Iterative numerical solution of scattering problems

Numerical solution of obstacle scattering problems

Some novel numerical approaches to solving direct and inverse obstacle scattering problems are presented. Scattering by finite obstacles and by periodic structures is considered. The emphasis for solving direct scattering problem is on the Modified Rayleigh Conjecture method, recently introduced and tested by the authors. This method is used numerically in scattering by finite obstacles and by ...

Eecient Iterative Solution of High Frequency Acoustic Scattering Problems

A ctitious domain method for the solution of the 3D Helmholtz equation with absorbing boundary conditions is considered. The nite element discretization leads to a large-scale linear system, which is solved by the algebraic ctitious domain method with GMRES iterations. With this approach the iterations can be realized in a low-dimensional subspace and thereby the partial solution method can be ...

Analytic Preconditioners for the Iterative Solution of Elastic Scattering Problems

We construct and analyze a family of well-conditioned boundary integral equations for the Krylov iterative solution of three-dimensional elastic scattering problems by a bounded rigid obstacle. We develop a new potential theory using a rewriting of the Somigliana integral representation formula. From these results, we generalize to linear elasticity the well-known Brakhage-Werner and Combined F...

Numerical Solution of Sawada-Kotera equation by using Iterative Methods

Iterative Solution of Piecewise Linear Systems for the Numerical Solution of Obstacle Problems

We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the numerical solution of free-surface problems. In particular, we here study their application to the numerical solution of both the (linear) parabolic obstacl...