Actual source code: rk.c
petsc-3.12.5 2020-03-29
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:
28: . -ts_rk_type 1fe
30: Level: advanced
32: .seealso: TSRK, TSRKType, TSRKSetType()
33: M*/
34: /*MC
35: TSRK2A - Second order RK scheme.
37: This method has two stages.
39: Options database:
40: . -ts_rk_type 2a
42: Level: advanced
44: .seealso: TSRK, TSRKType, TSRKSetType()
45: M*/
46: /*MC
47: TSRK3 - Third order RK scheme.
49: This method has three stages.
51: Options database:
52: . -ts_rk_type 3
54: Level: advanced
56: .seealso: TSRK, TSRKType, TSRKSetType()
57: M*/
58: /*MC
59: TSRK3BS - Third order RK scheme of Bogacki-Shampine with 2nd order embedded method.
61: This method has four stages with the First Same As Last (FSAL) property.
63: Options database:
64: . -ts_rk_type 3bs
66: Level: advanced
68: References: https://doi.org/10.1016/0893-9659(89)90079-7
70: .seealso: TSRK, TSRKType, TSRKSetType()
71: M*/
72: /*MC
73: TSRK4 - Fourth order RK scheme.
75: This is the classical Runge-Kutta method with four stages.
77: Options database:
78: . -ts_rk_type 4
80: Level: advanced
82: .seealso: TSRK, TSRKType, TSRKSetType()
83: M*/
84: /*MC
85: TSRK5F - Fifth order Fehlberg RK scheme with a 4th order embedded method.
87: This method has six stages.
89: Options database:
90: . -ts_rk_type 5f
92: Level: advanced
94: .seealso: TSRK, TSRKType, TSRKSetType()
95: M*/
96: /*MC
97: TSRK5DP - Fifth order Dormand-Prince RK scheme with the 4th order embedded method.
99: This method has seven stages with the First Same As Last (FSAL) property.
101: Options database:
102: . -ts_rk_type 5dp
104: Level: advanced
106: References: https://doi.org/10.1016/0771-050X(80)90013-3
108: .seealso: TSRK, TSRKType, TSRKSetType()
109: M*/
110: /*MC
111: TSRK5BS - Fifth order Bogacki-Shampine RK scheme with 4th order embedded method.
113: This method has eight stages with the First Same As Last (FSAL) property.
115: Options database:
116: . -ts_rk_type 5bs
118: Level: advanced
120: References: https://doi.org/10.1016/0898-1221(96)00141-1
122: .seealso: TSRK, TSRKType, TSRKSetType()
123: M*/
124: /*MC
125: TSRK6VR - Sixth order robust Verner RK scheme with fifth order embedded method.
127: This method has nine stages with the First Same As Last (FSAL) property.
129: Options database:
130: . -ts_rk_type 6vr
132: Level: advanced
134: References: http://people.math.sfu.ca/~jverner/RKV65.IIIXb.Robust.00010102836.081204.CoeffsOnlyRAT
136: .seealso: TSRK, TSRKType, TSRKSetType()
137: M*/
138: /*MC
139: TSRK7VR - Seventh order robust Verner RK scheme with sixth order embedded method.
141: This method has ten stages with the First Same As Last (FSAL) property.
143: Options database:
144: . -ts_rk_type 7vr
146: Level: advanced
148: References: http://people.math.sfu.ca/~jverner/RKV76.IIa.Robust.000027015646.081206.CoeffsOnlyRAT
150: .seealso: TSRK, TSRKType, TSRKSetType()
151: M*/
152: /*MC
153: TSRK8VR - Eigth order robust Verner RK scheme with seventh order embedded method.
155: This method has thirteen stages with the First Same As Last (FSAL) property.
157: Options database:
158: . -ts_rk_type 8vr
160: Level: advanced
162: References: http://people.math.sfu.ca/~jverner/RKV87.IIa.Robust.00000754677.081208.CoeffsOnlyRATandFLOAT
164: .seealso: TSRK, TSRKType, TSRKSetType()
165: M*/
167: /*@C
168: TSRKRegisterAll - Registers all of the Runge-Kutta explicit methods in TSRK
170: Not Collective, but should be called by all processes which will need the schemes to be registered
172: Level: advanced
174: .seealso: TSRKRegisterDestroy()
175: @*/
176: PetscErrorCode TSRKRegisterAll(void)
177: {
181: if (TSRKRegisterAllCalled) return(0);
182: TSRKRegisterAllCalled = PETSC_TRUE;
184: #define RC PetscRealConstant
185: {
186: const PetscReal
187: A[1][1] = {{0}},
188: b[1] = {RC(1.0)};
189: TSRKRegister(TSRK1FE,1,1,&A[0][0],b,NULL,NULL,0,NULL);
190: }
191: {
192: const PetscReal
193: A[2][2] = {{0,0},
194: {RC(1.0),0}},
195: b[2] = {RC(0.5),RC(0.5)},
196: bembed[2] = {RC(1.0),0};
197: TSRKRegister(TSRK2A,2,2,&A[0][0],b,NULL,bembed,0,NULL);
198: }
199: {
200: const PetscReal
201: A[3][3] = {{0,0,0},
202: {RC(2.0)/RC(3.0),0,0},
203: {RC(-1.0)/RC(3.0),RC(1.0),0}},
204: b[3] = {RC(0.25),RC(0.5),RC(0.25)};
205: TSRKRegister(TSRK3,3,3,&A[0][0],b,NULL,NULL,0,NULL);
206: }
207: {
208: const PetscReal
209: A[4][4] = {{0,0,0,0},
210: {RC(1.0)/RC(2.0),0,0,0},
211: {0,RC(3.0)/RC(4.0),0,0},
212: {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0}},
213: b[4] = {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0},
214: 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)};
215: TSRKRegister(TSRK3BS,3,4,&A[0][0],b,NULL,bembed,0,NULL);
216: }
217: {
218: const PetscReal
219: A[4][4] = {{0,0,0,0},
220: {RC(0.5),0,0,0},
221: {0,RC(0.5),0,0},
222: {0,0,RC(1.0),0}},
223: 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)};
224: TSRKRegister(TSRK4,4,4,&A[0][0],b,NULL,NULL,0,NULL);
225: }
226: {
227: const PetscReal
228: A[6][6] = {{0,0,0,0,0,0},
229: {RC(0.25),0,0,0,0,0},
230: {RC(3.0)/RC(32.0),RC(9.0)/RC(32.0),0,0,0,0},
231: {RC(1932.0)/RC(2197.0),RC(-7200.0)/RC(2197.0),RC(7296.0)/RC(2197.0),0,0,0},
232: {RC(439.0)/RC(216.0),RC(-8.0),RC(3680.0)/RC(513.0),RC(-845.0)/RC(4104.0),0,0},
233: {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}},
234: 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)},
235: 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};
236: TSRKRegister(TSRK5F,5,6,&A[0][0],b,NULL,bembed,0,NULL);
237: }
238: {
239: const PetscReal
240: A[7][7] = {{0,0,0,0,0,0,0},
241: {RC(1.0)/RC(5.0),0,0,0,0,0,0},
242: {RC(3.0)/RC(40.0),RC(9.0)/RC(40.0),0,0,0,0,0},
243: {RC(44.0)/RC(45.0),RC(-56.0)/RC(15.0),RC(32.0)/RC(9.0),0,0,0,0},
244: {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},
245: {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},
246: {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}},
247: 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},
248: 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)},
249: 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)},
250: {0,0,0,0,0},
251: {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)},
252: {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)},
253: {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)},
254: {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)},
