Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
SIAM Journal on Numerical Analysis
The immersed interface method: a numerical approach for partial differential equations with interfaces
SIAM Journal on Numerical Analysis
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
Theoretical and numerical analysis on a thermo-elastic system with discontinuities
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
SIAM Journal on Scientific Computing
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
Journal of Computational Physics
Numerical Solution of Partial Differential Equations: An Introduction
Numerical Solution of Partial Differential Equations: An Introduction
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)
The immersed interface method for two-dimensional heat-diffusion equations with singular own sources
Applied Numerical Mathematics
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The numerical method proposed in this paper is an improvement of the ADI method by Li and Mayo (1994). The proposed method is unconditionally stable for both two and three-dimensional heat conduction interface problems, while Li's ADI method is only stable for two-dimensional problems. The method is a modification of a Locally One-Dimensional (LOD) difference scheme, with correction term added to the right-hand side of the standard LOD difference scheme at irregular points. The correction term is determined so that the local truncation error is of order O(h) at irregular points. Then the method is two-order convergent in both time and space directions. Numerical examples show good agreement with exact solutions and confirm the order of convergence and stability.