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
SIAM Journal on Scientific Computing
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
Finite elements for elliptic problems with wild coefficients
Mathematics and Computers in Simulation - IMACS sponsored special issue: 1999 international symposium on computational sciences, to honor John R. Rice
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Fundamentals of Numerical Reservoir Simulation
Fundamentals of Numerical Reservoir Simulation
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
A numerical method for solving variable coefficient elliptic equation with interfaces
Journal of Computational Physics
International Journal of High Performance Computing Applications
A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
Journal of Computational Physics
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We address the solution of multiregion elliptic and parabolic problems with strongly discontinuous coefficients across interfaces. The underlying idea is, roughly, to perturb around the infinitely discontinuous coefficient solution, that is, to perturb the solution where one region is a perfect conductor. The result is partial decoupling of the interface conditions. The algorithm requires a small number of well-conditioned solves in the individual regions (in many cases only a single solve over each region is necessary) that are then assembled into an accurate global solution. The error from the assembly step is asymptotically small in the ratio of the discontinuous coefficients. Further, the framework can be extended to problems with moderately discontinuous coefficients using a series expansion in the discontinuity ratio in a manner similar to a Schwarz alternating method.