Two-dimensional modelling of the river Rhine
Journal of Computational and Applied Mathematics
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Numerical treatment of two-dimensional interfaces for acoustic and elastic waves
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A class of difference schemes with flexible local approximation
Journal of Computational Physics
Comparison of Taylor finite difference and window finite difference and their application in FDTD
Journal of Computational and Applied Mathematics
An immersed interface method for simulating the interaction of a fluid with moving boundaries
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
The immersed interface method for two-dimensional heat-diffusion equations with singular own sources
Applied Numerical Mathematics
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
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
Short Note: A proof that a discrete delta function is second-order accurate
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
Immersed Interface Difference Schemes for a Parabolic-Elliptic Interface Problem
Large-Scale Scientific Computing
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
An interpolation matched interface and boundary method for elliptic interface problems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
A new numerical method for nonlocal electrostatics in biomolecular simulations
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
Journal of Computational Physics
Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients
Journal of Computational Physics
MIB method for elliptic equations with multi-material interfaces
Journal of Computational Physics
The Immersed Interface Technique for Parabolic Problems with Mixed Boundary Conditions
SIAM Journal on Numerical Analysis
A rothe-immersed interface method for a class of parabolic interface problems
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Journal of Computational Physics
Immersed Interface Method for elliptic equations based on a piecewise second order polynomial
Computers & Mathematics with Applications
Semi-implicit formulation of the immersed finite element method
Computational Mechanics
Finite difference schemes for multilayer diffusion
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
Journal of Scientific Computing
Digital rock physics benchmarks-part II: Computing effective properties
Computers & Geosciences
A novel concept for the design of immersed interface methods
Journal of Computational Physics
A weak formulation for solving elliptic interface problems without body fitted grid
Journal of Computational Physics
A kernel-free boundary integral method for implicitly defined surfaces
Journal of Computational Physics
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
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Many boundary value problems (BVPs) or initial BVPs have nonsmooth solutions, with jumps along lower-dimensional interfaces. The explicit-jump immersed interface method (EJIIM) was developed following Li's fast iterative immersed interface method (FIIIM), recognizing that the foundation for the efficient solution of many such problems is a good solver for elliptic BVPs. EJIIM generalizes the class of problems for which FIIIM is applicable. It handles interfaces between constant and variable coefficients and extends the immersed interface method (IIM) to BVPs on irregular domains with Neumann and Dirichlet boundary conditions. Proofs of second order convergence for a one-dimensional (1D) problem with piecewise constant coefficients and for two-dimensional (2D) problems with singular sources are given. Other problems are reduced to the singular sources case, with additional equations determining the source strengths. The advantages of EJIIM are high quality of solutions even on coarse grids and easy adaptation to many problems with complicated geometries, while still maintaining the efficiency of the FIIIM.