255: {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)}};
257: TSRKRegister(TSRK5DP,5,7,&A[0][0],b,NULL,bembed,5,binterp[0]);
258: }
259: {
260: const PetscReal
261: A[8][8] = {{0,0,0,0,0,0,0,0},
262: {RC(1.0)/RC(6.0),0,0,0,0,0,0,0},
263: {RC(2.0)/RC(27.0),RC(4.0)/RC(27.0),0,0,0,0,0,0},
264: {RC(183.0)/RC(1372.0),RC(-162.0)/RC(343.0),RC(1053.0)/RC(1372.0),0,0,0,0,0},
265: {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},
266: {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},
267: {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},
268: {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}},
269: 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},
270: 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)};
271: TSRKRegister(TSRK5BS,5,8,&A[0][0],b,NULL,bembed,0,NULL);
272: }
273: {
274: const PetscReal
275: A[9][9] = {{0,0,0,0,0,0,0,0,0},
276: {RC(1.8000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0},
277: {RC(8.9506172839506172839506172839506172839506e-02),RC(7.7160493827160493827160493827160493827160e-02),0,0,0,0,0,0,0},
278: {RC(6.2500000000000000000000000000000000000000e-02),0,RC(1.8750000000000000000000000000000000000000e-01),0,0,0,0,0,0},
279: {RC(3.1651600000000000000000000000000000000000e-01),0,RC(-1.0449480000000000000000000000000000000000e+00),RC(1.2584320000000000000000000000000000000000e+00),0,0,0,0,0},
280: {RC(2.7232612736485626257225065566674305502508e-01),0,RC(-8.2513360323886639676113360323886639676113e-01),RC(1.0480917678812415654520917678812415654521e+00),RC(1.0471570799276856873679117969088177628396e-01),0,0,0,0},
281: {RC(-1.6699418599716514314329607278961797333198e-01),0,RC(6.3170850202429149797570850202429149797571e-01),RC(1.7461044552773876082146758838488161796432e-01),RC(-1.0665356459086066122525194734018680677781e+00),RC(1.2272108843537414965986394557823129251701e+00),0,0,0},
282: {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},
283: {RC(7.6388888888888888888888888888888888888889e-02),0,0,RC(3.6940836940836940836940836940836940836941e-01),0,RC(2.4801587301587301587301587301587301587302e-01),RC(2.3674242424242424242424242424242424242424e-01),RC(6.9444444444444444444444444444444444444444e-02),0}},
284: b[9] = {RC(7.6388888888888888888888888888888888888889e-02),0,0,RC(3.6940836940836940836940836940836940836941e-01),0,RC(2.4801587301587301587301587301587301587302e-01),RC(2.3674242424242424242424242424242424242424e-01),RC(6.9444444444444444444444444444444444444444e-02),0},
285: 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)};
286: TSRKRegister(TSRK6VR,6,9,&A[0][0],b,NULL,bembed,0,NULL);
287: }
288: {
289: const PetscReal
290: A[10][10] = {{0,0,0,0,0,0,0,0,0,0},
291: {RC(5.0000000000000000000000000000000000000000e-03),0,0,0,0,0,0,0,0,0},
292: {RC(-1.0767901234567901234567901234567901234568e+00),RC(1.1856790123456790123456790123456790123457e+00),0,0,0,0,0,0,0,0},
293: {RC(4.0833333333333333333333333333333333333333e-02),0,RC(1.2250000000000000000000000000000000000000e-01),0,0,0,0,0,0,0},
294: {RC(6.3607142857142857142857142857142857142857e-01),0,RC(-2.4444642857142857142857142857142857142857e+00),RC(2.2633928571428571428571428571428571428571e+00),0,0,0,0,0,0},
295: {RC(-2.5351211079349245229256383554660215487207e+00),0,RC(1.0299374654449267920438514460756024913612e+01),RC(-7.9513032885990579949493217458266876536482e+00),RC(7.9301148923100592201226014271115261823800e-01),0,0,0,0,0},
296: {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},
297: {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},
298: {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},
299: {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}},
300: 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},
301: bembed[10] = {RC(4.7485247699299631037531273805727961552268e-02),0,0,RC(2.5599412588690633297154918245905393870497e-01),RC(2.7058478081067688722530891099268135732387e-01),RC(1.2505618684425992913638822323746917920448e-01),RC(2.5204468723743860507184043820197442562182e-01),0,0,RC(4.8834971521418614557381971303093137592592e-02)};
302: TSRKRegister(TSRK7VR,7,10,&A[0][0],b,NULL,bembed,0,NULL);
303: }
304: {
305: const PetscReal
306: A[13][13] = {{0,0,0,0,0,0,0,0,0,0,0,0,0},
307: {RC(2.5000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0,0,0,0,0},
308: {RC(8.7400846504915232052686327594877411977046e-02),RC(2.5487604938654321753087950620345685135815e-02),0,0,0,0,0,0,0,0,0,0,0},
309: {RC(4.2333169291338582677165354330708661417323e-02),0,RC(1.2699950787401574803149606299212598425197e-01),0,0,0,0,0,0,0,0,0,0},
310: {RC(4.2609505888742261494881445237572274090942e-01),0,RC(-1.5987952846591523265427733230657181117089e+00),RC(1.5967002257717297115939588706899953707994e+00),0,0,0,0,0,0,0,0,0},
311: {RC(5.0719337296713929515090618138513639239329e-02),0,0,RC(2.5433377264600407582754714408877778031369e-01),RC(2.0394689005728199465736223777270858044698e-01),0,0,0,0,0,0,0,0},
312: {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},
313: {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},
314: {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},
315: {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},
316: {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},
317: {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},
318: {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}},
319: 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},
320: 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)};
321: TSRKRegister(TSRK8VR,8,13,&A[0][0],b,NULL,bembed,0,NULL);
322: }
323: #undef RC
324: return(0);
325: }
327: /*@C
328: TSRKRegisterDestroy - Frees the list of schemes that were registered by TSRKRegister().
330: Not Collective
332: Level: advanced
334: .seealso: TSRKRegister(), TSRKRegisterAll()
335: @*/
336: PetscErrorCode TSRKRegisterDestroy(void)
337: {
339: RKTableauLink link;
342: while ((link = RKTableauList)) {
343: RKTableau t = &link->tab;
344: RKTableauList = link->next;
345: PetscFree3(t->A,t->b,t->c);
346: PetscFree (t->bembed);
347: PetscFree (t->binterp);
348: PetscFree (t->name);
349: PetscFree (link);
350: }
351: TSRKRegisterAllCalled = PETSC_FALSE;
352: return(0);
353: }
355: /*@C
356: TSRKInitializePackage - This function initializes everything in the TSRK package. It is called
357: from TSInitializePackage().
