scholarly journals An FFT Based Fast Poisson Solver on Spherical Shells

2011 ◽  
Vol 9 (3) ◽  
pp. 649-667 ◽  
Author(s):  
Yin-Liang Huang ◽  
Jian-Guo Liu ◽  
Wei-Cheng Wang
Keyword(s):  
Fourier Transform ◽  
Differential Operator ◽  
Constant Coefficient ◽  
Radial Part ◽  
Spherical Shells ◽  
Numerical Examples ◽  
Poisson Solver ◽  
The Poisson Equation ◽  
Change Of Variable ◽  
Fast Poisson Solver

AbstractWe present a fast Poisson solver on spherical shells. With a special change of variable, the radial part of the Laplacian transforms to a constant coefficient differential operator. As a result, the Fast Fourier Transform can be applied to solve the Poisson equation with operations. Numerical examples have confirmed the accuracy and robustness of the new scheme.

A Domain-Decomposed Fast Poisson Solver on a Rectangle

1987 ◽  
Vol 8 (1) ◽  
pp. s14-s26 ◽  
Author(s):  
Tony F. Chan ◽  
Diana C. Resasco
Keyword(s):  
Poisson Solver ◽  
Fast Poisson Solver

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

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