plus boundary conditions. I have noticed that for semi-definite problems, where $\sigma=0$ in part of the domain or all of it, I cannot get the FGMRES solver any further than ~2e-16 in terms of final relative error, as the solver plateaus there with a convergence rate of 1. Depending on the shape of the function that characterises $\sigma$, this error floor gets raised by several orders of magnitude. In contrast, in the definite Maxwell problem, I can get the final relative error to arbitrarily low values by changing the tolerance.
Remembering to set HYPRE_AMSSetBetaPoissonMatrix(solver, NULL) and applying boundary conditions does not solve the issue but it is what allows me to get to ~2e-16 relative error since otherwise I can only get to ~1e-1. I believe this issue is not limited to my implementation, since from my experiments in the Tesla miniapp in MFEM (which uses Hypre's AMS), the same error floor can be verified.
I would like to ask whether this is a known issue and whether there is a solution that allows me to reach arbitrarily low relative errors in the semi-definite problem. Thank you for the support!
Dear developers,
I have been using HypreAMS to solve the Maxwell curl-curl formulation for an $H(curl)$ problem:
$(\mu^{-1}\vec\nabla\times \vec A,\vec\nabla\times \vec v)+(\sigma(\partialt\vec A+\vec\nabla V),\vec v)=(\vec J{ext},\vec v)$,
plus boundary conditions. I have noticed that for semi-definite problems, where $\sigma=0$ in part of the domain or all of it, I cannot get the FGMRES solver any further than ~2e-16 in terms of final relative error, as the solver plateaus there with a convergence rate of 1. Depending on the shape of the function that characterises $\sigma$, this error floor gets raised by several orders of magnitude. In contrast, in the definite Maxwell problem, I can get the final relative error to arbitrarily low values by changing the tolerance.
Remembering to set
HYPRE_AMSSetBetaPoissonMatrix(solver, NULL)and applying boundary conditions does not solve the issue but it is what allows me to get to ~2e-16 relative error since otherwise I can only get to ~1e-1. I believe this issue is not limited to my implementation, since from my experiments in theTeslaminiapp in MFEM (which uses Hypre's AMS), the same error floor can be verified.I would like to ask whether this is a known issue and whether there is a solution that allows me to reach arbitrarily low relative errors in the semi-definite problem. Thank you for the support!