Plane wave approximation of homogeneous Helmholtz solutions

Homogeneous Plane-wave Spacetimes and their Stability

We consider the stability of spatially homogeneous plane-wave spacetimes. We carry out a full analysis for plane-wave spacetimes in (4 + 1) dimensions, and find there are two cases to consider; what we call nonexceptional and exceptional. In the non-exceptional case the plane waves are stable to (spatially homogeneous) vacuum perturbations as well as a restricted set of matter perturbations. In...

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...

Plane wave approximation in linear elasticity

Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models

Parallel Preconditioners for Plane Wave Helmholtz and Maxwell Systems with Large Wave Numbers

A kind of non-overlapping domain decomposition preconditioner was proposed to solve the systems generated by the plane wave least-squares (PWLS) method for discretization of Helmholtz equation and Maxwell equations respectively in [13] and [14]. In this paper we introduce overlapping variants of this kind of preconditioner and give some comparison among these domain decomposition preconditioner...