CMMEXP
CMMPAK - the capacitance matrix software package The capacitance matrix method (CMM) extends the usefulness of fast elliptic solvers to non-rectangular regions. An iterative variant of CMM developed by D. P. O’Leary and O. Widlhund [Math. Comput. 33, 849-879 (1979; Zbl 0407.65047)] and the author’s paper [ACM Trans. Math. Software 5, 36-49 (1979; Zbl 0394.65029)] makes use of the fact that only a product of the capacitance matrix C and a given vector is required (without any explicit knowledge of the matrix C) and this product can be obtained essentially at the cost of a fast solver. The author presents the outline of the existing CMM package in 2D. For details see the author’s paper, ibid. 9, 117-124 (1983; Zbl 0503.65064). The package consists of three solvers: CMMIMP, CMMEXP and CMMSIX. Each of these solvers computes the finite difference approximation to the solution of the Helmholtz equation in cartesian coordinates -Δu(x,y)+cu(x,y)=f(x,y) on a non-rectangular 2D region. Here Δ is the Laplacian and c is a real constant. On the boundary of this region either the solution (Dirichlet condition) or the normal derivative of the solution is specified (Neumann condition).
(Source: http://dl.acm.org/)
This software is also peer reviewed by journal TOMS.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 5 articles , 1 standard article )
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Sorted by year (- Feng, Hongsong; Zhao, Shan: FFT-based high order central difference schemes for three-dimensional Poisson’s equation with various types of boundary conditions (2020)
- Cummins, P. F.; Vallis, G. K.: Algorithm 732: Solvers for self-adjoint elliptic problems in irregular two-dimensional domains (1994)
- Boisvert, Ronald F.: A fourth-order-accurate Fourier method for the Helmholtz equation in three dimensions (1987)
- Proskurowski, Wlodzimierz: CMMPAK - the capacitance matrix software package (1984)
- Kannan, R.; Proskurowski, W.: A numerical method for the nonlinear Neumann problem (1983)