A rapidly converging domain decomposition method for the Helmholtz equation

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 ...

A Domain Decomposition Method for the Helmholtz equation and related Optimal Control Problems

We present an iterative domain decomposition method to solve the Helmholtz equation and related optimal control problems. The proof of convergence of this method relies on energy techniques. This method leads to eecient algorithms for the numerical resolution of harmonic wave propagation problems in heterogeneous media and their control. Une m ethode de d ecomposition de domaine pour l' equatio...

A Rapidly Converging Recursive Method for MobileRobot

This paper proposes a simple method for estimating the position of a robot from relatively few sensor readings. Our algorithms are intended for applications where sensor readings are expensive or otherwise limited and the readings that are taken are subject to considerable errors or noise. Our method is capable of converging to a position estimate with greater accuracy using fewer measurements ...

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

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...