359: Level: developer
361: .seealso: PetscInitialize()
362: @*/
363: PetscErrorCode TSRKInitializePackage(void)
364: {
368: if (TSRKPackageInitialized) return(0);
369: TSRKPackageInitialized = PETSC_TRUE;
370: TSRKRegisterAll();
371: PetscRegisterFinalize(TSRKFinalizePackage);
372: return(0);
373: }
375: /*@C
376: TSRKFinalizePackage - This function destroys everything in the TSRK package. It is
377: called from PetscFinalize().
379: Level: developer
381: .seealso: PetscFinalize()
382: @*/
383: PetscErrorCode TSRKFinalizePackage(void)
384: {
388: TSRKPackageInitialized = PETSC_FALSE;
389: TSRKRegisterDestroy();
390: return(0);
391: }
393: /*@C
394: TSRKRegister - register an RK scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation
396: Not Collective, but the same schemes should be registered on all processes on which they will be used
398: Input Parameters:
399: + name - identifier for method
400: . order - approximation order of method
401: . s - number of stages, this is the dimension of the matrices below
402: . A - stage coefficients (dimension s*s, row-major)
403: . b - step completion table (dimension s; NULL to use last row of A)
404: . c - abscissa (dimension s; NULL to use row sums of A)
405: . bembed - completion table for embedded method (dimension s; NULL if not available)
406: . p - Order of the interpolation scheme, equal to the number of columns of binterp
407: - binterp - Coefficients of the interpolation formula (dimension s*p; NULL to reuse b with p=1)
409: Notes:
410: Several RK methods are provided, this function is only needed to create new methods.
412: Level: advanced
414: .seealso: TSRK
415: @*/
416: PetscErrorCode TSRKRegister(TSRKType name,PetscInt order,PetscInt s,
417: const PetscReal A[],const PetscReal b[],const PetscReal c[],
418: const PetscReal bembed[],PetscInt p,const PetscReal binterp[])
419: {
420: PetscErrorCode ierr;
421: RKTableauLink link;
422: RKTableau t;
423: PetscInt i,j;
433: TSRKInitializePackage();
434: PetscNew(&link);
435: t = &link->tab;
437: PetscStrallocpy(name,&t->name);
438: t->order = order;
439: t->s = s;
440: PetscMalloc3(s*s,&t->A,s,&t->b,s,&t->c);
441: PetscArraycpy(t->A,A,s*s);
442: if (b) { PetscArraycpy(t->b,b,s); }
443: else for (i=0; i<s; i++) t->b[i] = A[(s-1)*s+i];
444: if (c) { PetscArraycpy(t->c,c,s); }
445: else for (i=0; i<s; i++) for (j=0,t->c[i]=0; j<s; j++) t->c[i] += A[i*s+j];
446: t->FSAL = PETSC_TRUE;
447: for (i=0; i<s; i++) if (t->A[(s-1)*s+i] != t->b[i]) t->FSAL = PETSC_FALSE;
449: if (bembed) {
450: PetscMalloc1(s,&t->bembed);
451: PetscArraycpy(t->bembed,bembed,s);
452: }
454: if (!binterp) { p = 1; binterp = t->b; }
455: t->p = p;
456: PetscMalloc1(s*p,&t->binterp);
457: PetscArraycpy(t->binterp,binterp,s*p);
459: link->next = RKTableauList;
460: RKTableauList = link;
461: return(0);
462: }
464: /*
465: This is for single-step RK method
466: The step completion formula is
468: x1 = x0 + h b^T YdotRHS
470: This function can be called before or after ts->vec_sol has been updated.
471: Suppose we have a completion formula (b) and an embedded formula (be) of different order.
472: We can write
474: x1e = x0 + h be^T YdotRHS
475: = x1 - h b^T YdotRHS + h be^T YdotRHS
476: = x1 + h (be - b)^T YdotRHS
478: so we can evaluate the method with different order even after the step has been optimistically completed.
479: */
480: static PetscErrorCode TSEvaluateStep_RK(TS ts,PetscInt order,Vec X,PetscBool *done)
481: {
482: TS_RK *rk = (TS_RK*)ts->data;
483: RKTableau tab = rk->tableau;
484: PetscScalar *w = rk->work;
485: PetscReal h;
486: PetscInt s = tab->s,j;
490: switch (rk->status) {
491: case TS_STEP_INCOMPLETE:
492: case TS_STEP_PENDING:
493: h = ts->time_step; break;
494: case TS_STEP_COMPLETE:
495: h = ts->ptime - ts->ptime_prev; break;
496: default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
497: }
498: if (order == tab->order) {
499: if (rk->status == TS_STEP_INCOMPLETE) {
500: VecCopy(ts->vec_sol,X);
501: for (j=0; j<s; j++) w[j] = h*tab->b[j]/rk->dtratio;
502: VecMAXPY(X,s,w,rk->YdotRHS);
503: } else {VecCopy(ts->vec_sol,X);}
504: return(0);
505: } else if (order == tab->order-1) {
506: if (!tab->bembed) goto unavailable;
507: if (rk->status == TS_STEP_INCOMPLETE) { /*Complete with the embedded method (be)*/
508: VecCopy(ts->vec_sol,X);
509: for (j=0; j<s; j++) w[j] = h*tab->bembed[j];
510: VecMAXPY(X,s,w,rk->YdotRHS);
511: } else { /*Rollback and re-complete using (be-b) */
512: VecCopy(ts->vec_sol,X);
513: for (j=0; j<s; j++) w[j] = h*(tab->bembed[j] - tab->b[j]);
514: VecMAXPY(X,s,w,rk->YdotRHS);
515: }
516: if (done) *done = PETSC_TRUE;
517: return(0);
518: }
519: unavailable:
520: if (done) *done = PETSC_FALSE;
521: else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"RK '%s' of order %D cannot evaluate step at order %D. Consider using -ts_adapt_type none or a different method that has an embedded estimate.",tab->name,tab->order,order);
522: return(0);
523: }
525: static PetscErrorCode TSForwardCostIntegral_RK(TS ts)
526: {
527: TS_RK *rk = (TS_RK*)ts->data;
528: TS quadts = ts->quadraturets;
529: RKTableau tab = rk->tableau;
530: const PetscInt s = tab->s;
531: const PetscReal *b = tab->b,*c = tab->c;
532: Vec *Y = rk->Y;
533: PetscInt i;
534: PetscErrorCode ierr;
537: /* No need to backup quadts->vec_sol since it can be reverted in TSRollBack_RK */
538: for (i=s-1; i>=0; i--) {
539: /* Evolve quadrature TS solution to compute integrals */
540: TSComputeRHSFunction(quadts,rk->ptime+rk->time_step*c[i],Y[i],ts->vec_costintegrand);
541: VecAXPY(quadts->vec_sol,rk->time_step*b[i],ts->vec_costintegrand);
