);
593: PetscFunctionReturn(PETSC_SUCCESS);
594: }
596: static PetscErrorCode TSForwardCostIntegral_RK(TS ts)
597: {
598: TS_RK *rk = (TS_RK *)ts->data;
599: TS quadts = ts->quadraturets;
600: RKTableau tab = rk->tableau;
601: const PetscInt s = tab->s;
602: const PetscReal *b = tab->b, *c = tab->c;
603: Vec *Y = rk->Y;
604: PetscInt i;
606: PetscFunctionBegin;
607: /* No need to backup quadts->vec_sol since it can be reverted in TSRollBack_RK */
608: for (i = s - 1; i >= 0; i--) {
609: /* Evolve quadrature TS solution to compute integrals */
610: PetscCall(TSComputeRHSFunction(quadts, rk->ptime + rk->time_step * c[i], Y[i], ts->vec_costintegrand));
611: PetscCall(VecAXPY(quadts->vec_sol, rk->time_step * b[i], ts->vec_costintegrand));
612: }
613: PetscFunctionReturn(PETSC_SUCCESS);
614: }
616: static PetscErrorCode TSAdjointCostIntegral_RK(TS ts)
617: {
618: TS_RK *rk = (TS_RK *)ts->data;
619: RKTableau tab = rk->tableau;
620: TS quadts = ts->quadraturets;
621: const PetscInt s = tab->s;
622: const PetscReal *b = tab->b, *c = tab->c;
623: Vec *Y = rk->Y;
624: PetscInt i;
626: PetscFunctionBegin;
627: for (i = s - 1; i >= 0; i--) {
628: /* Evolve quadrature TS solution to compute integrals */
629: PetscCall(TSComputeRHSFunction(quadts, ts->ptime + ts->time_step * (1.0 - c[i]), Y[i], ts->vec_costintegrand));
630: PetscCall(VecAXPY(quadts->vec_sol, -ts->time_step * b[i], ts->vec_costintegrand));
631: }
632: PetscFunctionReturn(PETSC_SUCCESS);
633: }
635: static PetscErrorCode TSRollBack_RK(TS ts)
636: {
637: TS_RK *rk = (TS_RK *)ts->data;
638: TS quadts = ts->quadraturets;
639: RKTableau tab = rk->tableau;
640: const PetscInt s = tab->s;
641: const PetscReal *b = tab->b, *c = tab->c;
642: PetscScalar *w = rk->work;
643: Vec *Y = rk->Y, *YdotRHS = rk->YdotRHS;
644: PetscInt j;
645: PetscReal h;
647: PetscFunctionBegin;
648: switch (rk->status) {
649: case TS_STEP_INCOMPLETE:
650: case TS_STEP_PENDING:
651: h = ts->time_step;
652: break;
653: case TS_STEP_COMPLETE:
654: h = ts->ptime - ts->ptime_prev;
655: break;
656: default:
657: SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
658: }
659: for (j = 0; j < s; j++) w[j] = -h * b[j];
660: PetscCall(VecMAXPY(ts->vec_sol, s, w, YdotRHS));
661: if (quadts && ts->costintegralfwd) {
662: for (j = 0; j < s; j++) {
663: /* Revert the quadrature TS solution */
664: PetscCall(TSComputeRHSFunction(quadts, rk->ptime + h * c[j], Y[j], ts->vec_costintegrand));
665: PetscCall(VecAXPY(quadts->vec_sol, -h * b[j], ts->vec_costintegrand));
666: }
667: }
668: PetscFunctionReturn(PETSC_SUCCESS);
669: }
671: static PetscErrorCode TSForwardStep_RK(TS ts)
672: {
673: TS_RK *rk = (TS_RK *)ts->data;
674: RKTableau tab = rk->tableau;
675: Mat J, *MatsFwdSensipTemp = rk->MatsFwdSensipTemp;
676: const PetscInt s = tab->s;
677: const PetscReal *A = tab->A, *c = tab->c, *b = tab->b;
678: Vec *Y = rk->Y;
679: PetscInt i, j;
680: PetscReal stage_time, h = ts->time_step;
681: PetscBool zero;
683: PetscFunctionBegin;
684: PetscCall(MatCopy(ts->mat_sensip, rk->MatFwdSensip0, SAME_NONZERO_PATTERN));
685: PetscCall(TSGetRHSJacobian(ts, &J, NULL, NULL, NULL));
687: for (i = 0; i < s; i++) {
688: stage_time = ts->ptime + h * c[i];
689: zero = PETSC_FALSE;
690: if (b[i] == 0 && i == s - 1) zero = PETSC_TRUE;
691: /* TLM Stage values */
692: if (!i) {
693: PetscCall(MatCopy(ts->mat_sensip, rk->MatsFwdStageSensip[i], SAME_NONZERO_PATTERN));
694: } else if (!zero) {
695: PetscCall(MatZeroEntries(rk->MatsFwdStageSensip[i]));
696: for (j = 0; j < i; j++) PetscCall(MatAXPY(rk->MatsFwdStageSensip[i], h * A[i * s + j], MatsFwdSensipTemp[j], SAME_NONZERO_PATTERN));
697: PetscCall(MatAXPY(rk->MatsFwdStageSensip[i], 1., ts->mat_sensip, SAME_NONZERO_PATTERN));
698: } else {
699: PetscCall(MatZeroEntries(rk->MatsFwdStageSensip[i]));
700: }
702: PetscCall(TSComputeRHSJacobian(ts, stage_time, Y[i], J, J));
703: PetscCall(MatMatMult(J, rk->MatsFwdStageSensip[i], MAT_REUSE_MATRIX, PETSC_DEFAULT, &MatsFwdSensipTemp[i]));
704: if (ts->Jacprhs) {
705: PetscCall(TSComputeRHSJacobianP(ts, stage_time, Y[i], ts->Jacprhs)); /* get f_p */
706: if (ts->vecs_sensi2p) { /* TLM used for 2nd-order adjoint */
707: PetscScalar *xarr;
708: PetscCall(MatDenseGetColumn(MatsFwdSensipTemp[i], 0, &xarr));
709: PetscCall(VecPlaceArray(rk->VecDeltaFwdSensipCol, xarr));
710: PetscCall(MatMultAdd(ts->Jacprhs, ts->vec_dir, rk->VecDeltaFwdSensipCol, rk->VecDeltaFwdSensipCol));
711: PetscCall(VecResetArray(rk->VecDeltaFwdSensipCol));
