Implementing Explicit Runge Kutta Methods #951
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| using Pkg | |||
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The whole my_tests folder should not be pushed to the main gridap project
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started clean branch of master fork. my_tests folder is removed
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| using Pkg | |||
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Are all these tests related to the ExRK dev?
If not, we do not need these tests here.
I do recommend to start from a fresh Gridap fork, add the ExRK dev, and we start again
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started clean branch of master fork.
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| using Pkg | |||
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Please try to stick to gridap code style guide, e.g., the way we name files here is not following it
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removed in clean version
| @@ -52,7 +52,7 @@ function _solve_nr!(x,A,b,dx,ns,nls,op) | |||
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| # Newton-like iterations | |||
| for nliter in 1:nls.max_nliters | |||
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Remove this (better start from scratch as indicated above)
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removed in clean version
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| @publish_gridapodes ODETools ThetaMethod | |||
| @publish_gridapodes ODETools RungeKutta | |||
| @publish_gridapodes ODETools IMEXRungeKutta | |||
| @publish_gridapodes ODETools EXRungeKutta | |||
| @publish_gridapodes ODETools DIRungeKutta | |||
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better first EX -> accept
then we start with DI
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removed in clean version
| ki = [similar(u0) for i in 1:s] | ||
| M = allocate_jacobian(op,t0,uf,ode_cache) | ||
| get_mass_matrix!(M,op,t0,uf,ode_cache) | ||
| nl_cache = nothing |
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no need for this cache, we are storing nothing
| ode_cache, vi, ki, M, nl_cache = cache | ||
| end | ||
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| nlop = EXRungeKuttaStageNonlinearOperator(op,t0,dt,u0,ode_cache,vi,ki,0,a,M) |
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changed to EXRungeKuttaStageOperator < RungeKuttaNonlinearOperator.
| ti = t0 + c[i]*dt | ||
| ode_cache = update_cache!(ode_cache,op,ti) | ||
| update!(nlop,ti,ki[i],i) | ||
| nl_cache = solve!(uf,solver.nls,nlop,nl_cache) |
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this is the LinearSolver cache, no nonlinear
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changed to l_cache
| For other explicit methods, i = 1,…,s -> ui = u0 + dt ∑_{j<i} a_ij * kj | ||
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| For EX-RK, the Jacobian is always M. At each solve_step, compute and store M in | ||
| nlop |
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M is not a nlop, change notation
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changed notation in clean version
| EX-RK: A(t,u,ki) = M ki + K(ti,u0 + dt ∑_{j<i} a_ij * kj) = 0 -> solve for ki | ||
| = M ki + K(ti,ui) = 0 | ||
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| For forward euler, i = 1 -> ui = u0 |
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don't you think this is just a particular case of the general case in which there is only one stage, I think you can accommodate it in the same implementation / def'on
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updated this comment to be more general in clean version
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As discussed @tamaratambyah will create a new PR |
In this PR, I have implemented multi-stage, explicit Runge Kutta method in EXRungeKutta.jl. This follows the format and structure of RungeKutta.jl and IMEXRungeKutta.jl.
I have added an additional operator
TransientEXRungeKuttaFEOperator. However, I think this can be combined withTransientRungeKuttaFEOperatorto have one operator which works for both explicit and diagonally implicit Runge Kutta (IMEX will probably still require its own operator). Once DIRK is working properly, I will look to tidy this up.Note, there are some preliminary implementations of DIRK on this branch. I have created a different branch for this now.
@santiagobadia can you please review this PR.
Thanks