Fast Poisson solvers for problems with sparsity
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Algorithms are developed that allow considerable savings in computer storage as well as execution speed for fast Poisson solvers for certain applications where data is sparse and the solution is only required at relatively few mesh points.Abstract:
Fast Poisson solvers, which provide the numerical solution of Poisson's equation on regions that permit the separation of variables, have proven very useful in many applications. In certain of these applications the data is sparse and the solution is only required at relatively few mesh points. For such problems this paper develops algorithms that allow considerable savings in computer storage as well as execution speed. Results of numerical experiments are given.read more
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Journal ArticleDOI
A Parallel Fast Direct Solver for Block Tridiagonal Systems with Separable Matrices of Arbitrary Dimension
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Book
Capacitance Matrix Methods for the Helmholtz Equation on General Three-Dimensional Regions
TL;DR: A fast Poisson solver is developed which is numerically very stable even for indefinite Helmholtz equations, and a discrete analogue of classical potential theory is used as a guide in the design of rapidly convergent iterative methods.
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Matrix decomposition algorithms for elliptic boundary value problems: a survey
TL;DR: An overview of matrix decomposition algorithms (MDAs) for the solution of systems of linear equations arising when various discretization techniques are applied in the numerical solution of certain separable elliptic boundary value problems in the unit square is provided.
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Fictitious Domain Methods for the Numerical Solution of Two-Dimensional Scattering Problems
TL;DR: Fictitious domain methods for the numerical solution of two-dimensional scattering problems are considered and a special finite element method using nonmatching meshes is considered that uses the macro-hybrid formulation based on domain decomposition to couple polar and cartesian coordinate systems.
References
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Journal ArticleDOI
Methods in Computational Physics
The potential calculation and some applications
TL;DR: A potential calculation from given source distribution, including direct and iterative methods, error analysis, convergence, computer programs and applications in plasma physics, can be found in this article, where the authors present a detailed discussion.
Journal ArticleDOI
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
TL;DR: This work has developed a direct method of solution involving Fourier analysis which can solve Poisson''s equation in a square region covered by a 48 x 48 mesh in 0.9 seconds on the IBM 7090.
Journal ArticleDOI
On Direct Methods for Solving Poisson’s Equations
TL;DR: Some efficient and accurate direct methods are developed for solving certain elliptic partial difference equations over a rectangle with Dirichlet, Neumann or periodic boundary conditions.
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