Book ChapterDOI
On fast poisson solvers and applications
Johann Schröder,Ulrich Trottenberg,Kristian Witsch +2 more
- pp 153-187
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The article was published on 1978-01-01. It has received 20 citations till now. The article focuses on the topics: Poisson distribution.read more
Citations
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Book ChapterDOI
Multigrid methods: Fundamental algorithms, model problem analysis and applications
Klaus Stüben,Ulrich Trottenberg +1 more
Journal ArticleDOI
Fast Numerical Solution of the Biharmonic Dirichlet Problem on Rectangles
TL;DR: The conjugate gradient method is shown to have a superlinear rate of convergence when applied to this formulation of the problem and is an order of magnitude more efficient than previously known methods with the possible exception of multi-grid.
Journal ArticleDOI
A multiscale Darcy–Brinkman model for fluid flow in fractured porous media
TL;DR: In this paper, the authors presented a reduced mathematical model for describing fluid flow in porous media featuring open channels or fractures, where the Darcy's law is assumed in the porous domain while the Stokes-Brinkman equations are considered in the fractures.
Journal ArticleDOI
Computing entries of the inverse of a sparse matrix using the FIND algorithm
TL;DR: An accurate and efficient algorithm, called fast inverse using nested dissection (FIND), for computing non-equilibrium Green's functions (NEGF) for nanoscale transistors has been developed and applied in the simulation of a novel dual-gate metal-oxide-semiconductor field-effect transistor (MOSFET) device structure.
Journal ArticleDOI
A note on MGR methods
TL;DR: In this paper, a class of special, highly efficient multigrid methods for solving h-discrete elliptic differential equations is introduced, which are characterized by intermediate grids (between the given h-grid and the 2h-grid) and by special fine-to-coarse and coarse-tofine grid transfer techniques.
References
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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
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.
Journal ArticleDOI
The direct solution of the discrete Poisson equation on irregular regions
TL;DR: There are several very fast direct methods which can be used to solve the discrete Poisson equation on rectangular domains as discussed by the authors, and these methods can be also used to treat problems on irregular regions.
Journal ArticleDOI
The Direct Solution of the Discrete Poisson Equation on a Rectangle
TL;DR: In this article, the authors provide a survey of direct methods for solving finite difference equations with rectilinear domains. But the authors do not discuss whether the methods are easily adaptable to more general regions, and to general elliptic partial differential equations.
Journal ArticleDOI
Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations.
Paul Concus,Gene H. Golub +1 more
TL;DR: In this paper, an iterative technique for the numerical solution of strongly elliptic equations of divergence form in two dimensions with Dirichlet boundary conditions on a rectangle is proposed. But the problem is suitably scaled before iteration, and Chebyshev acceleration is applied to improve convergence.