Introduction to numerical linear algebra and optimisation
Introduction to numerical linear algebra and optimisation
SIAM Journal on Numerical Analysis
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Journal of the ACM (JACM)
SIAM Journal on Numerical Analysis
Superconvergence of the Shortley-Weller approximation for Dirichlet problems
Journal of Computational and Applied Mathematics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
Osculatory interpolation in the method of fundamental solution for nonlinear Poisson problems
Journal of Computational Physics
SIAM Journal on Scientific Computing
A general fictitious domain method with immersed jumps and multilevel nested structured meshes
Journal of Computational Physics
The Immersed Interface Technique for Parabolic Problems with Mixed Boundary Conditions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 31.45 |
This paper describes a method for the solution of the 3D Poisson equation, subject to mixed boundary conditions, on an irregularly shaped domain. A finite difference method is used, with the domain embedded in a rectangular grid. Quadratic treatment of the boundary conditions is shown to be necessary to obtain uniform error of O(@D^2). This contrasts with the Dirichlet case where both quadratic and linear treatments give O(@D^2) error, although the coefficient of error may be much larger for the linear case. Explicit error estimates demonstrating this behaviour are found for the 1D case with similar behaviour found in 2D and 3D numerical examples. Finally, the extension of this approach to the N-dimensional case is given, where N3.