Year: 2024
Type: article
Abstract: A preconditioner is proposed for Laplace exterior boundary value problems on multi-screens. To achieve this, the quotient-space boundary element method and operator preconditioning are combined. For a fairly general subclass of multi-screens, it is shown that this approach paves the way for block diagonal Calderón preconditioners which achieve a spectral condition number that grows only logarithmically with decreasing mesh size, just as in the case of simple screens. Since the resulting scheme contains many more degrees of freedom than strictly required, strategies are presented to remove almost all redundancy without significant loss of effectiveness of the preconditioner. The performance of this method is verified by providing representative numerical results. Further numerical experiments suggest that these results can be extended to a much wider class of multi-screens that cover essentially all geometries encountered in practice, leading to a significantly reduced simulation cost.
Source: BIT Numerical Mathematics
Authors: Kristof Cools, Carolina Urzúa-Torres
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4402199740