An Additive Overlapping Domain Decomposition Method for the Helmholtz Equation

A Non-overlapping Quasi-optimal Optimized Schwarz Domain Decomposition Algorithm for the Helmholtz Equation

Quasi-Optimal Convergence of Non-Overlapping Domain Decomposition Algorithm for the Helmholtz Equation

This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results valida...

A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation

This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results valida...

A Non-Overlapping Domain Decomposition Method for the Exterior Helmholtz Problem

In this paper, we first show that the domain decomposition methods that are usually efficient for solving elliptic problems typically fail when applied to acoustics problems. Next, we present an alternative domain decomposition algorithm that is better suited for the exterior Helmholtz problem. We describe it in a formalism that can use either one or two Lagrange multiplier fields for solving t...

Domain Decomposition Methods for the Helmholtz Equation: A Numerical Investigation

where k := 2π f/c is the wavenumber with frequency f ∈ R and c := c(x,y,z) is the velocity of the medium, which varies in space. The geophysical model SEG– SALT is used as a benchmark problem on which we will test some existing domain decomposition methods in this paper. In this model, the domain Ω is defined as (0,13520)× (0,13520)× (0,4200) m, the velocity is described as piecewise constants ...