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 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
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
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
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
SIAM Journal on Scientific Computing
An Immersed Interface Method for Incompressible Navier-Stokes Equations
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
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
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
Journal of Computational Physics
Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
Journal of Computational Physics
Multiscale molecular dynamics using the matched interface and boundary method
Journal of Computational Physics
Hi-index | 31.45 |
Elliptic partial differential equations (PDEs) are widely used to model real-world problems. Due to the heterogeneous characteristics of many naturally occurring materials and man-made structures, devices, and equipments, one frequently needs to solve elliptic PDEs with discontinuous coefficients and singular sources. The development of high-order elliptic interface schemes has been an active research field for decades. However, challenges remain in the construction of high-order schemes and particularly, for nonsmooth interfaces, i.e., interfaces with geometric singularities. The challenge of geometric singularities is amplified when they are originated from two or more material interfaces joining together or crossing each other. High-order methods for elliptic equations with multi-material interfaces have not been reported in the literature to our knowledge. The present work develops matched interface and boundary (MIB) method based schemes for solving two-dimensional (2D) elliptic PDEs with geometric singularities of multi-material interfaces. A number of new MIB schemes are constructed to account for all possible topological variations due to two-material interfaces. The geometric singularities of three-material interfaces are significantly more difficult to handle. Three new MIB schemes are designed to handle a variety of geometric situations and topological variations, although not all of them. The performance of the proposed new MIB schemes is validated by numerical experiments with a wide range of coefficient contrasts, geometric singularities, and solution types. Extensive numerical studies confirm the designed second order accuracy of the MIB method for multi-material interfaces, including a case where the derivative of the solution diverges.