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commit 3322092 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Fri Mar 21 12:47:43 2025 -0400 DIRK solver All tests passing commit a487023 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Thu Mar 20 17:58:46 2025 -0400 Simplification commit 445c630 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Thu Mar 20 13:59:40 2025 -0400 Trapezoid method working All tests pass. To Do: Add a Diagonally Implicit Runge Kutta (DIRK) solver commit 62fb87c Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Wed Mar 19 14:14:50 2025 -0400 Simplify commit 2f8ee35 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Wed Mar 19 13:18:07 2025 -0400 Getting tests to work commit 9d2bd87 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Tue Mar 18 15:15:16 2025 -0400 Add warning commit 380ef76 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Tue Mar 18 14:36:31 2025 -0400 Residual should converge to 0 commit 53fa05b Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Tue Mar 18 11:44:27 2025 -0400 Broyden's method in Torch to solve system commit e2e4ef6 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Mon Mar 17 17:27:07 2025 -0400 Update rk_common.py commit f9ee7cc Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Mon Mar 17 16:37:17 2025 -0400 Working for arrays commit 9e99dec Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Mon Mar 17 16:10:01 2025 -0400 Using scipy root commit d6c8ef5 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Tue Mar 11 11:42:47 2025 -0400 Don't zip beta Only needed for a special case commit df96be0 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Tue Mar 11 11:04:15 2025 -0400 Update fixed_grid_implicit.py commit 1318fa5 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Tue Mar 11 10:58:50 2025 -0400 Make this work for vectors commit b5b8c34 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Mon Mar 10 20:41:55 2025 -0400 Using matmul commit a509be9 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Mon Mar 10 19:01:44 2025 -0400 Much Faster commit 0a91246 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Thu Mar 6 16:41:46 2025 -0500 All zeros case commit 9fab648 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Thu Mar 6 16:18:04 2025 -0500 Many solvers included commit 6ebe639 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Tue Feb 25 17:11:28 2025 -0500 Update rk_common.py commit 7a5d83a Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Tue Feb 25 17:10:48 2025 -0500 Methods with zero alpha and nonzero beta commit 91cce15 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Tue Feb 25 16:27:29 2025 -0500 Abstract classes working commit 7b6704d Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Mon Feb 24 19:57:56 2025 -0500 Abstract commit 3cf9065 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Thu Feb 20 14:10:56 2025 -0500 Abstract Implicit Class commit b210355 Merge: 6758985 f3135f3 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Thu Feb 13 15:38:45 2025 -0500 Merge branch 'master' into add-implicit-solvers commit 6758985 Author: psv4 <44118604+psv4@users.noreply.github.com> Date: Thu Feb 6 11:11:50 2025 -0500 Implicit Solvers
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This looks great! Thanks for updating the tests as well. Main thing I can think of to make this better is to implement the version of Broyden's method with the Sherman-Morrison formula to directly update the Jacobian inverse and avoid the expensive linalg.solve. But this can be addressed in a separate PR should anyone want to make the change. |
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Thanks @rtqichen ! I'll add that as an issue for the Sherman-Morrison formula. The textbook I was using did not mention that. Other future work for this could be adding adaptive implicit solvers and auto-switching algorithms between explicit and implicit. |
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Closes #254 and is related to #263.
This adds abstract Fully Implicit Runge Kutta (FIRK) and Diagonally Implicit Runge Kutta (DIRK) solver classes and defines many different implicit solvers based on their tableaus. The nonlinear system of equations is solved using Broyden's method. The solvers were added to the tests and are passing.
Solvers
More can be added following the Butcher Tableau structure.