Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions
SIAM Journal on Numerical Analysis
Fast evaluation of electro-static interactions in multi-phase dielectric media
Journal of Computational Physics
A fast direct solver for scattering problems involving elongated structures
Journal of Computational Physics
Krylov deferred correction accelerated method of lines transpose for parabolic problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A Fast Direct Solver for a Class of Elliptic Partial Differential Equations
Journal of Scientific Computing
Faster convergence and higher accuracy for the Dirichlet-Neumann map
Journal of Computational Physics
Integral equation methods for elliptic problems with boundary conditions of mixed type
Journal of Computational Physics
A fast algorithm for the inversion of general Toeplitz matrices
Computers & Mathematics with Applications
Efficient discretization of Laplace boundary integral equations on polygonal domains
Journal of Computational Physics
Journal of Computational Physics
Fast and accurate numerical methods for solving elliptic difference equations defined on lattices
Journal of Computational Physics
Fast integral equation methods for the modified Helmholtz equation
Journal of Computational Physics
Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices
SIAM Journal on Matrix Analysis and Applications
A fast direct solver for the integral equations of scattering theory on planar curves with corners
Journal of Computational Physics
A fast direct solver for elliptic problems on general meshes in 2D
Journal of Computational Physics
Journal of Computational Physics
A Fast Randomized Algorithm for Computing a Hierarchically Semiseparable Representation of a Matrix
SIAM Journal on Matrix Analysis and Applications
Journal of Computational Physics
Second kind integral equation formulation for the modified biharmonic equation and its applications
Journal of Computational Physics
Journal of Scientific Computing
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
Journal of Computational Physics
Journal of Computational Physics
Advances in Computational Mathematics
Hi-index | 31.54 |
We describe an algorithm for the direct solution of systems of linear algebraic equations associated with the discretization of boundary integral equations with non-oscillatory kernels in two dimensions. The algorithm is ''fast'' in the sense that its asymptotic complexity is O(n), where n is the number of nodes in the discretization. Unlike previous fast techniques based on iterative solvers, the present algorithm directly constructs a compressed factorization of the inverse of the matrix; thus it is suitable for problems involving relatively ill-conditioned matrices, and is particularly efficient in situations involving multiple right hand sides. The performance of the scheme is illustrated with several numerical examples. rformance of the scheme is illustrated with several numerical examples. ples.