Three-dimensional elliptic solvers for interface problems and applications
Journal of Computational Physics
Solving a Nonlinear Problem in Magneto-Rheological Fluids Using the Immersed Interface Method
Journal of Scientific Computing
Journal of Computational Physics
A level-set method for interfacial flows with surfactant
Journal of Computational Physics
Journal of Computational Physics
Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain
Journal of Computational and Applied Mathematics
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
Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A velocity decomposition approach for moving interfaces in viscous fluids
Journal of Computational Physics
A sharp interface finite volume method for elliptic equations on Cartesian grids
Journal of Computational Physics
Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain
Journal of Computational and Applied Mathematics
An interpolation matched interface and boundary method for elliptic interface problems
Journal of Computational and Applied Mathematics
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
MIB method for elliptic equations with multi-material interfaces
Journal of Computational Physics
Second-order Poisson-Nernst-Planck solver for ion transport
Journal of Computational Physics
Augmented strategies for interface and irregular domain problems
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Journal of Computational Physics
Journal of Computational Physics
Adaptive mesh refinement techniques for the immersed interface method applied to flow problems
Computers and Structures
A novel concept for the design of immersed interface methods
Journal of Computational Physics
Journal of Computational and Applied Mathematics
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New finite difference methods using Cartesian grids are developed for elliptic interface problems with variable discontinuous coefficients, singular sources, and nonsmooth or even discontinuous solutions. The new finite difference schemes are constructed to satisfy the sign property of the discrete maximum principle using quadratic optimization techniques. The methods are shown to converge under certain conditions using comparison functions. The coefficient matrix of the resulting linear system of equations is an M-matrix and is coupled with a multigrid solver. Numerical examples are also provided to show the efficiency of the proposed methods.