542: }
543: return(0);
544: }
546: static PetscErrorCode TSAdjointCostIntegral_RK(TS ts)
547: {
548: TS_RK *rk = (TS_RK*)ts->data;
549: RKTableau tab = rk->tableau;
550: TS quadts = ts->quadraturets;
551: const PetscInt s = tab->s;
552: const PetscReal *b = tab->b,*c = tab->c;
553: Vec *Y = rk->Y;
554: PetscInt i;
555: PetscErrorCode ierr;
558: for (i=s-1; i>=0; i--) {
559: /* Evolve quadrature TS solution to compute integrals */
560: TSComputeRHSFunction(quadts,ts->ptime+ts->time_step*(1.0-c[i]),Y[i],ts->vec_costintegrand);
561: VecAXPY(quadts->vec_sol,-ts->time_step*b[i],ts->vec_costintegrand);
562: }
563: return(0);
564: }
566: static PetscErrorCode TSRollBack_RK(TS ts)
567: {
568: TS_RK *rk = (TS_RK*)ts->data;
569: TS quadts = ts->quadraturets;
570: RKTableau tab = rk->tableau;
571: const PetscInt s = tab->s;
572: const PetscReal *b = tab->b,*c = tab->c;
573: PetscScalar *w = rk->work;
574: Vec *Y = rk->Y,*YdotRHS = rk->YdotRHS;
575: PetscInt j;
576: PetscReal h;
577: PetscErrorCode ierr;
580: switch (rk->status) {
581: case TS_STEP_INCOMPLETE:
582: case TS_STEP_PENDING:
583: h = ts->time_step; break;
584: case TS_STEP_COMPLETE:
585: h = ts->ptime - ts->ptime_prev; break;
586: default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
587: }
588: for (j=0; j<s; j++) w[j] = -h*b[j];
589: VecMAXPY(ts->vec_sol,s,w,YdotRHS);
590: if (quadts && ts->costintegralfwd) {
591: for (j=0; j<s; j++) {
592: /* Revert the quadrature TS solution */
593: TSComputeRHSFunction(quadts,rk->ptime+h*c[j],Y[j],ts->vec_costintegrand);
594: VecAXPY(quadts->vec_sol,-h*b[j],ts->vec_costintegrand);
595: }
596: }
597: return(0);
598: }
600: static PetscErrorCode TSForwardStep_RK(TS ts)
601: {
602: TS_RK *rk = (TS_RK*)ts->data;
603: RKTableau tab = rk->tableau;
604: Mat J,*MatsFwdSensipTemp = rk->MatsFwdSensipTemp;
605: const PetscInt s = tab->s;
606: const PetscReal *A = tab->A,*c = tab->c,*b = tab->b;
607: Vec *Y = rk->Y;
608: PetscInt i,j;
609: PetscReal stage_time,h = ts->time_step;
610: PetscBool zero;
611: PetscErrorCode ierr;
614: MatCopy(ts->mat_sensip,rk->MatFwdSensip0,SAME_NONZERO_PATTERN);
615: TSGetRHSJacobian(ts,&J,NULL,NULL,NULL);
617: for (i=0; i<s; i++) {
618: stage_time = ts->ptime + h*c[i];
619: zero = PETSC_FALSE;
620: if (b[i] == 0 && i == s-1) zero = PETSC_TRUE;
621: /* TLM Stage values */
622: if(!i) {
623: MatCopy(ts->mat_sensip,rk->MatsFwdStageSensip[i],SAME_NONZERO_PATTERN);
624: } else if (!zero) {
625: MatZeroEntries(rk->MatsFwdStageSensip[i]);
626: for (j=0; j<i; j++) {
627: MatAXPY(rk->MatsFwdStageSensip[i],h*A[i*s+j],MatsFwdSensipTemp[j],SAME_NONZERO_PATTERN);
628: }
629: MatAXPY(rk->MatsFwdStageSensip[i],1.,ts->mat_sensip,SAME_NONZERO_PATTERN);
630: } else {
631: MatZeroEntries(rk->MatsFwdStageSensip[i]);
632: }
634: TSComputeRHSJacobian(ts,stage_time,Y[i],J,J);
635: MatMatMult(J,rk->MatsFwdStageSensip[i],MAT_REUSE_MATRIX,PETSC_DEFAULT,&MatsFwdSensipTemp[i]);
636: if (ts->Jacprhs) {
637: TSComputeRHSJacobianP(ts,stage_time,Y[i],ts->Jacprhs); /* get f_p */
638: if (ts->vecs_sensi2p) { /* TLM used for 2nd-order adjoint */
639: PetscScalar *xarr;
640: MatDenseGetColumn(MatsFwdSensipTemp[i],0,&xarr);
641: VecPlaceArray(rk->VecDeltaFwdSensipCol,xarr);
642: MatMultAdd(ts->Jacprhs,ts->vec_dir,rk->VecDeltaFwdSensipCol,rk->VecDeltaFwdSensipCol);
643: VecResetArray(rk->VecDeltaFwdSensipCol);
644: MatDenseRestoreColumn(MatsFwdSensipTemp[i],&xarr);
645: } else {
646: MatAXPY(MatsFwdSensipTemp[i],1.,ts->Jacprhs,SUBSET_NONZERO_PATTERN);
647: }
648: }
649: }
651: for (i=0; i<s; i++) {
652: MatAXPY(ts->mat_sensip,h*b[i],rk->MatsFwdSensipTemp[i],SAME_NONZERO_PATTERN);
653: }
654: rk->status = TS_STEP_COMPLETE;
655: return(0);
656: }
658: static PetscErrorCode TSForwardGetStages_RK(TS ts,PetscInt *ns,Mat **stagesensip)
659: {
660: TS_RK *rk = (TS_RK*)ts->data;
661: RKTableau tab = rk->tableau;
664: if (ns) *ns = tab->s;
665: if (stagesensip) *stagesensip = rk->MatsFwdStageSensip;
666: return(0);
667: }
669: static PetscErrorCode TSForwardSetUp_RK(TS ts)
670: {
671: TS_RK *rk = (TS_RK*)ts->data;
672: RKTableau tab = rk->tableau;
673: PetscInt i;
677: /* backup sensitivity results for roll-backs */
678: MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatFwdSensip0);
680: PetscMalloc1(tab->s,&rk->MatsFwdStageSensip);
681: PetscMalloc1(tab->s,&rk->MatsFwdSensipTemp);
682: for(i=0; i<tab->s; i++) {
683: MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdStageSensip[i]);
684: MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdSensipTemp[i]);
685: }
686: VecDuplicate(ts->vec_sol,&rk->VecDeltaFwdSensipCol);
687: return(0);
688: }
690: static PetscErrorCode TSForwardReset_RK(TS ts)
691: {
692: TS_RK *rk = (TS_RK*)ts->data;
693: RKTableau tab = rk->tableau;
694: PetscInt i;
698: MatDestroy(&rk->MatFwdSensip0);
699: if (rk->MatsFwdStageSensip) {
700: for (i=0; i<tab->s; i++) {
701: MatDestroy(&rk->MatsFwdStageSensip[i]);
702: }
703: PetscFree(rk->MatsFwdStageSensip);
704: }
705: if (rk->MatsFwdSensipTemp) {
706: for (i=0; i<tab->s; i++) {
707: MatDestroy(&rk->MatsFwdSensipTemp[i]);
708: }
709: PetscFree(rk->MatsFwdSensipTemp);
710: }
711: VecDestroy(&rk->VecDeltaFwdSensipCol);
712: return(0);
713: }
715: static PetscErrorCode TSStep_RK(TS ts)
716: {
717: TS_RK *rk = (TS_RK*)ts->data;
718: RKTableau tab = rk->tableau;
719: const PetscInt s = tab->s;
720: const PetscReal *A = tab->A,*c = tab->c;
721: PetscScalar *w = rk->work;
722: Vec *Y = rk->Y,*YdotRHS = rk->YdotRHS;
723: PetscBool FSAL = tab->FSAL;
724: TSAdapt adapt;
725: PetscInt i,j;
726: PetscInt rejections = 0;