712: PetscCall(MatDenseRestoreColumn(MatsFwdSensipTemp[i], &xarr));
713: } else {
714: PetscCall(MatAXPY(MatsFwdSensipTemp[i], 1., ts->Jacprhs, SUBSET_NONZERO_PATTERN));
715: }
716: }
717: }
719: for (i = 0; i < s; i++) PetscCall(MatAXPY(ts->mat_sensip, h * b[i], rk->MatsFwdSensipTemp[i], SAME_NONZERO_PATTERN));
720: rk->status = TS_STEP_COMPLETE;
721: PetscFunctionReturn(PETSC_SUCCESS);
722: }
724: static PetscErrorCode TSForwardGetStages_RK(TS ts, PetscInt *ns, Mat **stagesensip)
725: {
726: TS_RK *rk = (TS_RK *)ts->data;
727: RKTableau tab = rk->tableau;
729: PetscFunctionBegin;
730: if (ns) *ns = tab->s;
731: if (stagesensip) *stagesensip = rk->MatsFwdStageSensip;
732: PetscFunctionReturn(PETSC_SUCCESS);
733: }
735: static PetscErrorCode TSForwardSetUp_RK(TS ts)
736: {
737: TS_RK *rk = (TS_RK *)ts->data;
738: RKTableau tab = rk->tableau;
739: PetscInt i;
741: PetscFunctionBegin;
742: /* backup sensitivity results for roll-backs */
743: PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &rk->MatFwdSensip0));
745: PetscCall(PetscMalloc1(tab->s, &rk->MatsFwdStageSensip));
746: PetscCall(PetscMalloc1(tab->s, &rk->MatsFwdSensipTemp));
747: for (i = 0; i < tab->s; i++) {
748: PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &rk->MatsFwdStageSensip[i]));
749: PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &rk->MatsFwdSensipTemp[i]));
750: }
751: PetscCall(VecDuplicate(ts->vec_sol, &rk->VecDeltaFwdSensipCol));
752: PetscFunctionReturn(PETSC_SUCCESS);
753: }
755: static PetscErrorCode TSForwardReset_RK(TS ts)
756: {
757: TS_RK *rk = (TS_RK *)ts->data;
758: RKTableau tab = rk->tableau;
759: PetscInt i;
761: PetscFunctionBegin;
762: PetscCall(MatDestroy(&rk->MatFwdSensip0));
763: if (rk->MatsFwdStageSensip) {
764: for (i = 0; i < tab->s; i++) PetscCall(MatDestroy(&rk->MatsFwdStageSensip[i]));
765: PetscCall(PetscFree(rk->MatsFwdStageSensip));
766: }
767: if (rk->MatsFwdSensipTemp) {
768: for (i = 0; i < tab->s; i++) PetscCall(MatDestroy(&rk->MatsFwdSensipTemp[i]));
769: PetscCall(PetscFree(rk->MatsFwdSensipTemp));
770: }
771: PetscCall(VecDestroy(&rk->VecDeltaFwdSensipCol));
772: PetscFunctionReturn(PETSC_SUCCESS);
773: }
775: static PetscErrorCode TSStep_RK(TS ts)
776: {
777: TS_RK *rk = (TS_RK *)ts->data;
778: RKTableau tab = rk->tableau;
779: const PetscInt s = tab->s;
780: const PetscReal *A = tab->A, *c = tab->c;
781: PetscScalar *w = rk->work;
782: Vec *Y = rk->Y, *YdotRHS = rk->YdotRHS;
783: PetscBool FSAL = (PetscBool)(tab->FSAL && !rk->newtableau);
784: TSAdapt adapt;
785: PetscInt i, j;
786: PetscInt rejections = 0;
787: PetscBool stageok, accept = PETSC_TRUE;
788: PetscReal next_time_step = ts->time_step;
790: PetscFunctionBegin;
791: if (ts->steprollback || ts->steprestart) FSAL = PETSC_FALSE;
792: if (FSAL) PetscCall(VecCopy(YdotRHS[s - 1], YdotRHS[0]));
793: rk->newtableau = PETSC_FALSE;
795: rk->status = TS_STEP_INCOMPLETE;
796: while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
797: PetscReal t = ts->ptime;
798: PetscReal h = ts->time_step;
799: for (i = 0; i < s; i++) {
800: rk->stage_time = t + h * c[i];
801: PetscCall(TSPreStage(ts, rk->stage_time));
802: PetscCall(VecCopy(ts->vec_sol, Y[i]));
803: for (j = 0; j < i; j++) w[j] = h * A[i * s + j];
804: PetscCall(VecMAXPY(Y[i], i, w, YdotRHS));
805: PetscCall(TSPostStage(ts, rk->stage_time, i, Y));
806: PetscCall(TSGetAdapt(ts, &adapt));
807: PetscCall(TSAdaptCheckStage(adapt, ts, rk->stage_time, Y[i], &stageok));
808: if (!stageok) goto reject_step;
809: if (FSAL && !i) continue;
810: PetscCall(TSComputeRHSFunction(ts, t + h * c[i], Y[i], YdotRHS[i]));
811: }
813: rk->status = TS_STEP_INCOMPLETE;
814: PetscCall(TSEvaluateStep(ts, tab->order, ts->vec_sol, NULL));
815: rk->status = TS_STEP_PENDING;
816: PetscCall(TSGetAdapt(ts, &adapt));
817: PetscCall(TSAdaptCandidatesClear(adapt));
818: PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
819: PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
820: rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
821: if (!accept) { /* Roll back the current step */
822: PetscCall(TSRollBack_RK(ts));
823: ts->time_step = next_time_step;
824: goto reject_step;
825: }
827: if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */
828: rk->ptime = ts->ptime;
829: rk->time_step = ts->time_step;
830: }
832: ts->ptime += ts->time_step;
833: ts->time_step = next_time_step;
834: break;
836: reject_step:
837: ts->reject++;
838: accept = PETSC_FALSE;
