Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Superconvergence of the Shortley-Weller approximation for Dirichlet problems
Journal of Computational and Applied Mathematics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Analysis of the cell-centred finite volume method for the diffusion equation
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Is 1.7 x 10^10 Unknowns the Largest Finite Element System that Can Be Solved Today?
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A general fictitious domain method with immersed jumps and multilevel nested structured meshes
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Scientific Computing
Short Note: Controlling self-force errors at refinement boundaries for AMR-PIC
Journal of Computational Physics
Journal of Computational Physics
A fast parallel Poisson solver on irregular domains applied to beam dynamics simulations
Journal of Computational Physics
Journal of Computational Physics
Improvements of a fast parallel poisson solver on irregular domains
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
A Particle-in-cell Method with Adaptive Phase-space Remapping for Kinetic Plasmas
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Journal of Computational Physics
Hi-index | 31.51 |
This paper presents a method for solving Poisson's equation with Dirichlet boundary conditions on an irregular bounded three-dimensional region. The method uses a nodal-point discretization and adaptive mesh refinement (AMR) on Cartesian grids, and the AMR multigrid solver of Almgren. The discrete Laplacian operator at internal boundaries comes from either linear or quadratic (Shortley Weller) extrapolation, and the two methods are compared. It is shown that either way, solution error is second order in the mesh spacing. Error in the gradient of the solution is first order with linear extrapolation, but second order with Shortley-Weller. Examples are given with comparison with the exact solution. The method is also applied to a heavy-ion fusion accelerator problem, showing the advantage of adaptivity.