A fast algorithm for particle simulations
Journal of Computational Physics
A new concept in near-singular integral evaluation: the continuation approach
SIAM Journal on Applied Mathematics
Wavelet-like bases for the fast solutions of second-kind integral equations
SIAM Journal on Scientific Computing
Integral equations: theory and numerical treatment
Integral equations: theory and numerical treatment
Integral equation methods for Stokes flow and isotropic elasticity in the plane
Journal of Computational Physics
A New Spectral Boundary Integral Collocation Method for Three-Dimensional Potential Problems
SIAM Journal on Numerical Analysis
Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nystro¨m discretization
Journal of Computational Physics
Wavelet Galerkin Algorithms for Boundary Integral Equations
SIAM Journal on Scientific Computing
An efficient algorithm for hydrodynamical interaction of many deformable drops
Journal of Computational Physics
Journal of Computational Physics
Boundary integral methods for multicomponent fluids and multiphase materials
Journal of Computational Physics
A Method for Computing Nearly Singular Integrals
SIAM Journal on Numerical Analysis
Multiscale Bases for the Sparse Representation of Boundary Integral Operators on Complex Geometry
SIAM Journal on Scientific Computing
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
A New Parallel Kernel-Independent Fast Multipole Method
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
On the evaluation of layer potentials close to their sources
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A spectral boundary integral method for flowing blood cells
Journal of Computational Physics
Journal of Computational Physics
Spectrally accurate fast summation for periodic Stokes potentials
Journal of Computational Physics
Fast integral equation methods for the modified Helmholtz equation
Journal of Computational Physics
Manifold-based surfaces with boundaries
Computer Aided Geometric Design
Applying a second-kind boundary integral equation for surface tractions in Stokes flow
Journal of Computational Physics
A fast algorithm for simulating vesicle flows in three dimensions
Journal of Computational Physics
SIAM Journal on Scientific Computing
Advances in Computational Mathematics
Journal of Computational Physics
Quadrature by expansion: A new method for the evaluation of layer potentials
Journal of Computational Physics
On the numerical evaluation of the singular integrals of scattering theory
Journal of Computational Physics
Hi-index | 31.51 |
We present a high-order boundary integral equation solver for 3D elliptic boundary value problems on domains with smooth boundaries. We use Nyström's method for discretization, and combine it with special quadrature rules for the singular kernels that appear in the boundary integrals. The overall asymptotic complexity of our method is O(N3/2), where N is the number of discretization points on the boundary of the domain, and corresponds to linear complexity in the number of uniformly sampled evaluation points. A kernel-independent fast summation algorithm is used to accelerate the evaluation of the discretized integral operators. We describe a high-order accurate method for evaluating the solution at arbitrary points inside the domain, including points close to the domain boundary. We demonstrate how our solver, combined with a regular-grid spectral solver, can be applied to problems with distributed sources. We present numerical results for the Stokes, Navier, and Poisson problems.