On coupling wavelets with fictitious domain approaches

Coupling wavelets/vaguelets and smooth fictitious domain methods for elliptic problems; the univariate case

This work is devoted to the definition, the analysis and the implementation in the univariate case of a new numerical method for the approximation of partial differential equations solutions defined on complex domains. It couples a smooth fictitious domain method of Haslinger et al. [Projected Schur complement method for solving non-symmetric systems arising from a smooth fictitious domain appr...

On Fictitious Domain Formulations for Maxwell's Equations

On Solving Non-symmetric Saddle-point Systems Arising from Fictitious Domain Approaches∗

where the diagonal block A is an (n × n) matrix, the off-diagonal blocks B1 and B2 are (m× n) matrices with full row-rank and vectors f , g are of order n, m, respectively. Our contribution is inspired by a class of saddle-point systems arising from fictitious domain formulations of PDEs [3, 4]. Therefore we will be interested especially in systems (1) with n large, A singular and B1, B2 sparse...

On a Fictitious Domain Method for Unilateral Problems

This contribution deals with numerical realization of elliptic boundary value problems with unilateral boundary conditions using a fictitious domain method. Any fictitious domain formulation [2] extends the original problem defined in a domain ω to a new (fictitious) domainΩ with a simple geometry (e.g. a box) which contains ω . The main advantage consists in possibility to use a uniform mesh i...

A Fictitious Domain Method with Mixed Finite Elements for Elastodynamics

We consider in this paper the wave scattering problem by an object with Neumann boundary conditions in an anisotropic elastic body. To obtain an efficient numerical method (permitting the use of regular grids) we follow a fictitious domain approach coupled with a first order velocity stress formulation for elastodynamics. We first observe that the method does not always converge when the Qdiv 1...