An Optimal successive overrelaxtion technique for solving second order finite difference equations for triangular meshes
✍ Scribed by Geoffrey R. Tomlin
- Publisher
- John Wiley and Sons
- Year
- 1972
- Tongue
- English
- Weight
- 860 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0029-5981
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✦ Synopsis
Abstract
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.