Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
A fast Poisson solver for complex geometries
Journal of Computational Physics
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
The immersed interface method using a finite element formulation
Applied Numerical Mathematics
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
SIAM Journal on Numerical Analysis
A boundary condition capturing method for Poisson's equation on irregular domains
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
Journal of Computational Physics
How to Incorporate the Spring-Mass Conditions in Finite-Difference Schemes
SIAM Journal on Scientific Computing
Conjugate filter approach for solving Burgers' equation
Journal of Computational and Applied Mathematics
Two-dimensional modelling of the river Rhine
Journal of Computational and Applied Mathematics
Reactive autophobic spreading of drops
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
High resolution conjugate filters for the simulation of flows
Journal of Computational Physics
New Formulations for Interface Problems in Polar Coordinates
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
A Jump Condition Capturing Finite Difference Scheme for Elliptic Interface Problems
SIAM Journal on Scientific Computing
New Geometric Immersed Interface Multigrid Solvers
SIAM Journal on Scientific Computing
Simulations of the Whirling Instability by the Immersed Boundary Method
SIAM Journal on Scientific Computing
Flow simulations in rotary volumetric pumps and compressors with the fictitious domain method
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
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
Fourth order accurate evaluation of integrals in potential theory on exterior 3D regions
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
Journal of Computational Physics
Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
Journal of Computational Physics
Journal of Computational Physics
A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth
Journal of Scientific Computing
A Coupling Interface Method for a Nonlinear Parabolic-Elliptic Problem
Numerical Analysis and Its Applications
Immersed Interface Difference Schemes for a Parabolic-Elliptic Interface Problem
Large-Scale Scientific Computing
A sharp interface finite volume method for elliptic equations on Cartesian grids
Journal of Computational Physics
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
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Journal of Computational Physics
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
Journal of Computational Physics
Differential geometry based solvation model I: Eulerian formulation
Journal of Computational Physics
Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients
Journal of Computational Physics
Multiscale molecular dynamics using the matched interface and boundary method
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
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A weak formulation for solving elliptic interface problems without body fitted grid
Journal of Computational Physics
Weak Galerkin methods for second order elliptic interface problems
Journal of Computational Physics
A kernel-free boundary integral method for implicitly defined surfaces
Journal of Computational Physics
Mathematics and Computers in Simulation
Multiscale geometric modeling of macromolecules I: Cartesian representation
Journal of Computational Physics
Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations
Journal of Computational Physics
A molecular level prototype for mechanoelectrical transducer in mammalian hair cells
Journal of Computational Neuroscience
An asymptotic solution approach for elliptic equations with discontinuous coefficients
Journal of Computational Physics
Hi-index | 31.60 |
This paper introduces a novel high order interface scheme, the matched interface and boundary (MIB) method, for solving elliptic equations with discontinuous coefficients and singular sources on Cartesian grids. By appropriate use of auxiliary line and/or fictitious points, physical jump conditions are enforced at the interface. Unlike other existing interface schemes, the proposed method disassociates the enforcement of physical jump conditions from the discretization of the differential equation under study. To construct higher order interface schemes, the proposed MIB method bypasses the major challenge of implementing high order jump conditions by repeatedly enforcing the lowest order jump conditions. The proposed MIB method is of arbitrarily high order, in principle. In treating straight, regular interfaces we construct MIB schemes up to 16th-order. For more general elliptic problems with curved, irregular interfaces and boundary, up to 6th-order MIB schemes have been demonstrated. By employing the standard high-order finite difference schemes to discretize the Laplacian, the present MIB method automatically reduces to the standard central difference scheme when the interface is absent. The immersed interface method (IIM) is regenerated for a comparison study of the proposed method. The robustness of the MIB method is verified against the large magnitude of the jump discontinuity across the interface. The nature of high efficiency and low memory requirement of the MIB method is extensively validated via solving various elliptic immersed interface problems in two- and three-dimensions. ee-dimensions.