839: if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
840: ts->reason = TS_DIVERGED_STEP_REJECTED;
841: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
842: }
843: }
844: PetscFunctionReturn(PETSC_SUCCESS);
845: }
847: static PetscErrorCode TSAdjointSetUp_RK(TS ts)
848: {
849: TS_RK *rk = (TS_RK *)ts->data;
850: RKTableau tab = rk->tableau;
851: PetscInt s = tab->s;
853: PetscFunctionBegin;
854: if (ts->adjointsetupcalled++) PetscFunctionReturn(PETSC_SUCCESS);
855: PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], s * ts->numcost, &rk->VecsDeltaLam));
856: PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &rk->VecsSensiTemp));
857: if (ts->vecs_sensip) PetscCall(VecDuplicate(ts->vecs_sensip[0], &rk->VecDeltaMu));
858: if (ts->vecs_sensi2) {
859: PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], s * ts->numcost, &rk->VecsDeltaLam2));
860: PetscCall(VecDuplicateVecs(ts->vecs_sensi2[0], ts->numcost, &rk->VecsSensi2Temp));
861: }
862: if (ts->vecs_sensi2p) PetscCall(VecDuplicate(ts->vecs_sensi2p[0], &rk->VecDeltaMu2));
863: PetscFunctionReturn(PETSC_SUCCESS);
864: }
866: /*
867: Assumptions:
868: - TSStep_RK() always evaluates the step with b, not bembed.
869: */
870: static PetscErrorCode TSAdjointStep_RK(TS ts)
871: {
872: TS_RK *rk = (TS_RK *)ts->data;
873: TS quadts = ts->quadraturets;
874: RKTableau tab = rk->tableau;
875: Mat J, Jpre, Jquad;
876: const PetscInt s = tab->s;
877: const PetscReal *A = tab->A, *b = tab->b, *c = tab->c;
878: PetscScalar *w = rk->work, *xarr;
879: Vec *Y = rk->Y, *VecsDeltaLam = rk->VecsDeltaLam, VecDeltaMu = rk->VecDeltaMu, *VecsSensiTemp = rk->VecsSensiTemp;
880: Vec *VecsDeltaLam2 = rk->VecsDeltaLam2, VecDeltaMu2 = rk->VecDeltaMu2, *VecsSensi2Temp = rk->VecsSensi2Temp;
881: Vec VecDRDUTransCol = ts->vec_drdu_col, VecDRDPTransCol = ts->vec_drdp_col;
882: PetscInt i, j, nadj;
883: PetscReal t = ts->ptime;
884: PetscReal h = ts->time_step;
886: PetscFunctionBegin;
887: rk->status = TS_STEP_INCOMPLETE;
889: PetscCall(TSGetRHSJacobian(ts, &J, &Jpre, NULL, NULL));
890: if (quadts) PetscCall(TSGetRHSJacobian(quadts, &Jquad, NULL, NULL, NULL));
891: for (i = s - 1; i >= 0; i--) {
892: if (tab->FSAL && i == s - 1) {
893: /* VecsDeltaLam[nadj*s+s-1] are initialized with zeros and the values never change.*/
894: continue;
895: }
896: rk->stage_time = t + h * (1.0 - c[i]);
897: PetscCall(TSComputeSNESJacobian(ts, Y[i], J, Jpre));
898: if (quadts) { PetscCall(TSComputeRHSJacobian(quadts, rk->stage_time, Y[i], Jquad, Jquad)); /* get r_u^T */ }
899: if (ts->vecs_sensip) {
900: PetscCall(TSComputeRHSJacobianP(ts, rk->stage_time, Y[i], ts->Jacprhs)); /* get f_p */
901: if (quadts) { PetscCall(TSComputeRHSJacobianP(quadts, rk->stage_time, Y[i], quadts->Jacprhs)); /* get f_p for the quadrature */ }
902: }
904: if (b[i]) {
905: for (j = i + 1; j < s; j++) w[j - i - 1] = A[j * s + i] / b[i]; /* coefficients for computing VecsSensiTemp */
906: } else {
907: for (j = i + 1; j < s; j++) w[j - i - 1] = A[j * s + i]; /* coefficients for computing VecsSensiTemp */
908: }
910: for (nadj = 0; nadj < ts->numcost; nadj++) {
911: /* Stage values of lambda */
912: if (b[i]) {
913: /* lambda_{n+1} + \sum_{j=i+1}^s a_{ji}/b[i]*lambda_{s,j} */
914: PetscCall(VecCopy(ts->vecs_sensi[nadj], VecsSensiTemp[nadj])); /* VecDeltaLam is an vec array of size s by numcost */
915: PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
916: PetscCall(MatMultTranspose(J, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i])); /* VecsSensiTemp will be reused by 2nd-order adjoint */
917: PetscCall(VecScale(VecsDeltaLam[nadj * s + i], -h * b[i]));
918: if (quadts) {
919: PetscCall(MatDenseGetColumn(Jquad, nadj, &xarr));
920: PetscCall(VecPlaceArray(VecDRDUTransCol, xarr));
921: PetscCall(VecAXPY(VecsDeltaLam[nadj * s + i], -h * b[i], VecDRDUTransCol));
922: PetscCall(VecResetArray(VecDRDUTransCol));
923: PetscCall(MatDenseRestoreColumn(Jquad, &xarr));
924: }
925: } else {
926: /* \sum_{j=i+1}^s a_{ji}*lambda_{s,j} */
927: PetscCall(VecSet(VecsSensiTemp[nadj], 0));
928: PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
929: PetscCall(MatMultTranspose(J, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i]));
930: PetscCall(VecScale(VecsDeltaLam[nadj * s + i], -h));
931: }
933: /* Stage values of mu */
934: if (ts->vecs_sensip) {
935: if (b[i]) {
936: PetscCall(MatMultTranspose(ts->Jacprhs, VecsSensiTemp[nadj], VecDeltaMu));
937: PetscCall(VecScale(VecDeltaMu, -h * b[i]));
938: if (quadts) {
