Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
Analysis of a one-dimensional model for the immersed boundary method
SIAM Journal on Numerical Analysis
A continuum method for modeling surface tension
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
Journal of Scientific Computing
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
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
Comparison of Taylor finite difference and window finite difference and their application in FDTD
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
A coupling interface method for elliptic interface problems
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
A kernel-free boundary integral method for elliptic boundary value problems
Journal of Computational Physics
Journal of Computational Physics
Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
Journal of Computational Physics
Journal of Computational Physics
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients
Journal of Computational Physics
Journal of Computational Physics
Immersed Interface Method for elliptic equations based on a piecewise second order polynomial
Computers & Mathematics with Applications
International Journal of Computing Science and Mathematics
A kernel-free boundary integral method for implicitly defined surfaces
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Hi-index | 31.51 |
A second order accurate finite difference method is presented for solving two-dimensional variable coefficient elliptic equations on Cartesian grids, in which the coefficients, the source term, the solution and its derivatives may be nonsmooth or discontinuous across an interface. A correction term is introduced to the standard central difference stencil so that the numerical discretization is well-defined across the interface. We also propose a new method to approximate the correction term as part of the iterative procedure. The method is easy to implement since the correction term only needs to be added to the right-hand-side of the system. Therefore, the coefficient matrix remains symmetric and diagonally dominant, allowing for most standard solvers to be used. Numerical examples show good agreements with exact solutions, and the order of accuracy is comparable with other immersed interface methods.