Vol. 9, No. 3, 2014

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ISSN: 1559-3959
B-splines collocation eigenanalysis of 2D acoustic problems

Christopher G. Provatidis

Vol. 9 (2014), No. 3, 259–285
Abstract

We continue our research on the performance of CAD-based global approximation to the analysis of 2D acoustic problems. In addition to previous “boundary-only” Coons and transfinite Gordon–Coons interpolations, we now investigate the quality of the solution when utilizing “tensor product B-splines” interpolation. For the latter, we propose a global collocation method that is successfully compared with the well known Galerkin–Ritz formulation. Particular attention is paid to the handling of Neumann boundary conditions as well as to the role of multiplicity of internal knots. The theory is supported by two numerical examples, one for a rectangular and the other for a circular acoustic cavity in which the approximate solution rapidly converges towards the exact solution.

Keywords
B-splines, Galerkin–Ritz, global collocation, eigenvalues, CAD/CAE
Milestones
Received: 19 October 2011
Revised: 10 March 2014
Accepted: 21 March 2014
Published: 4 October 2014
Authors
Christopher G. Provatidis
School of Mechanical Engineering, Mechanical Design and Control Systems Department
National Technical University of Athens
Heroon Polytechniou 9
Zografou Campus
157 80 Athens
Greece