939: PetscCall(MatDenseGetColumn(quadts->Jacprhs, nadj, &xarr));
940: PetscCall(VecPlaceArray(VecDRDPTransCol, xarr));
941: PetscCall(VecAXPY(VecDeltaMu, -h * b[i], VecDRDPTransCol));
942: PetscCall(VecResetArray(VecDRDPTransCol));
943: PetscCall(MatDenseRestoreColumn(quadts->Jacprhs, &xarr));
944: }
945: } else {
946: PetscCall(VecScale(VecDeltaMu, -h));
947: }
948: PetscCall(VecAXPY(ts->vecs_sensip[nadj], 1., VecDeltaMu)); /* update sensip for each stage */
949: }
950: }
952: if (ts->vecs_sensi2 && ts->forward_solve) { /* 2nd-order adjoint, TLM mode has to be turned on */
953: /* Get w1 at t_{n+1} from TLM matrix */
954: PetscCall(MatDenseGetColumn(rk->MatsFwdStageSensip[i], 0, &xarr));
955: PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
956: /* lambda_s^T F_UU w_1 */
957: PetscCall(TSComputeRHSHessianProductFunctionUU(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_sensip_col, ts->vecs_guu));
958: if (quadts) {
959: /* R_UU w_1 */
960: PetscCall(TSComputeRHSHessianProductFunctionUU(quadts, rk->stage_time, Y[i], NULL, ts->vec_sensip_col, ts->vecs_guu));
961: }
962: if (ts->vecs_sensip) {
963: /* lambda_s^T F_UP w_2 */
964: PetscCall(TSComputeRHSHessianProductFunctionUP(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_dir, ts->vecs_gup));
965: if (quadts) {
966: /* R_UP w_2 */
967: PetscCall(TSComputeRHSHessianProductFunctionUP(quadts, rk->stage_time, Y[i], NULL, ts->vec_sensip_col, ts->vecs_gup));
968: }
969: }
970: if (ts->vecs_sensi2p) {
971: /* lambda_s^T F_PU w_1 */
972: PetscCall(TSComputeRHSHessianProductFunctionPU(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_sensip_col, ts->vecs_gpu));
973: /* lambda_s^T F_PP w_2 */
974: PetscCall(TSComputeRHSHessianProductFunctionPP(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_dir, ts->vecs_gpp));
975: if (b[i] && quadts) {
976: /* R_PU w_1 */
977: PetscCall(TSComputeRHSHessianProductFunctionPU(quadts, rk->stage_time, Y[i], NULL, ts->vec_sensip_col, ts->vecs_gpu));
978: /* R_PP w_2 */
979: PetscCall(TSComputeRHSHessianProductFunctionPP(quadts, rk->stage_time, Y[i], NULL, ts->vec_dir, ts->vecs_gpp));
980: }
981: }
982: PetscCall(VecResetArray(ts->vec_sensip_col));
983: PetscCall(MatDenseRestoreColumn(rk->MatsFwdStageSensip[i], &xarr));
985: for (nadj = 0; nadj < ts->numcost; nadj++) {
986: /* Stage values of lambda */
987: if (b[i]) {
988: /* J_i^T*(Lambda_{n+1}+\sum_{j=i+1}^s a_{ji}/b_i*Lambda_{s,j} */
989: PetscCall(VecCopy(ts->vecs_sensi2[nadj], VecsSensi2Temp[nadj]));
990: PetscCall(VecMAXPY(VecsSensi2Temp[nadj], s - i - 1, w, &VecsDeltaLam2[nadj * s + i + 1]));
991: PetscCall(MatMultTranspose(J, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj * s + i]));
992: PetscCall(VecScale(VecsDeltaLam2[nadj * s + i], -h * b[i]));
993: PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h * b[i], ts->vecs_guu[nadj]));
994: if (ts->vecs_sensip) PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h * b[i], ts->vecs_gup[nadj]));
995: } else {
996: /* \sum_{j=i+1}^s a_{ji}*Lambda_{s,j} */
997: PetscCall(VecSet(VecsDeltaLam2[nadj * s + i], 0));
998: PetscCall(VecMAXPY(VecsSensi2Temp[nadj], s - i - 1, w, &VecsDeltaLam2[nadj * s + i + 1]));
999: PetscCall(MatMultTranspose(J, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj * s + i]));
1000: PetscCall(VecScale(VecsDeltaLam2[nadj * s + i], -h));
1001: PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h, ts->vecs_guu[nadj]));
1002: if (ts->vecs_sensip) PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h, ts->vecs_gup[nadj]));
1003: }
1004: if (ts->vecs_sensi2p) { /* 2nd-order adjoint for parameters */
1005: PetscCall(MatMultTranspose(ts->Jacprhs, VecsSensi2Temp[nadj], VecDeltaMu2));
1006: if (b[i]) {
1007: PetscCall(VecScale(VecDeltaMu2, -h * b[i]));
1008: PetscCall(VecAXPY(VecDeltaMu2, -h * b[i], ts->vecs_gpu[nadj]));
1009: PetscCall(VecAXPY(VecDeltaMu2, -h * b[i], ts->vecs_gpp[nadj]));
1010: } else {
1011: PetscCall(VecScale(VecDeltaMu2, -h));
1012: PetscCall(VecAXPY(VecDeltaMu2, -h, ts->vecs_gpu[nadj]));
1013: PetscCall(VecAXPY(VecDeltaMu2, -h, ts->vecs_gpp[nadj]));
1014: }
1015: PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], 1, VecDeltaMu2)); /* update sensi2p for each stage */
1016: }
1017: }
1018: }
1019: }
1021: for (j = 0; j < s; j++) w[j] = 1.0;
1022: for (nadj = 0; nadj < ts->numcost; nadj++) { /* no need to do this for mu's */
1023: PetscCall(VecMAXPY(ts->vecs_sensi[nadj], s, w, &VecsDeltaLam[nadj * s]));
