A fast algorithm for particle simulations
Journal of Computational Physics
Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
The electric potential of a macromolecule in a solvent: A fundamental approach
Journal of Computational Physics
Multipole translation theory for the three-dimensional Laplace and Helmholtz equations
SIAM Journal on Scientific Computing
A direct adaptive Poisson solver of arbitrary order accuracy
Journal of Computational Physics
Journal of Computational Physics
Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators
SIAM Journal on Scientific Computing
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
High-Order Fast Elliptic Equation Solvers
ACM Transactions on Mathematical Software (TOMS)
A New Fast-Multipole Accelerated Poisson Solver in Two Dimensions
SIAM Journal on Scientific Computing
Coulomb Interactions on Planar Structures: Inverting the Square Root of the Laplacian
SIAM Journal on Scientific Computing
Accelerating Fast Multipole Methods for the Helmholtz Equation at Low Frequencies
IEEE Computational Science & Engineering
A new version of the fast multipole method for screened Coulomb interactions in three 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,
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Integral and integrable algorithms for a nonlinear shallow-water wave equation
Journal of Computational Physics
Krylov deferred correction accelerated method of lines transpose for parabolic problems
Journal of Computational Physics
The Fourier regularization for solving the Cauchy problem for the Helmholtz equation
Applied Numerical Mathematics
Mathematics and Computers in Simulation
Journal of Computational Physics
Fast integral equation methods for the modified Helmholtz equation
Journal of Computational Physics
Fast integral equation methods for Rothe's method applied to the isotropic heat equation
Computers & Mathematics with Applications
A Fourier-series-based kernel-independent fast multipole method
Journal of Computational Physics
A Boundary Integral Method for Computing the Dynamics of an Epitaxial Island
SIAM Journal on Scientific Computing
A tuned and scalable fast multipole method as a preeminent algorithm for exascale systems
International Journal of High Performance Computing Applications
Second kind integral equation formulation for the modified biharmonic equation and its applications
Journal of Computational Physics
Hi-index | 31.48 |
In this paper, we present a fast multipole-accelerated integral equation method for solving the modified Helmholtz equation @Du(x-)-@b^2u(x-)=f(x-) in two dimensions. The method is direct, and unlike classical FFT based fast solvers, it allows for adaptive mesh refinement but with comparable amount of work per grid point. When the computational domain is rectangular, Dirichlet, Neumann, periodic, and free-space boundary conditions can be imposed analytically without the need to solve a system of linear equations. Several important features of the algorithm are discussed, including the use of precomputed tables, diagonal translation operators, and lattice sums to impose periodic boundary conditions. Numerical experiments show that, for a wide range of the parameter @b, the algorithm is stable and high-order accurate.