Numerical Implementation of the Fictitious Domain Method for Elliptic Equations

An Adaptive Fictitious Domain Method for elliptic problems

In the Fictitious Domain Method with Lagrange multiplier (FDM) the physical domain is embedded into a simpler but larger domain called the fictitious domain. The partial differential equation is extended to the fictitious domain using a Lagrange multiplier to enforce the prescribed boundary conditions on the physical domain while all the other data are extended to the fictitious domain. This le...

Parallel Fictitious Domain Method for a Nonlinear Elliptic Neumann Boundary Value Problem Parallel Fictitious Domain Method for a Nonlinear Elliptic Neumann Boundary Value Problem

Parallelization of the algebraic ctitious domain method is considered for solving Neumann boundary value problems with variable coeecients. The resulting method is applied to the parallel solution of the subsonic full potential ow problem which is linearized by the Newton method. Good scalability of the method is demonstrated in Cray T3E distributed memory parallel computer using MPI in communi...

On Fictitious Domain Formulations for Maxwell's Equations

Analysis of the Fictitious Domain Method with L 2 - Penalty for Elliptic and Parabolic Problems

Analysis of the fictitious domain method with L 2-penalty for elliptic and parabolic problems Abstract. The fictitious domain method with L 2-penalty for elliptic and parabolic problems are considered, respectively. The regularity theorems and a priori estimates for L 2-penalty problems are given. We derive error estimates for penalization and finite element interpolation with P 1-element. Nume...

Analysis of the Fictitious Domain Method with Penalty for Elliptic Problems

The fictitious domain method with H1-penalty for elliptic problems is considered. We propose a new way to derive the sharp error estimates between the solutions of original elliptic problems and their H1-penalty problems. We find our method of analysis is applicable to parabolic problems while retaining the sharpness of the error estimates. We also prove some regularity theorems for H1-penalty ...