1024: if (ts->vecs_sensi2) PetscCall(VecMAXPY(ts->vecs_sensi2[nadj], s, w, &VecsDeltaLam2[nadj * s]));
1025: }
1026: rk->status = TS_STEP_COMPLETE;
1027: PetscFunctionReturn(PETSC_SUCCESS);
1028: }
1030: static PetscErrorCode TSAdjointReset_RK(TS ts)
1031: {
1032: TS_RK *rk = (TS_RK *)ts->data;
1033: RKTableau tab = rk->tableau;
1035: PetscFunctionBegin;
1036: PetscCall(VecDestroyVecs(tab->s * ts->numcost, &rk->VecsDeltaLam));
1037: PetscCall(VecDestroyVecs(ts->numcost, &rk->VecsSensiTemp));
1038: PetscCall(VecDestroy(&rk->VecDeltaMu));
1039: PetscCall(VecDestroyVecs(tab->s * ts->numcost, &rk->VecsDeltaLam2));
1040: PetscCall(VecDestroy(&rk->VecDeltaMu2));
1041: PetscCall(VecDestroyVecs(ts->numcost, &rk->VecsSensi2Temp));
1042: PetscFunctionReturn(PETSC_SUCCESS);
1043: }
1045: static PetscErrorCode TSInterpolate_RK(TS ts, PetscReal itime, Vec X)
1046: {
1047: TS_RK *rk = (TS_RK *)ts->data;
1048: PetscInt s = rk->tableau->s, p = rk->tableau->p, i, j;
1049: PetscReal h;
1050: PetscReal tt, t;
1051: PetscScalar *b;
1052: const PetscReal *B = rk->tableau->binterp;
1054: PetscFunctionBegin;
1055: PetscCheck(B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSRK %s does not have an interpolation formula", rk->tableau->name);
1057: switch (rk->status) {
1058: case TS_STEP_INCOMPLETE:
1059: case TS_STEP_PENDING:
1060: h = ts->time_step;
1061: t = (itime - ts->ptime) / h;
1062: break;
1063: case TS_STEP_COMPLETE:
1064: h = ts->ptime - ts->ptime_prev;
1065: t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
1066: break;
1067: default:
1068: SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1069: }
1070: PetscCall(PetscMalloc1(s, &b));
1071: for (i = 0; i < s; i++) b[i] = 0;
1072: for (j = 0, tt = t; j < p; j++, tt *= t) {
1073: for (i = 0; i < s; i++) b[i] += h * B[i * p + j] * tt;
1074: }
1075: PetscCall(VecCopy(rk->Y[0], X));
1076: PetscCall(VecMAXPY(X, s, b, rk->YdotRHS));
1077: PetscCall(PetscFree(b));
1078: PetscFunctionReturn(PETSC_SUCCESS);
1079: }
1081: /*------------------------------------------------------------*/
1083: static PetscErrorCode TSRKTableauReset(TS ts)
1084: {
1085: TS_RK *rk = (TS_RK *)ts->data;
1086: RKTableau tab = rk->tableau;
1088: PetscFunctionBegin;
1089: if (!tab) PetscFunctionReturn(PETSC_SUCCESS);
1090: PetscCall(PetscFree(rk->work));
1091: PetscCall(VecDestroyVecs(tab->s, &rk->Y));
1092: PetscCall(VecDestroyVecs(tab->s, &rk->YdotRHS));
1093: PetscFunctionReturn(PETSC_SUCCESS);
1094: }
1096: static PetscErrorCode TSReset_RK(TS ts)
1097: {
1098: PetscFunctionBegin;
1099: PetscCall(TSRKTableauReset(ts));
1100: if (ts->use_splitrhsfunction) {
1101: PetscTryMethod(ts, "TSReset_RK_MultirateSplit_C", (TS), (ts));
1102: } else {
1103: PetscTryMethod(ts, "TSReset_RK_MultirateNonsplit_C", (TS), (ts));
1104: }
1105: PetscFunctionReturn(PETSC_SUCCESS);
1106: }
1108: static PetscErrorCode DMCoarsenHook_TSRK(DM fine, DM coarse, void *ctx)
1109: {
1110: PetscFunctionBegin;
1111: PetscFunctionReturn(PETSC_SUCCESS);
1112: }
1114: static PetscErrorCode DMRestrictHook_TSRK(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
1115: {
1116: PetscFunctionBegin;
1117: PetscFunctionReturn(PETSC_SUCCESS);
1118: }
1120: static PetscErrorCode DMSubDomainHook_TSRK(DM dm, DM subdm, void *ctx)
1121: {
1122: PetscFunctionBegin;
1123: PetscFunctionReturn(PETSC_SUCCESS);
1124: }
1126: static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
1127: {
1128: PetscFunctionBegin;
1129: PetscFunctionReturn(PETSC_SUCCESS);
1130: }
1132: static PetscErrorCode TSRKTableauSetUp(TS ts)
1133: {
1134: TS_RK *rk = (TS_RK *)ts->data;
1135: RKTableau tab = rk->tableau;
1137: PetscFunctionBegin;
1138: PetscCall(PetscMalloc1(tab->s, &rk->work));
1139: PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &rk->Y));
1140: PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &rk->YdotRHS));
1141: rk->newtableau = PETSC_TRUE;
1142: PetscFunctionReturn(PETSC_SUCCESS);
1143: }
1145: static PetscErrorCode TSSetUp_RK(TS ts)
1146: {
1147: TS quadts = ts->quadraturets;
1148: DM dm;
1150: PetscFunctionBegin;
1151: PetscCall(TSCheckImplicitTerm(ts));
1152: PetscCall(TSRKTableauSetUp(ts));
1153: if (quadts && ts->costintegralfwd) {
1154: Mat Jquad;
1155: PetscCall(TSGetRHSJacobian(quadts, &Jquad, NULL, NULL, NULL));
1156: }
1157: PetscCall(TSGetDM(ts, &dm));
1158: PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSRK, DMRestrictHook_TSRK, ts));
1159: PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSRK, DMSubDomainRestrictHook_TSRK, ts));
