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04/10/01 Colloquium
DR. RICHARD BIALECKI
DEPARTMENT OF MECHANICAL, MATERIAL AND AEROSPACE ENGINEERING
UNIVERSITY OF CENTRAL FLORIDA
DEPARTMENT OF MECHANICAL, MATERIAL AND AEROSPACE ENGINEERING
UNIVERSITY OF CENTRAL FLORIDA
BEM Applied to Potential Problems
Abstract: The Boundary Element Method (BEM) is a general purpose numerical technique widely applied to solve problems of mathematical physics. The first step of this approach is the transformation of the original boundary value problem into an equivalent singular integral equation. In many cases this equation is defined only on the boundary of the domain and this reduces the dimensionality of the problem by one.The lecture addresses some basic issues of the technique: derivation of the integral equation, discretization using locally supported interpolation (shape) functions and nodal collocation, adaptive integration, and equation solving. More advanced problems such as the treatment of nonlinearities in both boundary conditions and material properties are discussed. This is illustrated by some solved industrial problems.
Special attention is given to coupling of conduction with radiation. The similarities of the integral equation of heat radiation with those arising in BEM when applied to potential problems are demonstrated. The possibility of using BEM software to discretize the heat radiation equation is discussed. An algorithm to deal with shadow zones is presented.
A consistent technique of solving the problem of heat transfer in bodies containing concave, self irradiating portion of the boundary along with a numerical technique to deal with these types of problems is developed in this lecture. A technique which addresses non-local boundary conditions arising in this case is discussed followed by some numerical examples.
The lecture concludes with a comparison of BEM with other numerical techniques pointing out the advantages and disadvantages of each technique and the field of their efficient application.
