Journal of Computational Physics
SIAM Journal on Numerical Analysis
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
SIAM Journal on Numerical Analysis
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
SIAM Journal on Numerical Analysis
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
How to Incorporate the Spring-Mass Conditions in Finite-Difference Schemes
SIAM Journal on Scientific Computing
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
New Formulations for Interface Problems in Polar Coordinates
SIAM Journal on Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
An Immersed Interface Method for Incompressible Navier-Stokes Equations
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
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
Journal of Computational Physics
Journal of Computational Physics
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
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
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
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
An Analysis of a Broken $P_1$-Nonconforming Finite Element Method for Interface Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Iterative Filtering Decomposition Based on Local Spectral Evolution Kernel
Journal of Scientific Computing
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
Hi-index | 31.52 |
Elliptic problems with sharp-edged interfaces, thin-layered interfaces and interfaces that intersect with geometric boundary, are notoriously challenging to existing numerical methods, particularly when the solution is highly oscillatory. This work generalizes the matched interface and boundary (MIB) method previously designed for solving elliptic problems with curved interfaces to the aforementioned problems. We classify these problems into five distinct topological relations involving the interfaces and the Cartesian mesh lines. Flexible strategies are developed to systematically extends the computational domains near the interface so that the standard central finite difference scheme can be applied without the loss of accuracy. Fictitious values on the extended domains are determined by enforcing the physical jump conditions on the interface according to the local topology of the irregular point. The concepts of primary and secondary fictitious values are introduced to deal with sharp-edged interfaces. For corner singularity or tip singularity, an appropriate polynomial is multiplied to the solution to remove the singularity. Extensive numerical experiments confirm the designed second order convergence of the proposed method.