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
School of Mechanical Engineering,
Mechanical Design and Control Systems Department
National Technical University of Athens
Heroon Polytechniou 9
Zografou Campus
157 80 Athens
Greece
