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Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow

D. Pepper
D. Pepper
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A. Kassab
A. Kassab
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E. Divo
E. Divo
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ASME Press
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The BEM came of age in the early 1960’s when its indirect formulation and implementation was developed in the aerospace industry in the pioneering work of Hess and Smith into the panel method and in the work of Jaswon in potential theory. The indirect BEM refers to the fact that the unknowns appearing in the discretized integral equations are indirectly related to the field variable. For instance, in panel methods, the magnitudes strengths of points sources, sinks, vortices or doublets at sought on the boundary to determine the potential, and these quantities have no physical meaning. As a matter of fact, the concepts underlying the indirect BEM actually may be thought to date back to the developments of the Prandtl lifting line theory where horseshoe vortices of appropriate strengths were superimposed along the span of a wing to provide the effective flow field and lift.

A Familiar Example: Green’s Third Identity for Potential Problems
The 2D Heat Conduction Problem
Generating the Integral Equation: Weighting Function and Green’s Second Identity
Analytical Solution: Green’s Function Method and the Auxiliary Problem
Numerical Solution: The BEM and the Boundary Integral Equation
Appendix A
Derivation of the Green’s Function for the 2D Problem in a Square
Appendix B
Derivation of the Green’s Free Space (Fundamental) Solution to the Laplace Equation
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