Journal of Computational Physics
Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
SIAM Journal on Numerical Analysis
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
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
Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions
SIAM Journal on Scientific Computing
Journal of Computational Physics
Immersed Interface Method for a Reaction-Diffusion Equation with a Moving Own Concentrated Source
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Three-dimensional elliptic solvers for interface problems and applications
Journal of Computational Physics
SIAM Journal on Scientific Computing
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Journal of Computational Physics
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
A numerical method for solving variable coefficient elliptic equation with interfaces
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An immersed interface method for the Vortex-In-Cell algorithm
Computers and Structures
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
Journal of Computational Physics
A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth
Journal of Scientific Computing
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
Differential geometry based solvation model I: Eulerian formulation
Journal of Computational Physics
Multiscale molecular dynamics using the matched interface and boundary method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Weak Galerkin methods for second order elliptic interface problems
Journal of Computational Physics
Multiscale geometric modeling of macromolecules I: Cartesian representation
Journal of Computational Physics
Hi-index | 31.51 |
This work overcomes the difficulty of dealing with large curvatures in a high order matched interface and boundary (MIB) method proposed for solving elliptic interface problems. The MIB method smoothly extends the solution across the interface so that standard high order central finite difference schemes can be used without the loss of accuracy. One feature of the MIB is that it disassociates the discretization of the elliptic equation from the enforcement of interface jump conditions. The other is to make iterative use of only the lowest order jump conditions to determine the fictitious values on extended domains. It is of arbitrarily high order in convergence, in principle. However, its applicability was hindered by the lack of sufficiently many grid points to determine all the fictitious values required for high order schemes at the location where the curvature of the interface is relatively large. We remove this obstacle by introducing a new concept, the disassociation between the discretization and the domain extension. We show that the improved MIB method is robust for handling general irregular interfaces by extensive numerical experiments on the Poisson equation and the Helmholtz equation. To better understand the MIB method and other potential high order interface schemes, we propose an alternative interpolation formulation of the MIB method and show that the new formulation is essentially equivalent to the improved one.