GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
Journal of Computational Physics
Integral equation methods for Stokes flow and isotropic elasticity in the plane
Journal of Computational Physics
A direct adaptive Poisson solver of arbitrary order accuracy
Journal of Computational Physics
An Integral Equation Approach to the Incompressible Navier--Stokes Equations in Two Dimensions
SIAM Journal on Scientific Computing
Hybrid Gauss-Trapezoidal Quadrature Rules
SIAM Journal on Scientific Computing
A new version of the fast multipole method for screened Coulomb interactions in three dimensions
Journal of Computational Physics
A fast direct solver for boundary integral equations in two dimensions
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
An adaptive fast solver for the modified Helmholtz equation in two dimensions
Journal of Computational Physics
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
A meshless, spectrally accurate, integral equation solver for molecular surface electrostatics
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Fast integral equation methods for Rothe's method applied to the isotropic heat equation
Computers & Mathematics with Applications
A Boundary Integral Method for Computing the Dynamics of an Epitaxial Island
SIAM Journal on Scientific Computing
Second kind integral equation formulation for the modified biharmonic equation and its applications
Journal of Computational Physics
Hi-index | 31.45 |
We present integral equation methods for the solution to the two-dimensional, modified Helmholtz equation, u(x)-@a^2@Du(x)=0, in bounded or unbounded multiply-connected domains. We consider both Dirichlet and Neumann problems. We derive well-conditioned Fredholm integral equations of the second kind, which are discretized using high-order, hybrid Gauss-trapezoid rules. Our fast multipole-based iterative solution procedure requires only O(N) operations, where N is the number of nodes in the discretization of the boundary. We demonstrate the performance of our methods on several numerical examples, and we show that they have both the ability to handle highly complex geometry and the potential to solve large-scale problems.