A numerical investigation on iterative methods for the two-dimensional Poisson equation discretized with high-order mimetic operators
Keywords:
Mimetic operators, Poisson equation, iterative methods, Krylov subspace, numerical experimentsAbstract
Mimetic operators are of increasing interest to the scientific computing community due to their ability to preserve many important properties of the continuous problem (e.g., conservation laws) while maintaining the same order of accuracy on the boundary as in the interior points. This mathematical framework results in locally dense and potentially ill-conditioned linear systems that are challenging to solve. This issue can partially be addressed using adequate iterative solvers, which is the focus of this work. Using the two-dimensional Poisson equation and mimetic operators of order k ∈ {2, 4}, we compare the computational times and number of iterations obtained with different Krylov-subspace-based iterative methods used for the resolution of the linear systems.
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References
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