A Cartesian grid embedded boundary method for Poisson's equation on irregular domains

A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions

Journal of Computational Physics

A second-order-accurate symmetric discretization of the Poisson equation on irregular domains

Journal of Computational Physics

A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing

Journal of Computational Physics

A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid

Journal of Computational Physics

Convergence of the ghost fluid method for elliptic equations with interfaces

Mathematics of Computation

Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries

Journal of Computational Physics

A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow

Journal of Computational Physics

A fast solver for the Stokes equations with distributed forces in complex geometries

Journal of Computational Physics

A ghost-cell immersed boundary method for flow in complex geometry

Journal of Computational Physics

Richtmyer-Meshkov instability in liquid metal flows: influence of cavitation and magnetic fields

Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications

A node-centered local refinement algorithm for Poisson's equation in complex geometries

Journal of Computational Physics

The embedded finite difference method for the Poisson equation in a domain with an irregular boundary and Dirichlet boundary conditions

Journal of Computational Physics

A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem

Journal of Computational Physics

Semi-implicit, semi-Lagrangian modelling for environmental problems on staggered Cartesian grids with cut cells

Journal of Computational Physics

A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies

Journal of Computational Physics

A computational approach to simulate subsurface light diffusion in arbitrarily shaped objects

GI '05 Proceedings of Graphics Interface 2005

A fourth-order accurate local refinement method for Poisson's equation

Journal of Computational Physics

Is 1.7 x 10^10 Unknowns the Largest Finite Element System that Can Be Solved Today?

SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing

A Cartesian grid embedded boundary method for hyperbolic conservation laws

Journal of Computational Physics

High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources

Journal of Computational Physics

A Cartesian grid embedded boundary method for the heat equation and Poisson's equation in three dimensions

Journal of Computational Physics

An adaptive fast solver for the modified Helmholtz equation in two dimensions

Journal of Computational Physics

An embedded boundary method for viscous, conducting compressible flow

Journal of Computational Physics

An anelastic allspeed projection method for gravitationally stratified flows

Journal of Computational Physics

Cartesian grid fluid simulation with irregular boundary voxels

SIGGRAPH '05 ACM SIGGRAPH 2005 Sketches

A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids

Journal of Computational Physics

A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces

Journal of Computational Physics

Fourth order accurate evaluation of integrals in potential theory on exterior 3D regions

Journal of Computational Physics

On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method

Journal of Computational Physics

A Supra-Convergent Finite Difference Scheme for the Poisson and Heat Equations on Irregular Domains and Non-Graded Adaptive Cartesian Grids

Journal of Scientific Computing

A large jump asymptotic framework for solving elliptic and parabolic equations with interfaces and strong coefficient discontinuities

Applied Numerical Mathematics

Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces

Journal of Computational Physics

A fast variational framework for accurate solid-fluid coupling

ACM SIGGRAPH 2007 papers

A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity

Journal of Computational Physics

A coupling interface method for elliptic interface problems

Journal of Computational Physics

A general fictitious domain method with immersed jumps and multilevel nested structured meshes

Journal of Computational Physics

An efficient, scalable numerical algorithm for the simulation of electrochemical systems on irregular domains

Journal of Computational Physics

A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers

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

Solving partial differential equations on irregular domains with moving interfaces, with applications to superconformal electrodeposition in semiconductor manufacturing

Journal of Computational Physics

An iterative boundary potential method for the infinite domain Poisson problem with interior Dirichlet boundaries

Journal of Computational Physics

A sharp interface finite volume method for elliptic equations on Cartesian grids

Journal of Computational Physics

A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate

Journal of Computational Physics

A point-based method for animating incompressible flow

Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation

An efficient fluid-solid coupling algorithm for single-phase flows

Journal of Computational Physics

On the accuracy of direct forcing immersed boundary methods with projection methods

Journal of Computational Physics

A stable and convergent scheme for viscoelastic flow in contraction channels

Journal of Computational Physics

The Shortley-Weller embedded finite-difference method for the 3D Poisson equation with mixed boundary conditions

Journal of Computational Physics

Handling solid-fluid interfaces for viscous flows: Explicit jump approximation vs. ghost cell approaches

Journal of Computational Physics

An improved immersed boundary-lattice Boltzmann method for simulating three-dimensional incompressible flows

Journal of Computational Physics

A second order virtual node method for elliptic problems with interfaces and irregular domains

Journal of Computational Physics

A conservative immersed interface method for Large-Eddy Simulation of incompressible flows

Journal of Computational Physics

Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces

Journal of Computational Physics

A high-order cut-cell method for numerical simulation of hypersonic boundary-layer instability with surface roughness

Journal of Computational Physics

The moving boundary node method: A level set-based, finite volume algorithm with applications to cell motility

Journal of Computational Physics

A discrete model for compressible flows in heterogeneous media

Journal of Computational Physics

A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

Journal of Computational Physics

Simulating Biochemical Signaling Networks in Complex Moving Geometries

SIAM Journal on Scientific Computing

MIB method for elliptic equations with multi-material interfaces

Journal of Computational Physics

A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries

Journal of Computational Physics

A conservative numerical method for the Cahn-Hilliard equation in complex domains

Journal of Computational Physics

The Immersed Interface Technique for Parabolic Problems with Mixed Boundary Conditions

SIAM Journal on Numerical Analysis

A Second Order Discretization of Maxwell's Equations in the Quasi-Static Regime on OcTree Grids

SIAM Journal on Scientific Computing

Augmented strategies for interface and irregular domain problems

NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications

A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions

Journal of Computational Physics

Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients

Journal of Computational Physics

A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation

SIAM Journal on Scientific Computing

Self-gravitational force calculation of infinitesimally thin gaseous disks

Journal of Computational Physics

Heterogeneous mixtures of elliptical particles: Directly resolving local and global properties and responses

Journal of Computational Physics

A Neumann-Neumann preconditioned iterative substructuring approach for computing solutions to Poisson's equation with prescribed jumps on an embedded boundary

Journal of Computational Physics

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

Journal of Scientific Computing

A novel concept for the design of immersed interface methods

Journal of Computational Physics

A weak formulation for solving elliptic interface problems without body fitted grid

Journal of Computational Physics

A kernel-free boundary integral method for implicitly defined surfaces

Journal of Computational Physics

A consistent and conservative scheme for MHD flows with complex boundaries on an unstructured Cartesian adaptive system

Journal of Computational Physics

Compact cell-centered discretization stencils at fine-coarse block structured grid interfaces

Journal of Computational Physics

An ALE formulation of embedded boundary methods for tracking boundary layers in turbulent fluid-structure interaction problems

Journal of Computational Physics