1160: if (ts->use_splitrhsfunction) {
1161: PetscTryMethod(ts, "TSSetUp_RK_MultirateSplit_C", (TS), (ts));
1162: } else {
1163: PetscTryMethod(ts, "TSSetUp_RK_MultirateNonsplit_C", (TS), (ts));
1164: }
1165: PetscFunctionReturn(PETSC_SUCCESS);
1166: }
1168: static PetscErrorCode TSSetFromOptions_RK(TS ts, PetscOptionItems *PetscOptionsObject)
1169: {
1170: TS_RK *rk = (TS_RK *)ts->data;
1172: PetscFunctionBegin;
1173: PetscOptionsHeadBegin(PetscOptionsObject, "RK ODE solver options");
1174: {
1175: RKTableauLink link;
1176: PetscInt count, choice;
1177: PetscBool flg, use_multirate = PETSC_FALSE;
1178: const char **namelist;
1180: for (link = RKTableauList, count = 0; link; link = link->next, count++);
1181: PetscCall(PetscMalloc1(count, (char ***)&namelist));
1182: for (link = RKTableauList, count = 0; link; link = link->next, count++) namelist[count] = link->tab.name;
1183: PetscCall(PetscOptionsBool("-ts_rk_multirate", "Use interpolation-based multirate RK method", "TSRKSetMultirate", rk->use_multirate, &use_multirate, &flg));
1184: if (flg) PetscCall(TSRKSetMultirate(ts, use_multirate));
1185: PetscCall(PetscOptionsEList("-ts_rk_type", "Family of RK method", "TSRKSetType", (const char *const *)namelist, count, rk->tableau->name, &choice, &flg));
1186: if (flg) PetscCall(TSRKSetType(ts, namelist[choice]));
1187: PetscCall(PetscFree(namelist));
1188: }
1189: PetscOptionsHeadEnd();
1190: PetscOptionsBegin(PetscObjectComm((PetscObject)ts), NULL, "Multirate methods options", "");
1191: PetscCall(PetscOptionsInt("-ts_rk_dtratio", "time step ratio between slow and fast", "", rk->dtratio, &rk->dtratio, NULL));
1192: PetscOptionsEnd();
1193: PetscFunctionReturn(PETSC_SUCCESS);
1194: }
1196: static PetscErrorCode TSView_RK(TS ts, PetscViewer viewer)
1197: {
1198: TS_RK *rk = (TS_RK *)ts->data;
1199: PetscBool iascii;
1201: PetscFunctionBegin;
1202: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1203: if (iascii) {
1204: RKTableau tab = rk->tableau;
1205: TSRKType rktype;
1206: const PetscReal *c;
1207: PetscInt s;
1208: char buf[512];
1209: PetscBool FSAL;
1211: PetscCall(TSRKGetType(ts, &rktype));
1212: PetscCall(TSRKGetTableau(ts, &s, NULL, NULL, &c, NULL, NULL, NULL, &FSAL));
1213: PetscCall(PetscViewerASCIIPrintf(viewer, " RK type %s\n", rktype));
1214: PetscCall(PetscViewerASCIIPrintf(viewer, " Order: %" PetscInt_FMT "\n", tab->order));
1215: PetscCall(PetscViewerASCIIPrintf(viewer, " FSAL property: %s\n", FSAL ? "yes" : "no"));
1216: PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", s, c));
1217: PetscCall(PetscViewerASCIIPrintf(viewer, " Abscissa c = %s\n", buf));
1218: }
1219: PetscFunctionReturn(PETSC_SUCCESS);
1220: }
1222: static PetscErrorCode TSLoad_RK(TS ts, PetscViewer viewer)
1223: {
1224: TSAdapt adapt;
1226: PetscFunctionBegin;
1227: PetscCall(TSGetAdapt(ts, &adapt));
1228: PetscCall(TSAdaptLoad(adapt, viewer));
1229: PetscFunctionReturn(PETSC_SUCCESS);
1230: }
1232: /*@
1233: TSRKGetOrder - Get the order of the `TSRK` scheme
1235: Not Collective
1237: Input Parameter:
1238: . ts - timestepping context
1240: Output Parameter:
1241: . order - order of `TSRK` scheme
1243: Level: intermediate
1245: .seealso: [](ch_ts), `TSRK`, `TSRKGetType()`
1246: @*/
1247: PetscErrorCode TSRKGetOrder(TS ts, PetscInt *order)
1248: {
1249: PetscFunctionBegin;
1251: PetscAssertPointer(order, 2);
1252: PetscUseMethod(ts, "TSRKGetOrder_C", (TS, PetscInt *), (ts, order));
1253: PetscFunctionReturn(PETSC_SUCCESS);
1254: }
1256: /*@C
1257: TSRKSetType - Set the type of the `TSRK` scheme
1259: Logically Collective
1261: Input Parameters:
1262: + ts - timestepping context
1263: - rktype - type of `TSRK` scheme
1265: Options Database Key:
1266: . -ts_rk_type - <1fe,2a,3,3bs,4,5f,5dp,5bs>
1268: Level: intermediate
1270: .seealso: [](ch_ts), `TSRKGetType()`, `TSRK`, `TSRKType`, `TSRK1FE`, `TSRK2A`, `TSRK2B`, `TSRK3`, `TSRK3BS`, `TSRK4`, `TSRK5F`, `TSRK5DP`, `TSRK5BS`, `TSRK6VR`, `TSRK7VR`, `TSRK8VR`
1271: @*/
1272: PetscErrorCode TSRKSetType(TS ts, TSRKType rktype)
1273: {
1274: PetscFunctionBegin;
1276: PetscAssertPointer(rktype, 2);
1277: PetscTryMethod(ts, "TSRKSetType_C", (TS, TSRKType), (ts, rktype));
1278: PetscFunctionReturn(PETSC_SUCCESS);
1279: }
1281: /*@C
1282: TSRKGetType - Get the type of `TSRK` scheme
1284: Not Collective
1286: Input Parameter:
1287: . ts - timestepping context
1289: Output Parameter:
1290: . rktype - type of `TSRK`-scheme
1292: Level: intermediate
