Solving elliptic problems using ELLPACK
Solving elliptic problems using ELLPACK
Numerical Solution of Helmholtz's Equation by Implicit Capacitance Matrix Methods
ACM Transactions on Mathematical Software (TOMS)
High-Order Fast Elliptic Equation Solvers
ACM Transactions on Mathematical Software (TOMS)
Algorithm 593: A Package for the Helmholtz Equation in Nonrectangular Planar Regions
ACM Transactions on Mathematical Software (TOMS)
Algorithm 685: a program for solving separable elliptic equations
ACM Transactions on Mathematical Software (TOMS)
Algorithm 651: Algorithm HFFT–high-order fast-direct solution of the Helmholtz equation
ACM Transactions on Mathematical Software (TOMS)
Matrix decomposition algorithms for elliptic boundary value problems: a survey
Numerical Algorithms
Compact optimal quadratic spline collocation methods for the Helmholtz equation
Journal of Computational Physics
A Fourth Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Square
Journal of Scientific Computing
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We present fourth-order-accurate compact discretizations of the Helmholtz equation on rectangular domains in two and three dimensions with any combination of Dirichlet, Neumann, or periodic boundary conditions. The resulting systems of linear algebraic equations have the same block-tridiagonal structure as traditional central differences and hence may be solved efficiently using the Fourier method. The performance of the method for a variety of test cases, including problems with nonsmooth solutions, is presented. The method is seen to be roughly twice as fast as deferred corrections and, in many cases, results in a smaller discretization error.