Reduced Vector Helmholtz Wave Equation Analysis on the Wave-Number Side

Wave chaos for the Helmholtz equation

hp-Discontinuous Galerkin methods for the Helmholtz equation with large wave number

This paper develops some interior penalty hp-discontinuous Galerkin (hp-DG) methods for the Helmholtz equation in two and three dimensions. The proposed hp-DG methods are defined using a sesquilinear form which is not only mesh-dependent but also degree-dependent. In addition, the sesquilinear form contains penalty terms which not only penalize the jumps of the function values across the elemen...

Spectral Approximation of the Helmholtz Equation with High Wave Numbers

A complete error analysis is performed for the spectral-Galerkin approximation of a model Helmholtz equation with high wave numbers. The analysis presented in this paper does not rely on the explicit knowledge of continuous/discrete Green’s functions and does not require any mesh condition to be satisfied. Furthermore, new error estimates are also established for multidimensional radial and sph...

Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number

This paper develops and analyzes some interior penalty discontinuous Galerkin methods using piecewise linear polynomials for the Helmholtz equation with the first order absorbing boundary condition in the two and three dimensions. It is proved that the proposed discontinuous Galerkin methods are stable (hence well-posed) without any mesh constraint. For each fixed wave number k, optimal order (...

Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number

Several studies have presented compact fourth order accurate finite difference approximation for the Helmholtz equation in two or three dimensions. Several of these formulae allow for the wave number k to be variable. Other papers have extended this further to include variable coefficients within the Laplacian which models non-homogeneous materials in electromagnetism. Later papers considered m...