Numerical analysis of the Half-Space Matching method with Robin traces on a convex polygonal scatterer - Archive ouverte HAL Access content directly
Book Sections Year : 2019

## Numerical analysis of the Half-Space Matching method with Robin traces on a convex polygonal scatterer

(1) , (1) , (2, 1)
1
2
Anne-Sophie Bonnet-Ben Dhia
Sonia Fliss
Yohanes Tjandrawidjaja

#### Abstract

We consider the 2D Helmholtz equation with a complex wavenumber in the exterior of a convex polygonal obstacle, with a Robin type boundary condition. Using the principle of the Half-Space Matching method, the problem is formulated as a system of coupled Fourier-integral equations, the unknowns being the Robin traces on the infinite straight lines supported by the edges of the polygon. We prove that this system is a Fredholm equation of the second kind, in an $L^2$ functional framework. The truncation of the Fourier integrals and the finite element approximation of the corresponding numerical method are also analyzed. The theoretical results are supported by various numerical experiments.

#### Domains

Mathematics [math] Analysis of PDEs [math.AP]

### Dates and versions

hal-01793511 , version 1 (16-05-2018)
hal-01793511 , version 2 (23-11-2018)
hal-01793511 , version 3 (05-12-2019)

### Identifiers

• HAL Id : hal-01793511 , version 3

### Cite

Anne-Sophie Bonnet-Ben Dhia, Sonia Fliss, Yohanes Tjandrawidjaja. Numerical analysis of the Half-Space Matching method with Robin traces on a convex polygonal scatterer. Maxwell's equations: Analysis and numerics, 24, De Gruyter, 2019, Radon Series on Computational and Applied Mathematics. ⟨hal-01793511v3⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

375 View