1294: .seealso: [](ch_ts), `TSRKSetType()`
1295: @*/
1296: PetscErrorCode TSRKGetType(TS ts, TSRKType *rktype)
1297: {
1298: PetscFunctionBegin;
1300: PetscUseMethod(ts, "TSRKGetType_C", (TS, TSRKType *), (ts, rktype));
1301: PetscFunctionReturn(PETSC_SUCCESS);
1302: }
1304: static PetscErrorCode TSRKGetOrder_RK(TS ts, PetscInt *order)
1305: {
1306: TS_RK *rk = (TS_RK *)ts->data;
1308: PetscFunctionBegin;
1309: *order = rk->tableau->order;
1310: PetscFunctionReturn(PETSC_SUCCESS);
1311: }
1313: static PetscErrorCode TSRKGetType_RK(TS ts, TSRKType *rktype)
1314: {
1315: TS_RK *rk = (TS_RK *)ts->data;
1317: PetscFunctionBegin;
1318: *rktype = rk->tableau->name;
1319: PetscFunctionReturn(PETSC_SUCCESS);
1320: }
1322: static PetscErrorCode TSRKSetType_RK(TS ts, TSRKType rktype)
1323: {
1324: TS_RK *rk = (TS_RK *)ts->data;
1325: PetscBool match;
1326: RKTableauLink link;
1328: PetscFunctionBegin;
1329: if (rk->tableau) {
1330: PetscCall(PetscStrcmp(rk->tableau->name, rktype, &match));
1331: if (match) PetscFunctionReturn(PETSC_SUCCESS);
1332: }
1333: for (link = RKTableauList; link; link = link->next) {
1334: PetscCall(PetscStrcmp(link->tab.name, rktype, &match));
1335: if (match) {
1336: if (ts->setupcalled) PetscCall(TSRKTableauReset(ts));
1337: rk->tableau = &link->tab;
1338: if (ts->setupcalled) PetscCall(TSRKTableauSetUp(ts));
1339: ts->default_adapt_type = rk->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1340: PetscFunctionReturn(PETSC_SUCCESS);
1341: }
1342: }
1343: SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", rktype);
1344: }
1346: static PetscErrorCode TSGetStages_RK(TS ts, PetscInt *ns, Vec **Y)
1347: {
1348: TS_RK *rk = (TS_RK *)ts->data;
1350: PetscFunctionBegin;
1351: if (ns) *ns = rk->tableau->s;
1352: if (Y) *Y = rk->Y;
1353: PetscFunctionReturn(PETSC_SUCCESS);
1354: }
1356: static PetscErrorCode TSDestroy_RK(TS ts)
1357: {
1358: PetscFunctionBegin;
1359: PetscCall(TSReset_RK(ts));
1360: if (ts->dm) {
1361: PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSRK, DMRestrictHook_TSRK, ts));
1362: PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSRK, DMSubDomainRestrictHook_TSRK, ts));
1363: }
1364: PetscCall(PetscFree(ts->data));
1365: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetOrder_C", NULL));
1366: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetType_C", NULL));
1367: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetType_C", NULL));
1368: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetTableau_C", NULL));
1369: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetMultirate_C", NULL));
1370: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetMultirate_C", NULL));
1371: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateSplit_C", NULL));
1372: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateSplit_C", NULL));
1373: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateNonsplit_C", NULL));
1374: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateNonsplit_C", NULL));
1375: PetscFunctionReturn(PETSC_SUCCESS);
1376: }
1378: /*
1379: This defines the nonlinear equation that is to be solved with SNES
1380: We do not need to solve the equation; we just use SNES to approximate the Jacobian
1381: */
1382: static PetscErrorCode SNESTSFormFunction_RK(SNES snes, Vec x, Vec y, TS ts)
1383: {
1384: TS_RK *rk = (TS_RK *)ts->data;
1385: DM dm, dmsave;
1387: PetscFunctionBegin;
1388: PetscCall(SNESGetDM(snes, &dm));
1389: /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
1390: dmsave = ts->dm;
1391: ts->dm = dm;
1392: PetscCall(TSComputeRHSFunction(ts, rk->stage_time, x, y));
1393: ts->dm = dmsave;
1394: PetscFunctionReturn(PETSC_SUCCESS);
1395: }
1397: static PetscErrorCode SNESTSFormJacobian_RK(SNES snes, Vec x, Mat A, Mat B, TS ts)
1398: {
1399: TS_RK *rk = (TS_RK *)ts->data;
1400: DM dm, dmsave;
1402: PetscFunctionBegin;
1403: PetscCall(SNESGetDM(snes, &dm));
1404: dmsave = ts->dm;
1405: ts->dm = dm;
1406: PetscCall(TSComputeRHSJacobian(ts, rk->stage_time, x, A, B));
1407: ts->dm = dmsave;
1408: PetscFunctionReturn(PETSC_SUCCESS);
1409: }
1411: /*@C
1412: TSRKSetMultirate - Use the interpolation-based multirate `TSRK` method
1414: Logically Collective
1416: Input Parameters:
1417: + ts - timestepping context
1418: - 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
1420: Options Database Key:
1421: . -ts_rk_multirate - <true,false>
1423: Level: intermediate
1425: Note:
1426: 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).