727: PetscBool stageok,accept = PETSC_TRUE;
728: PetscReal next_time_step = ts->time_step;
729: PetscErrorCode ierr;
732: if (ts->steprollback || ts->steprestart) FSAL = PETSC_FALSE;
733: if (FSAL) { VecCopy(YdotRHS[s-1],YdotRHS[0]); }
735: rk->status = TS_STEP_INCOMPLETE;
736: while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
737: PetscReal t = ts->ptime;
738: PetscReal h = ts->time_step;
739: for (i=0; i<s; i++) {
740: rk->stage_time = t + h*c[i];
741: TSPreStage(ts,rk->stage_time);
742: VecCopy(ts->vec_sol,Y[i]);
743: for (j=0; j<i; j++) w[j] = h*A[i*s+j];
744: VecMAXPY(Y[i],i,w,YdotRHS);
745: TSPostStage(ts,rk->stage_time,i,Y);
746: TSGetAdapt(ts,&adapt);
747: TSAdaptCheckStage(adapt,ts,rk->stage_time,Y[i],&stageok);
748: if (!stageok) goto reject_step;
749: if (FSAL && !i) continue;
750: TSComputeRHSFunction(ts,t+h*c[i],Y[i],YdotRHS[i]);
751: }
753: rk->status = TS_STEP_INCOMPLETE;
754: TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);
755: rk->status = TS_STEP_PENDING;
756: TSGetAdapt(ts,&adapt);
757: TSAdaptCandidatesClear(adapt);
758: TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,(PetscReal)tab->s,PETSC_TRUE);
759: TSAdaptChoose(adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
760: rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
761: if (!accept) { /* Roll back the current step */
762: TSRollBack_RK(ts);
763: ts->time_step = next_time_step;
764: goto reject_step;
765: }
767: if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */
768: rk->ptime = ts->ptime;
769: rk->time_step = ts->time_step;
770: }
772: ts->ptime += ts->time_step;
773: ts->time_step = next_time_step;
774: break;
776: reject_step:
777: ts->reject++; accept = PETSC_FALSE;
778: if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
779: ts->reason = TS_DIVERGED_STEP_REJECTED;
780: PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
781: }
782: }
783: return(0);
784: }
786: static PetscErrorCode TSAdjointSetUp_RK(TS ts)
787: {
788: TS_RK *rk = (TS_RK*)ts->data;
789: RKTableau tab = rk->tableau;
790: PetscInt s = tab->s;
794: if (ts->adjointsetupcalled++) return(0);
795: VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam);
796: VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&rk->VecsSensiTemp);
797: if(ts->vecs_sensip) {
798: VecDuplicate(ts->vecs_sensip[0],&rk->VecDeltaMu);
799: }
800: if (ts->vecs_sensi2) {
801: VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam2);
802: VecDuplicateVecs(ts->vecs_sensi2[0],ts->numcost,&rk->VecsSensi2Temp);
803: }
804: if (ts->vecs_sensi2p) {
805: VecDuplicate(ts->vecs_sensi2p[0],&rk->VecDeltaMu2);
806: }
807: return(0);
808: }
810: /*
811: Assumptions:
812: - TSStep_RK() always evaluates the step with b, not bembed.
813: */
814: static PetscErrorCode TSAdjointStep_RK(TS ts)
815: {
816: TS_RK *rk = (TS_RK*)ts->data;
817: TS quadts = ts->quadraturets;
818: RKTableau tab = rk->tableau;
819: Mat J,Jpre,Jquad;
820: const PetscInt s = tab->s;
821: const PetscReal *A = tab->A,*b = tab->b,*c = tab->c;
822: PetscScalar *w = rk->work,*xarr;
823: Vec *Y = rk->Y,*VecsDeltaLam = rk->VecsDeltaLam,VecDeltaMu = rk->VecDeltaMu,*VecsSensiTemp = rk->VecsSensiTemp;
824: Vec *VecsDeltaLam2 = rk->VecsDeltaLam2,VecDeltaMu2 = rk->VecDeltaMu2,*VecsSensi2Temp = rk->VecsSensi2Temp;
825: Vec VecDRDUTransCol = ts->vec_drdu_col,VecDRDPTransCol = ts->vec_drdp_col;
826: PetscInt i,j,nadj;
827: PetscReal t = ts->ptime;
828: PetscReal h = ts->time_step;
829: PetscErrorCode ierr;
832: rk->status = TS_STEP_INCOMPLETE;
834: TSGetRHSJacobian(ts,&J,&Jpre,NULL,NULL);
835: if (quadts) {
836: TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);
837: }
838: for (i=s-1; i>=0; i--) {
839: if (tab->FSAL && i == s-1) {
840: /* VecsDeltaLam[nadj*s+s-1] are initialized with zeros and the values never change.*/
841: continue;
842: }
843: rk->stage_time = t + h*(1.0-c[i]);
844: TSComputeSNESJacobian(ts,Y[i],J,Jpre);
845: if (quadts) {
846: TSComputeRHSJacobian(quadts,rk->stage_time,Y[i],Jquad,Jquad); /* get r_u^T */
847: }
848: if (ts->vecs_sensip) {
849: TSComputeRHSJacobianP(ts,rk->stage_time,Y[i],ts->Jacprhs); /* get f_p */
850: if (quadts) {
851: TSComputeRHSJacobianP(quadts,rk->stage_time,Y[i],quadts->Jacprhs); /* get f_p for the quadrature */
852: }
853: }
855: if (b[i]) {
856: for (j=i+1; j<s; j++) w[j-i-1] = A[j*s+i]/b[i]; /* coefficients for computing VecsSensiTemp */
857: } else {
858: for (j=i+1; j<s; j++) w[j-i-1] = A[j*s+i]; /* coefficients for computing VecsSensiTemp */
859: }
861: for (nadj=0; nadj<ts->numcost; nadj++) {
862: /* Stage values of lambda */
863: if (b[i]) {
864: /* lambda_{n+1} + \sum_{j=i+1}^s a_{ji}/b[i]*lambda_{s,j} */
865: VecCopy(ts->vecs_sensi[nadj],VecsSensiTemp[nadj]); /* VecDeltaLam is an vec array of size s by numcost */
866: VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);
867: MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]); /* VecsSensiTemp will be reused by 2nd-order adjoint */
868: VecScale(VecsDeltaLam[nadj*s+i],-h*b[i]);
869: if (quadts) {
870: MatDenseGetColumn(Jquad,nadj,&xarr);
871: VecPlaceArray(VecDRDUTransCol,xarr);
872: VecAXPY(VecsDeltaLam[nadj*s+i],-h*b[i],VecDRDUTransCol);
873: VecResetArray(VecDRDUTransCol);
874: MatDenseRestoreColumn(Jquad,&xarr);
875: }
876: } else {
877: /* \sum_{j=i+1}^s a_{ji}*lambda_{s,j} */
878: VecSet(VecsSensiTemp[nadj],0);
879: VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);
880: MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]);
881: VecScale(VecsDeltaLam[nadj*s+i],-h);
882: }
884: /* Stage values of mu */
885: if (ts->vecs_sensip) {
