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Signed-off-by: Umberto Zerbinati <[email protected]>
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Umberto Zerbinati committed Jul 12, 2024
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Expand Up @@ -56,7 +56,7 @@ ngsPETsc aims to assist with the solution of challenging PDEs on complex geometr
In this section we provide a few examples of results that can be obtained using ngsPETSc.
We begin by considering a simple Poisson problem on a unit square domain discretised with $P_2$ finite elements and compare the performance of different solvers available in NGSolve via ngsPETSc. In particular, we showcase PETSc's algebraic multigrid algorithm GAMG [@PETScGAMG], PETSc's domain decomposition BDDC algorithm [@PETScBDDC], NGSolve's own implementation of element-wise BDDC, Hypre [@hypre] and Trillinos ML [@ml].
In particular, we would like to pointout that there is no non-element wise BDDC preconditioner aveilable in NGSolve. The result is shown in Table 1 and the full example, with more details, can be found in the [ngsPETSc documentation](https://ngspetsc.readthedocs.io/en/latest/PETScKSP/poisson.py.html).
All the preconditioners here considered are robust as we refine the mesh for a $P_1$ discretisation, but out-of-the-box only BDDC type preconditioners are robust as we refine the mesh for a $P_2$ discretisation. A possible cure to this issue is discussed in the [ngsPETSc documentation](https://ngspetsc.readthedocs.io/en/latest/PETScPC/poisson.py.html).
All the preconditioners here considered are robust as we refine the mesh for a $P_1$ discretisation, but out-of-the-box only BDDC type preconditioners are robust as we refine the mesh for a $P_2$ discretisation. A possible cure for this issue is discussed in the [ngsPETSc documentation](https://ngspetsc.readthedocs.io/en/latest/PETScPC/poisson.py.html).

N. DoFs | PETSc GAMG | HYPRE | ML | PETSc BDDC* | Element-wise BDDC** |
---------|--------------|-------|-----|------------|--------------------|
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