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Iterative and direct methods for solving Poisson"s equation and their adaptability to ILLIAC IV

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Published by Dept. of Computer Science, University of Illinois at Urbana-Champaign in Urbana .
Written in English


  • Differential equations, Elliptic -- Data processing.,
  • Iterative methods (Mathematics) -- Data processing.,
  • Illiac computer -- Programming.

Book details:

Edition Notes

Includes bibliography.

Statementby James H. Ericksen.
LC ClassificationsQA76 .I4 no. 574, QA377 .I4 no. 574
The Physical Object
Pagination1 v. (various pagings)
ID Numbers
Open LibraryOL5027897M
LC Control Number73622718

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Abstract. The Poisson equation and its solution present a fundamental problem in the domain of the numerical solution of partial differential equations, and therefore it is the most important and most frequently encountered partial differential equation to be : Marián Vajteršic. In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical arises, for instance, to describe the potential field caused by a given charge or mass density distribution; with the potential field known, one can then calculate gravitational or electrostatic field.   The numerical solution of the three-dimensional Poisson equation with Dirichlet boundary conditions, which is of importance for a wide field of applications in Computational Physics and Theoretical Chemistry is considered using the method of finite elements for a model problem. The direct, the iterative and the factorized direct methods for solving the Cited by: 1. Direct methods: • use a clever numbering of the unknowns (not line by line but Iterative methods: • solve system line by line, but do this again and again ⇒ Jacobi or Gauss-Seidel relaxation, O(n4) • clever weghting of corrections ⇒ SOR (successive over-relaxation), O(n3) Poisson’s Equation in 2D a a.

At the end of comparing the results are observed using by alternating group explicit iterative methods converging to the analytical solution well rather than using SOR method. The initial value u (0) = 0 and the acceleration parameter r = 25 are taken to solve Poisson equation using by alternating group explicit iterative method and also Cited by: 6. Direct Methods for 1D problems! Elementary Iterative Methods! Iteration as Time Integration! Example! Boundary Conditions! Convergence of Iterative Methods!!1D Example!!Formal Discussion! Solving the Poisson equation! ij ijijijijijijS y fff x fff 2,,1,,1 2 1, 2,1, 2. Study on a Poisson’s Equation Solver Based On Deep Learning Technique Tao Shan,Wei Tang, Xunwang Dang, Maokun Li, Fan Yang, Shenheng Xu, and Ji Wu or iterative solvers such as the conjugate gradient method [2]. Typical methods in computational elec- Convolutional nueral network for solving Possion’s equation B. ConvNet model Neural Cited by: 6. Pergamon Press Ltd. FAST METHODS OF SOLVING POISSON'S EQUATION* N. S. BAKHVALOV and M. YU. OREKHOV Moscow (Received 5 June ) A METHOD is described whereby the solution of the Dirichlet problem for the Laplace mesh operator can be found in the mesh square 0 Cited by: 7.

Definitions and examples Complexity of integration Poisson’s problem on a disc Real functions Definition A real function f: [0,1] →R is calledcomputable, iff 1 f has a computable modulus of continuity. 2 the sequence of values of f on dyadic arguments is computable. It is File Size: KB. A numeric solution can be obtained by integrating equation (). The solution to the energy band diagram, the charge density, the electric field and the potential are shown in the figures below: Integration was started four Debye lengths to the right of the edge of the depletion region as obtained using the full depletion Size: 30KB. Iterative Methods. x x x x x x x x x x. 0 0 0 0 0 0. Sparse (large) Full-bandwidth Systems (frequent in practice) 0 0 0 0 0 0 0 0 0. Example of Iteration equation Analogous to iterative methods obtained for roots of equations, i.e. Open Methods: Fixed-point, Newton-Raphson, Secant. Iterative Methods are then efficient. 1 N N N ()N A x b A x b x File Size: KB. The Poisson equation arises in numerous physical contexts, including heat conduction, electrostatics, diffusion of substances, twisting of elastic rods, inviscid fluid flow, and water waves. Moreover, the equation appears in numerical splitting strategies for more complicated systems of PDEs, in particular the Navier - Stokes equations.