A new separation of variables method for complex geometries

Shankar, PN (2005) A new separation of variables method for complex geometries. Current Science, 88 (2). pp. 266-269. ISSN 0011-3891

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Abstract

A procedure has recently been discovered by which the classical separation of variables method can be extended to solve linear boundary value problems for complex geometries. In brief, the procedure consists of embedding the given complex geometry in a larger domain on which complete sets of eigenfunctions exist The latter are then used to represent the field in the given complex geometry. Since the eigenfunctions are not in general orthogonal on the given boundary, the unknown coefficients are evaluated by a least squares procedure. The details in a specific example, that of two-dimensional heat conduction in a solid of complex shape, are given so that the method can be easily understood and applied. In this case the field satisfies Laplace's equation with given data on the boundary. Since the method is simple and easy to apply, it provides an efficient, extremely accurate and elegant alternative to brute force computation. It is hoped that the method will be taught to college and university students who should have no difficulty in grasping it.

Item Type: Journal Article
Uncontrolled Keywords: Boundary-value problems;Eigenvalues and eigenfunctions;Heat conduction;Laplace equations;Least squares approximations
Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
Division/Department: Computational and Theoretical Fluid Dynamics Division
Depositing User: Mrs Manoranjitha M D
Date Deposited: 22 Mar 2007
Last Modified: 24 May 2010 09:55
URI: http://nal-ir.nal.res.in/id/eprint/4116

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