SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Numerical Analysis
Wavelet and finite element solutions for the Neumann problem using fictitious domains
Journal of Computational Physics
Fictitious domain method for unsteady problems: application to electromagnetic scattering
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions
SIAM Journal on Scientific Computing
A multilevel local mesh refinement projection method for low Mach number flows
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
A node-centered local refinement algorithm for Poisson's equation in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes
SIAM Journal on Scientific Computing
Local enrichment of the finite cell method for problems with material interfaces
Computational Mechanics
Hi-index | 31.46 |
This study addresses a new fictitious domain method for elliptic problems in order to handle general and possibly mixed embedded boundary conditions (E.B.C.): Robin, Neumann and Dirichlet conditions on an immersed interface. The main interest of this fictitious domain method is to use simple structured meshes, possibly uniform Cartesian nested grids, which do not generally fit the interface but define an approximate one. A cell-centered finite volume scheme with a non-conforming structured mesh is derived to solve the set of equations with additional algebraic transmission conditions linking both flux and solution jumps through the immersed approximate interface. Hence, a local correction is devised to take account of the relative surface ratios in each control volume for the Robin or Neumann boundary condition. Then, the numerical scheme conserves the first-order accuracy with respect to the mesh step. This opens the way to combine the E.B.C. method with a multilevel mesh refinement solver to increase the precision in the vicinity of the interface. Such a fictitious domain method is very efficient: the L^2- and L^~-norm errors vary like O(h"l"*) where h"l"* is the grid step of the finest refinement level around the interface until the residual first-order discretization error of the non-refined zone is reached. The numerical results reported here for convection-diffusion problems with Dirichlet, Robin and mixed (Dirichlet and Robin) boundary conditions confirm the expected accuracy as well as the performances of the present method.