886: MatMultTranspose(ts->Jacprhs,VecsSensiTemp[nadj],VecDeltaMu);
887: if (b[i]) {
888: VecScale(VecDeltaMu,-h*b[i]);
889: if (quadts) {
890: MatDenseGetColumn(quadts->Jacprhs,nadj,&xarr);
891: VecPlaceArray(VecDRDPTransCol,xarr);
892: VecAXPY(VecDeltaMu,-h*b[i],VecDRDPTransCol);
893: VecResetArray(VecDRDPTransCol);
894: MatDenseRestoreColumn(quadts->Jacprhs,&xarr);
895: }
896: } else {
897: VecScale(VecDeltaMu,-h);
898: }
899: VecAXPY(ts->vecs_sensip[nadj],1.,VecDeltaMu); /* update sensip for each stage */
900: }
901: }
903: if (ts->vecs_sensi2 && ts->forward_solve) { /* 2nd-order adjoint, TLM mode has to be turned on */
904: /* Get w1 at t_{n+1} from TLM matrix */
905: MatDenseGetColumn(rk->MatsFwdStageSensip[i],0,&xarr);
906: VecPlaceArray(ts->vec_sensip_col,xarr);
907: /* lambda_s^T F_UU w_1 */
908: TSComputeRHSHessianProductFunctionUU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_guu);
909: if (quadts) {
910: /* R_UU w_1 */
911: TSComputeRHSHessianProductFunctionUU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_guu);
912: }
913: if (ts->vecs_sensip) {
914: /* lambda_s^T F_UP w_2 */
915: TSComputeRHSHessianProductFunctionUP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gup);
916: if (quadts) {
917: /* R_UP w_2 */
918: TSComputeRHSHessianProductFunctionUP(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gup);
919: }
920: }
921: if (ts->vecs_sensi2p) {
922: /* lambda_s^T F_PU w_1 */
923: TSComputeRHSHessianProductFunctionPU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_gpu);
924: /* lambda_s^T F_PP w_2 */
925: TSComputeRHSHessianProductFunctionPP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gpp);
926: if (b[i] && quadts) {
927: /* R_PU w_1 */
928: TSComputeRHSHessianProductFunctionPU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gpu);
929: /* R_PP w_2 */
930: TSComputeRHSHessianProductFunctionPP(quadts,rk->stage_time,Y[i],NULL,ts->vec_dir,ts->vecs_gpp);
931: }
932: }
933: VecResetArray(ts->vec_sensip_col);
934: MatDenseRestoreColumn(rk->MatsFwdStageSensip[i],&xarr);
936: for (nadj=0; nadj<ts->numcost; nadj++) {
937: /* Stage values of lambda */
938: if (b[i]) {
939: /* J_i^T*(Lambda_{n+1}+\sum_{j=i+1}^s a_{ji}/b_i*Lambda_{s,j} */
940: VecCopy(ts->vecs_sensi2[nadj],VecsSensi2Temp[nadj]);
941: VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);
942: MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);
943: VecScale(VecsDeltaLam2[nadj*s+i],-h*b[i]);
944: VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_guu[nadj]);
945: if (ts->vecs_sensip) {
946: VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_gup[nadj]);
947: }
948: } else {
949: /* \sum_{j=i+1}^s a_{ji}*Lambda_{s,j} */
950: VecSet(VecsDeltaLam2[nadj*s+i],0);
951: VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);
952: MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);
953: VecScale(VecsDeltaLam2[nadj*s+i],-h);
954: VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_guu[nadj]);
955: if (ts->vecs_sensip) {
956: VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_gup[nadj]);
957: }
958: }
959: if (ts->vecs_sensi2p) { /* 2nd-order adjoint for parameters */
960: MatMultTranspose(ts->Jacprhs,VecsSensi2Temp[nadj],VecDeltaMu2);
961: if (b[i]) {
962: VecScale(VecDeltaMu2,-h*b[i]);
963: VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpu[nadj]);
964: VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpp[nadj]);
965: } else {
966: VecScale(VecDeltaMu2,-h);
967: VecAXPY(VecDeltaMu2,-h,ts->vecs_gpu[nadj]);
968: VecAXPY(VecDeltaMu2,-h,ts->vecs_gpp[nadj]);
969: }
970: VecAXPY(ts->vecs_sensi2p[nadj],1,VecDeltaMu2); /* update sensi2p for each stage */
971: }
972: }
973: }
974: }
976: for (j=0; j<s; j++) w[j] = 1.0;
977: for (nadj=0; nadj<ts->numcost; nadj++) { /* no need to do this for mu's */
978: VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecsDeltaLam[nadj*s]);
979: if (ts->vecs_sensi2) {
980: VecMAXPY(ts->vecs_sensi2[nadj],s,w,&VecsDeltaLam2[nadj*s]);
981: }
982: }
983: rk->status = TS_STEP_COMPLETE;
984: return(0);
985: }
987: static PetscErrorCode TSAdjointReset_RK(TS ts)
988: {
989: TS_RK *rk = (TS_RK*)ts->data;
990: RKTableau tab = rk->tableau;
994: VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam);
995: VecDestroyVecs(ts->numcost,&rk->VecsSensiTemp);
996: VecDestroy(&rk->VecDeltaMu);
997: VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam2);
998: VecDestroy(&rk->VecDeltaMu2);
999: VecDestroyVecs(ts->numcost,&rk->VecsSensi2Temp);
1000: return(0);
1001: }
1003: static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X)
1004: {
1005: TS_RK *rk = (TS_RK*)ts->data;
1006: PetscInt s = rk->tableau->s,p = rk->tableau->p,i,j;
1007: PetscReal h;
1008: PetscReal tt,t;
1009: PetscScalar *b;
1010: const PetscReal *B = rk->tableau->binterp;
1011: PetscErrorCode ierr;
1014: if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRK %s does not have an interpolation formula",rk->tableau->name);
1016: switch (rk->status) {
1017: case TS_STEP_INCOMPLETE:
1018: case TS_STEP_PENDING:
1019: h = ts->time_step;
1020: t = (itime - ts->ptime)/h;
1021: break;
1022: case TS_STEP_COMPLETE:
1023: h = ts->ptime - ts->ptime_prev;
1024: t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
1025: break;
1026: default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
1027: }
1028: PetscMalloc1(s,&b);
1029: for (i=0; i<s; i++) b[i] = 0;
1030: for (j=0,tt=t; j<p; j++,tt*=t) {
1031: for (i=0; i<s; i++) {
1032: b[i] += h * B[i*p+j] * tt;
1033: }
1034: }
1035: VecCopy(rk->Y[0],X);
1036: VecMAXPY(X,s,b,rk->YdotRHS);
1037: PetscFree(b);
1038: return(0);
1039: }
