A fast algorithm for particle simulations
Journal of Computational Physics
Journal of Computational Physics
Domain decomposition algorithms for indefinite elliptic problems
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
On the difficulty of triangulating three-dimensional nonconvex polyhedra.
Discrete & Computational Geometry
Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
Journal of Computational Physics
Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A fast Poisson solver for complex geometries
Journal of Computational Physics
Locally corrected multidimensional quadrature rules for singular functions
SIAM Journal on Scientific Computing
Integral equation methods for Stokes flow and isotropic elasticity in the plane
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
A fast method of moments solver for efficient parameter extraction of MCMs
DAC '97 Proceedings of the 34th annual Design Automation Conference
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
Rapid parallel evaluation of integrals in potential theory on general three-dimensional regions
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Algorithm 790: CSHEP2D: cubic Shepard method for bivariate interpolation of scattered data
ACM Transactions on Mathematical Software (TOMS)
Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations
Proceedings of the sixteenth annual symposium on Computational geometry
An efficient algorithm for hydrodynamical interaction of many deformable drops
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A parallel dynamic-mesh Lagrangian method for simulation of flows with dynamic interfaces
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
Interfacial dynamics for Stokes flow
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Evaluation of Single Layer Potentials over Curved Surfaces
SIAM Journal on Scientific Computing
Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions
SIAM Journal on Scientific Computing
A Method for Computing Nearly Singular Integrals
SIAM Journal on Numerical Analysis
IES3: Efficient Electrostatic and Electromagnetic Simulation
IEEE Computational Science & Engineering
A new version of the fast multipole method for screened Coulomb interactions in three dimensions
Journal of Computational Physics
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
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
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
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
On the evaluation of layer potentials close to their sources
Journal of Computational Physics
Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
Petascale Direct Numerical Simulation of Blood Flow on 200K Cores and Heterogeneous Architectures
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Fast integral equation methods for Rothe's method applied to the isotropic heat equation
Computers & Mathematics with Applications
A fast algorithm for simulating vesicle flows in three dimensions
Journal of Computational Physics
Accurate computation of Stokes flow driven by an open immersed interface
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.52 |
We present a new method for the solution of the Stokes equations. The main features of our method are: (1) it can be applied to arbitrary geometries in a black-box fashion; (2) it is second-order accurate; and (3) it has optimal algorithmic complexity. Our approach, to which we refer as the embedded boundary integral method (EBI), is based on Anita Mayo's work for the Poisson's equation: "The Fast Solution of Poisson's and the Biharmonic Equations on Irregular Regions", SIAM Journal on Numerical Analysis, 21 (1984) 285-299. We embed the domain in a rectangular domain, for which fast solvers are available, and we impose the boundary conditions as interface (jump) conditions on the velocities and tractions. We use an indirect boundary integral formulation for the homogeneous Stokes equations to compute the jumps. The resulting equations are discretized by Nyström's method. The rectangular domain problem is discretized by finite elements for a velocity-pressure formulation with equal order interpolation bilinear elements (Q1-Q1). Stabilization is used to circumvent the inf-sup condition for the pressure space. For the integral equations, fast matrix-vector multiplications are achieved via an N logN algorithm based on a block representation of the discrete integral operator, combined with (kernel independent) singular value decomposition to sparsify low-rank blocks. The regular grid solver is a Krylov method (conjugate residuals) combined with an optimal two-level Schwartz-preconditioner. For the integral equation we use GMRES. We have tested our algorithm on several numerical examples and we have observed optimal convergence rates.