1428: .seealso: [](ch_ts), `TSRK`, `TSRKGetMultirate()`
1429: @*/
1430: PetscErrorCode TSRKSetMultirate(TS ts, PetscBool use_multirate)
1431: {
1432: PetscFunctionBegin;
1433: PetscTryMethod(ts, "TSRKSetMultirate_C", (TS, PetscBool), (ts, use_multirate));
1434: PetscFunctionReturn(PETSC_SUCCESS);
1435: }
1437: /*@C
1438: TSRKGetMultirate - Gets whether to use the interpolation-based multirate `TSRK` method
1440: Not Collective
1442: Input Parameter:
1443: . ts - timestepping context
1445: Output Parameter:
1446: . use_multirate - `PETSC_TRUE` if the multirate RK method is enabled, `PETSC_FALSE` otherwise
1448: Level: intermediate
1450: .seealso: [](ch_ts), `TSRK`, `TSRKSetMultirate()`
1451: @*/
1452: PetscErrorCode TSRKGetMultirate(TS ts, PetscBool *use_multirate)
1453: {
1454: PetscFunctionBegin;
1455: PetscUseMethod(ts, "TSRKGetMultirate_C", (TS, PetscBool *), (ts, use_multirate));
1456: PetscFunctionReturn(PETSC_SUCCESS);
1457: }
1459: /*MC
1460: TSRK - ODE and DAE solver using Runge-Kutta schemes
1462: The user should provide the right-hand side of the equation
1463: using `TSSetRHSFunction()`.
1465: Level: beginner
1467: Notes:
1468: The default is `TSRK3BS`, it can be changed with `TSRKSetType()` or -ts_rk_type
1470: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSRK`, `TSSetType()`, `TSRKSetType()`, `TSRKGetType()`, `TSRK2D`, `TSRK2E`, `TSRK3`,
1471: `TSRK4`, `TSRK5`, `TSRKPRSSP2`, `TSRKBPR3`, `TSRKType`, `TSRKRegister()`, `TSRKSetMultirate()`, `TSRKGetMultirate()`, `TSType`
1472: M*/
1473: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
1474: {
1475: TS_RK *rk;
1477: PetscFunctionBegin;
1478: PetscCall(TSRKInitializePackage());
1480: ts->ops->reset = TSReset_RK;
1481: ts->ops->destroy = TSDestroy_RK;
1482: ts->ops->view = TSView_RK;
1483: ts->ops->load = TSLoad_RK;
1484: ts->ops->setup = TSSetUp_RK;
1485: ts->ops->interpolate = TSInterpolate_RK;
1486: ts->ops->step = TSStep_RK;
1487: ts->ops->evaluatestep = TSEvaluateStep_RK;
1488: ts->ops->rollback = TSRollBack_RK;
1489: ts->ops->setfromoptions = TSSetFromOptions_RK;
1490: ts->ops->getstages = TSGetStages_RK;
1492: ts->ops->snesfunction = SNESTSFormFunction_RK;
1493: ts->ops->snesjacobian = SNESTSFormJacobian_RK;
1494: ts->ops->adjointintegral = TSAdjointCostIntegral_RK;
1495: ts->ops->adjointsetup = TSAdjointSetUp_RK;
1496: ts->ops->adjointstep = TSAdjointStep_RK;
1497: ts->ops->adjointreset = TSAdjointReset_RK;
1499: ts->ops->forwardintegral = TSForwardCostIntegral_RK;
1500: ts->ops->forwardsetup = TSForwardSetUp_RK;
1501: ts->ops->forwardreset = TSForwardReset_RK;
1502: ts->ops->forwardstep = TSForwardStep_RK;
1503: ts->ops->forwardgetstages = TSForwardGetStages_RK;
1505: PetscCall(PetscNew(&rk));
1506: ts->data = (void *)rk;
1508: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetOrder_C", TSRKGetOrder_RK));
1509: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetType_C", TSRKGetType_RK));
1510: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetType_C", TSRKSetType_RK));
1511: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetTableau_C", TSRKGetTableau_RK));
1512: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetMultirate_C", TSRKSetMultirate_RK));
1513: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetMultirate_C", TSRKGetMultirate_RK));
1515: PetscCall(TSRKSetType(ts, TSRKDefault));
1516: rk->dtratio = 1;
1517: PetscFunctionReturn(PETSC_SUCCESS);
1518: }