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The Boundary Element Method Using CAD-Based Macroelements

  • Christopher G. ProvatidisEmail author
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 256)

Abstract

This chapter deals with the numerical solution of three-dimensional boundary value problems using the Boundary Element Method (BEM) in conjunction with CAD-based macroelements. In more details, the boundary is discretized into a certain number of CAD-based patches (Coons, Gordon, Bernstein–Bézier, B-splines, NURBS, Barnhill, etc.), where both the geometry \({\mathbf{x}}(\xi ,\eta )\) and the variable \(U(x,y,z)\) are interpolated through the same CAGD formula. Each of the aforementioned patches is a single isoparametric (or isogeometric) macroelement to which a global approximation of the variable U is applied. The theory is accompanied with numerical results in elasticity problems and acoustics.

Keywords

Integral equation Betti-Maxwell Direct BEM Coons/transfinite patch Brebbia–Nardini Elasticity Sound radiation 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringNational Technical University of AthensAthensGreece

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