1041: /*------------------------------------------------------------*/
1043: static PetscErrorCode TSRKTableauReset(TS ts)
1044: {
1045: TS_RK *rk = (TS_RK*)ts->data;
1046: RKTableau tab = rk->tableau;
1050: if (!tab) return(0);
1051: PetscFree(rk->work);
1052: VecDestroyVecs(tab->s,&rk->Y);
1053: VecDestroyVecs(tab->s,&rk->YdotRHS);
1054: VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam);
1055: VecDestroyVecs(ts->numcost,&rk->VecsSensiTemp);
1056: VecDestroy(&rk->VecDeltaMu);
1057: return(0);
1058: }
1060: static PetscErrorCode TSReset_RK(TS ts)
1061: {
1065: TSRKTableauReset(ts);
1066: if (ts->use_splitrhsfunction) {
1067: PetscTryMethod(ts,"TSReset_RK_MultirateSplit_C",(TS),(ts));
1068: } else {
1069: PetscTryMethod(ts,"TSReset_RK_MultirateNonsplit_C",(TS),(ts));
1070: }
1071: return(0);
1072: }
1074: static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx)
1075: {
1077: return(0);
1078: }
1080: static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
1081: {
1083: return(0);
1084: }
1087: static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx)
1088: {
1090: return(0);
1091: }
1093: static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
1094: {
1097: return(0);
1098: }
1100: static PetscErrorCode TSRKTableauSetUp(TS ts)
1101: {
1102: TS_RK *rk = (TS_RK*)ts->data;
1103: RKTableau tab = rk->tableau;
1107: PetscMalloc1(tab->s,&rk->work);
1108: VecDuplicateVecs(ts->vec_sol,tab->s,&rk->Y);
1109: VecDuplicateVecs(ts->vec_sol,tab->s,&rk->YdotRHS);
1110: return(0);
1111: }
1113: static PetscErrorCode TSSetUp_RK(TS ts)
1114: {
1115: TS quadts = ts->quadraturets;
1117: DM dm;
1120: TSCheckImplicitTerm(ts);
1121: TSRKTableauSetUp(ts);
1122: if (quadts && ts->costintegralfwd) {
1123: Mat Jquad;
1124: TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);
1125: }
1126: TSGetDM(ts,&dm);
1127: DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
1128: DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
1129: if (ts->use_splitrhsfunction) {
1130: PetscTryMethod(ts,"TSSetUp_RK_MultirateSplit_C",(TS),(ts));
1131: } else {
1132: PetscTryMethod(ts,"TSSetUp_RK_MultirateNonsplit_C",(TS),(ts));
1133: }
1134: return(0);
1135: }
1137: static PetscErrorCode TSSetFromOptions_RK(PetscOptionItems *PetscOptionsObject,TS ts)
1138: {
1139: TS_RK *rk = (TS_RK*)ts->data;
1143: PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");
1144: {
1145: RKTableauLink link;
1146: PetscInt count,choice;
1147: PetscBool flg,use_multirate = PETSC_FALSE;
1148: const char **namelist;
1150: for (link=RKTableauList,count=0; link; link=link->next,count++) ;
1151: PetscMalloc1(count,(char***)&namelist);
1152: for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
1153: PetscOptionsBool("-ts_rk_multirate","Use interpolation-based multirate RK method","TSRKSetMultirate",rk->use_multirate,&use_multirate,&flg);
1154: if (flg) {
1155: TSRKSetMultirate(ts,use_multirate);
1156: }
1157: PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rk->tableau->name,&choice,&flg);
1158: if (flg) {TSRKSetType(ts,namelist[choice]);}
1159: PetscFree(namelist);
1160: }
1161: PetscOptionsTail();
1162: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Multirate methods options","");
1163: PetscOptionsInt("-ts_rk_dtratio","time step ratio between slow and fast","",rk->dtratio,&rk->dtratio,NULL);
1164: PetscOptionsEnd();
1165: return(0);
1166: }
1168: static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer)
1169: {
1170: TS_RK *rk = (TS_RK*)ts->data;
1171: PetscBool iascii;
1175: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1176: if (iascii) {
1177: RKTableau tab = rk->tableau;
1178: TSRKType rktype;
1179: char buf[512];
1180: TSRKGetType(ts,&rktype);
1181: PetscViewerASCIIPrintf(viewer," RK type %s\n",rktype);
1182: PetscViewerASCIIPrintf(viewer," Order: %D\n",tab->order);
1183: PetscViewerASCIIPrintf(viewer," FSAL property: %s\n",tab->FSAL ? "yes" : "no");
1184: PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);
1185: PetscViewerASCIIPrintf(viewer," Abscissa c = %s\n",buf);
1186: }
1187: return(0);
1188: }
1190: static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer)
1191: {
1193: TSAdapt adapt;
1196: TSGetAdapt(ts,&adapt);
1197: TSAdaptLoad(adapt,viewer);
1198: return(0);
1199: }
1201: /*@C
1202: TSRKSetType - Set the type of RK scheme
1204: Logically collective
1206: Input Parameter:
1207: + ts - timestepping context
1208: - rktype - type of RK-scheme
1210: Options Database:
1211: . -ts_rk_type - <1fe,2a,3,3bs,4,5f,5dp,5bs>
1213: Level: intermediate
1215: .seealso: TSRKGetType(), TSRK, TSRKType, TSRK1FE, TSRK2A, TSRK3, TSRK3BS, TSRK4, TSRK5F, TSRK5DP, TSRK5BS, TSRK6VR, TSRK7VR, TSRK8VR
1216: @*/
1217: PetscErrorCode TSRKSetType(TS ts,TSRKType rktype)
1218: {
1224: PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));
1225: return(0);
1226: }
1228: /*@C
1229: TSRKGetType - Get the type of RK scheme
1231: Logically collective
1233: Input Parameter:
1234: . ts - timestepping context
1236: Output Parameter:
1237: . rktype - type of RK-scheme
1239: Level: intermediate
1241: .seealso: TSRKGetType()
1242: @*/
1243: PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype)
1244: {
1249: PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));
1250: return(0);
1251: }
1253: static PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype)
1254: {
1255: TS_RK *rk = (TS_RK*)ts->data;
1258: *rktype = rk->tableau->name;
1259: return(0);
1260: }
1262: static PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype)
1263: {
1264: TS_RK *rk = (TS_RK*)ts->data;
1266: PetscBool match;
1267: RKTableauLink link;
