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Add trivial adaptive DAE method #37
Description
Adding an adaptive half-explicit method (one file, not over-engineered) for solving the pendulum with invariants would be very helpful.
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Adding an adaptive half-explicit method (one file, not over-engineered) for solving the pendulum with invariants would be very helpful.
Activity
reid-g commentedon May 12, 2022
What order method do we want? For both Differential and Algebraic?
reid-g commentedon May 12, 2022
Also HERK is good for problems which have a differential that can be treated explicitly. This may not be the case for all Index-2 DAEs and there may be a need for a Index-2 IRK method.
AndreyAPopov commentedon May 12, 2022
I was literally thinking trapezoidal with Euler embedded. Call it dae12. if you have ready-made coefficients of higher order we can use them, but up to you.
I theoretically implemented enough derivatives in the pendulum problem to support a fully implicit method.
Steven-Roberts commentedon May 12, 2022
I'm reluctant to implement integrators in OTP. To me it is slightly out of scope. Also it would need to be advanced enough to support the
odesetoptions as that's whatsolveprovides. I say for these DAEs of high-index, we should always aim to provide reductions to index-1 as the default RHS so built-in solvers can be used.Steven-Roberts commentedon May 12, 2022
But if we do want to provide an integrator, I think it should be an SDIRK method instead of a HERK. HERK requires knowledge of which variables are diff and alg, and the default RHS does not provide that.
AndreyAPopov commentedon May 12, 2022
Ideally we would integrate with the new MATLODE, but this is a good stopgap
reid-g commentedon May 13, 2022
Do we want to couple OTP with MATLODE?
reid-g commentedon May 13, 2022
Also we would need to be carful with index reduced problems. Some index reductions are not stable.
reid-g commentedon May 13, 2022
If we do provide an integrator for index-2 problems I agree it should just be an SDIRK method.
How in depth does it need to be ie how many options should it have?
Steven-Roberts commentedon May 14, 2022
Couple: no. We can make them mutually compatible by having matlode use the same function signature as built in integrators. E.g.
problem.solve('Solver', matlode.rk....)Steven-Roberts commentedon May 14, 2022
It needs to accept
odesetoptions, although it may ignore many. At the minimum is needs to support Jacobian and Mass option. Ideally it should support time and state dependant mass matrices.[-]Add trivial adaptive half-explicit method[/-][+]Add trivial adaptive DAE method[/+]AndreyAPopov commentedon May 15, 2022
I have added a method that seems to work for the pendulum problem. There is a lot of cleanup that needs to be done, but it actually seems to work, which I am excited about.