Resolving Issue: Errors in Simple Handwritten PDEs as ODEs #1291
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For the psuedospectral, see the comment in #929. The ApproxFun dev mentioned we should change to OrthogonalPolynomials.jl for this part so we should take that recommendation. |
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@ChrisRackauckas Could you please run the workflow so I can check the logs for errors?
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Why are mass matrices required here? Most of these should resolve to not have any algebraic constraints if the right spectral discretization is chosen. (Singular) Mass matrices (DAEs) would prohibit most of the solvers from being used. Though if that's a requirement for one of them, then so bit and that changes the solvers that should be chosen there (and would be an interesting contrast) |
| L = 2.0 # Domain length | ||
| xs, prob = allen_cahn(N, L) | ||
| # @time sol = solve(prob, AutoVern7(RadauIIA5(autodiff=false)); dt=1e-2, abstol=1e-14, reltol=1e-14, adaptive=true) | ||
| @time sol = solve(prob, Tsit5(); abstol=1e-14, reltol=1e-14, adaptive=true) |
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Explicit methods usually have issues with convergence due to order loss. I'm not sure changing to an explicit method for these for the reference will work out well. Though you'll see the in the work-precision diagram if you have a problem with the convergence, since all of the other methods will hit a wall and only converge to the error of the reference solution.
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Good catch, I commented the wrong line in this commit. Thanks!
| reltols = 0.1 .^ (1:3) | ||
| multipliers = 0.5 .^ (0:3) | ||
| setups = [ | ||
| Dict(:alg => IMEXEuler(), :dts => 1e-4 * multipliers), |
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I'd keep the same sets as above. A set showing all of the exponential integrators, all of the IMEX methods, all of the normal methods, and then a comparison of the best between the families.
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Understood, planning to reincorporate the complete tests for the server builds as I can only prototype a few sets with the current local resources. Should these still be fixed time-steps or use adaptive time-stepping?
| Dict(:alg => Rodas4(), :dts => 1e-4 * multipliers), | ||
| Dict(:alg => Rodas5(), :dts => 1e-4 * multipliers), | ||
| Dict(:alg => GRK4T(), :dts => 1e-4 * multipliers), | ||
| Dict(:alg => GRK4A(), :dts => 1e-4 * multipliers), |
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the main ones to add to the mass matrices comparisons would be FBDF and QNDF. Also a DAEProblem formulation testing DASKR.jl and Sundials.IDA. You can benchmark multiple simultaneous problem implementations using the prob_choice setup, see the DAE benchmarks for how this is done.
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Great to know; thanks for the tips!
Checklist
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COLPRAC.
Additional context
This merges changes to resolve issue #1284 on the benchmarks of handwritten PDEs as ODEs via finite-difference and pseudo-spectral methods.
The package dependencies have been updated to remove unused ones, and the compat entries have been updated for Julia v1.10. The implementations have been tested on local machines (Macbook Pro M1 Pro on MacOS Sequoia and a beefier CPU running Ubuntu 22.04 LTS) by running
SciMLBenchmarks.weave_fileon the relevant.jmdfiles.At present, changes have been implemented for the following PDEs in one spatial and one time dimension:
The following changes have been implemented to the finite-difference method benchmarks:
SparseArrays.MatrixOperatorinterfaces are used from the updatedSciMLOperatorsforSplitODEProblem.These are functioning for certain solver algorithm choices (
IMEXEuler,CNAB2,CLAF2,ETDRK2,SBDF2)Commits will be progressively added in this pull (such as pseudo-spectral method updates), including revisions based on comments from the reviewers (@ChrisRackauckas).