1270: if (rk->tableau) {
1271: PetscStrcmp(rk->tableau->name,rktype,&match);
1272: if (match) return(0);
1273: }
1274: for (link = RKTableauList; link; link=link->next) {
1275: PetscStrcmp(link->tab.name,rktype,&match);
1276: if (match) {
1277: if (ts->setupcalled) {TSRKTableauReset(ts);}
1278: rk->tableau = &link->tab;
1279: if (ts->setupcalled) {TSRKTableauSetUp(ts);}
1280: ts->default_adapt_type = rk->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1281: return(0);
1282: }
1283: }
1284: SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype);
1285: return(0);
1286: }
1288: static PetscErrorCode TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y)
1289: {
1290: TS_RK *rk = (TS_RK*)ts->data;
1293: if (ns) *ns = rk->tableau->s;
1294: if (Y) *Y = rk->Y;
1295: return(0);
1296: }
1298: static PetscErrorCode TSDestroy_RK(TS ts)
1299: {
1303: TSReset_RK(ts);
1304: if (ts->dm) {
1305: DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
1306: DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
1307: }
1308: PetscFree(ts->data);
1309: PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);
1310: PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);
1311: PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",NULL);
1312: PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",NULL);
1313: return(0);
1314: }
1316: /*
1317: This defines the nonlinear equation that is to be solved with SNES
1318: We do not need to solve the equation; we just use SNES to approximate the Jacobian
1319: */
1320: static PetscErrorCode SNESTSFormFunction_RK(SNES snes,Vec x,Vec y,TS ts)
1321: {
1322: TS_RK *rk = (TS_RK*)ts->data;
1323: DM dm,dmsave;
1327: SNESGetDM(snes,&dm);
1328: /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
1329: dmsave = ts->dm;
1330: ts->dm = dm;
1331: TSComputeRHSFunction(ts,rk->stage_time,x,y);
1332: ts->dm = dmsave;
1333: return(0);
1334: }
1336: static PetscErrorCode SNESTSFormJacobian_RK(SNES snes,Vec x,Mat A,Mat B,TS ts)
1337: {
1338: TS_RK *rk = (TS_RK*)ts->data;
1339: DM dm,dmsave;
1343: SNESGetDM(snes,&dm);
1344: dmsave = ts->dm;
1345: ts->dm = dm;
1346: TSComputeRHSJacobian(ts,rk->stage_time,x,A,B);
1347: ts->dm = dmsave;
1348: return(0);
1349: }
1351: /*@C
1352: TSRKSetMultirate - Use the interpolation-based multirate RK method
1354: Logically collective
1356: Input Parameter:
1357: + ts - timestepping context
1358: - use_multirate - PETSC_TRUE enables the multirate RK method, sets the basic method to be RK2A and sets the ratio between slow stepsize and fast stepsize to be 2
1360: Options Database:
1361: . -ts_rk_multirate - <true,false>
1363: Notes:
1364: 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 coeffcients (binterp).
1366: Level: intermediate
1368: .seealso: TSRKGetMultirate()
1369: @*/
1370: PetscErrorCode TSRKSetMultirate(TS ts,PetscBool use_multirate)
1371: {
1375: PetscTryMethod(ts,"TSRKSetMultirate_C",(TS,PetscBool),(ts,use_multirate));
1376: return(0);
1377: }
1379: /*@C
1380: TSRKGetMultirate - Gets whether to Use the interpolation-based multirate RK method
1382: Not collective
1384: Input Parameter:
1385: . ts - timestepping context
1387: Output Parameter:
1388: . use_multirate - PETSC_TRUE if the multirate RK method is enabled, PETSC_FALSE otherwise
1390: Level: intermediate
1392: .seealso: TSRKSetMultirate()
1393: @*/
1394: PetscErrorCode TSRKGetMultirate(TS ts,PetscBool *use_multirate)
1395: {
1399: PetscUseMethod(ts,"TSRKGetMultirate_C",(TS,PetscBool*),(ts,use_multirate));
1400: return(0);
1401: }
1403: /*MC
1404: TSRK - ODE and DAE solver using Runge-Kutta schemes
1406: The user should provide the right hand side of the equation
1407: using TSSetRHSFunction().
1409: Notes:
1410: The default is TSRK3BS, it can be changed with TSRKSetType() or -ts_rk_type
1412: Level: beginner
1414: .seealso: TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRKSetFullyImplicit(), TSRK2D, TTSRK2E, TSRK3,
1415: TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister(), TSRKSetMultirate(), TSRKGetMultirate()
1417: M*/
1418: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
1419: {
1420: TS_RK *rk;
1424: TSRKInitializePackage();
1426: ts->ops->reset = TSReset_RK;
1427: ts->ops->destroy = TSDestroy_RK;
1428: ts->ops->view = TSView_RK;
1429: ts->ops->load = TSLoad_RK;
1430: ts->ops->setup = TSSetUp_RK;
1431: ts->ops->interpolate = TSInterpolate_RK;
1432: ts->ops->step = TSStep_RK;
1433: ts->ops->evaluatestep = TSEvaluateStep_RK;
1434: ts->ops->rollback = TSRollBack_RK;
1435: ts->ops->setfromoptions = TSSetFromOptions_RK;
1436: ts->ops->getstages = TSGetStages_RK;
1438: ts->ops->snesfunction = SNESTSFormFunction_RK;
1439: ts->ops->snesjacobian = SNESTSFormJacobian_RK;
1440: ts->ops->adjointintegral = TSAdjointCostIntegral_RK;
1441: ts->ops->adjointsetup = TSAdjointSetUp_RK;
1442: ts->ops->adjointstep = TSAdjointStep_RK;
1443: ts->ops->adjointreset = TSAdjointReset_RK;
1445: ts->ops->forwardintegral = TSForwardCostIntegral_RK;
1446: ts->ops->forwardsetup = TSForwardSetUp_RK;
1447: ts->ops->forwardreset = TSForwardReset_RK;
1448: ts->ops->forwardstep = TSForwardStep_RK;
1449: ts->ops->forwardgetstages= TSForwardGetStages_RK;
1451: PetscNewLog(ts,&rk);
1452: ts->data = (void*)rk;
1454: PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);
1455: PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);
1456: PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",TSRKSetMultirate_RK);
1457: PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",TSRKGetMultirate_RK);
1459: TSRKSetType(ts,TSRKDefault);
1460: rk->dtratio = 1;
1461: return(0);
1462: }