ISSN:
1432-0924
Keywords:
Key Words: Inhomogeneous-Nonlinear Problem
;
Boundary Element Method
;
Integral Equation
;
Polynomial Approximation
;
Least Square Method
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Abstract A new formulation is presented in this paper for the boundary element analysis of a nonlinear potential-type problem wherein the linear term is governed by the Laplace operator, and the nonlinear term is a function of the spatial coordinates as well as the unknown solution function. The formulation aims to transform the domain integral relevant to the inhomogeneous-nonlinear term to a corresponding boundary integral. The proposed approach is different from the more popular schemes for the purpose, such as the Dual Reciprocity and Multiple Reciprocity Methods. The inhomogeneous-nonlinear term is first approximated by a polynomial in terms of the space coordinates with unknown coefficients. Integral equations on the selected points (referred to “computing points”) on the boundary as well as inside domain are employed to determine the above-mentioned unknown coefficients using the least square method. The number of computing points affects the accuracy of the result, which is discussed through some numerical examples in two-dimensional space.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004660050368
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