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- W4387687995 abstract "We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a $2$-dimensional triangulated surface $Gamma$ in $mathbb{R}^3$. We allow $Gamma$ to belong to a large class of geometries that we call polygonal multiscreens, which can be non-manifold. After introducing a new, simple conforming Galerkin discretization, we analyze a substructuring domain-decomposition preconditioner based on ideas originally developed for the Finite Element Method. The surface $Gamma$ is subdivided into non-overlapping regions, and the application of the preconditioner is obtained via the solution of the hypersingular equation on each patch, plus a coarse subspace correction. We prove that the condition number of the preconditioned linear system grows poly-logarithmically with $H/h$, the ratio of the coarse mesh and fine mesh size, and our numerical results indicate that this bound is sharp. This domain-decomposition algorithm therefore guarantees significant speedups for iterative solvers, even when a large number of subdomains is used." @default.
- W4387687995 created "2023-10-17" @default.
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- W4387687995 date "2023-10-13" @default.
- W4387687995 modified "2023-10-18" @default.
- W4387687995 title "Boundary Element Methods for the Laplace Hypersingular Integral Equation on Multiscreens: a two-level Substructuring Preconditioner" @default.
- W4387687995 doi "https://doi.org/10.48550/arxiv.2310.09204" @default.
- W4387687995 hasPublicationYear "2023" @default.
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