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An Optimal successive overrelaxtion technique for solving second order finite difference equations for triangular meshes
Author(s) -
Tomlin Geoffrey R.
Publication year - 1972
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620050104
Subject(s) - polygon mesh , mathematics , finite difference , finite difference method , convergence (economics) , triangular matrix , rate of convergence , matrix (chemical analysis) , finite element method , triangle mesh , coefficient matrix , mathematical optimization , finite difference coefficient , mathematical analysis , geometry , computer science , mixed finite element method , structural engineering , eigenvalues and eigenvectors , physics , materials science , engineering , pure mathematics , economic growth , composite material , quantum mechanics , economics , invertible matrix , channel (broadcasting) , computer network
A finite difference method for analyzing two‐dimensional steady‐state potential flow in a zoned anisotropic material is described. A triangular mesh is used is as to avoid difficulties often occurring in the more familiar rectangular mesh where fractional mesh spaces exist at irregular boundaries. The system of finite difference equations based on the triangular mesh is assembled in a form such that the coefficient matrix is 3‐cylic and consistently ordered. 1, 2 This enables the optimum accelerating factor for successive overrelaxation to be closely estimated. Since the rate of convergence to the solution, and consequently the efficiency of the method, increases rapidly as the accelerating factor tends towards its optimum value, close determination of the optimum is important. The method is particularly suitable for problems having large numbers of nodes. Examples of the method on specific problems are given. The solution accuracy is assessed and has been found acceptable.