Journal of Computational Physics
A fast Poisson solver for complex geometries
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Direct simulations of 2D fluid-particle flows in biperiodic domains
Journal of Computational Physics
Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow
Journal of Computational Physics
Convergence of a finite element/ALE method for the Stokes equations in a domain depending on time
Journal of Computational and Applied Mathematics
A spectral fictitious domain method with internal forcing for solving elliptic PDEs
Journal of Computational Physics
Approximation of Single Layer Distributions by Dirac Masses in Finite Element Computations
Journal of Scientific Computing
A local projection stabilization of fictitious domain method for elliptic boundary value problems
Applied Numerical Mathematics
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We consider the Poisson equation with Dirichlet boundary conditions, in a domain Ω\¯B, where Ω⊂{\Bbb R}n, and B is a collection of smooth open subsets (typically balls). The objective is to split the initial problem into two parts: a problem set in the whole domain Ω, for which fast solvers can be used, and local subproblems set in narrow domains around the connected components of B, which can be solved in a fully parallel way. We shall present here a method based on a multi-domain formulation of the initial problem, which leads to a fixed point algorithm. The convergence of the algorithm is established, under some conditions on a relaxation parameter &thetas;. The dependence of the convergence interval for &thetas; upon the geometry is investigated. Some 2D computations based on a finite element discretization of both global and local problems are presented.