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Isogeometric indirect BEM solution based on virtual continuous sources placed directly on the boundary of 2D Helmholtz acoustic problems
Isogeometric indirect BEM solution based on virtual continuous sources placed directly on the boundary of 2D Helmholtz acoustic problems
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Date
2023
Authors
Ahmed Mostafa Shaaban
Cosmin Anitescu
Elena Atroshchenko
Timon Rabczuk
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Abstract
"An indirect boundary element method (BEM) based on isogeometric analysis (IGA) is proposed for 2D
Helmholtz acoustic problems using virtual continuous sources placed directly on the problem boundary. The
virtual sources form a virtual boundary identical to the main problem boundary. The proposed solution
couples the CAD model with the analysis model by approximating both the CAD model and the virtual
continuous sources with the same non-uniform rational B-spline functions (NURBS). Moreover, neither domain
discretization nor truncation boundaries at the far-field are required. This solution creates only one coefficient
matrix by directly arranging the linear system of equations.
The solution follows a collocation scheme on the boundaries based on Greville abscissae with offsets
wherever 𝐶0 continuity is encountered to permit an easy prediction for the normal directions and the free-terms
at the collocation points required in the cases of Neumann and Robin boundary conditions. It allows us also
to treat all integrals with standard Gauss quadrature points.
Several numerical examples for exterior and interior acoustic problems are discussed to verify the proposed
solution with comparisons to analytical solutions and previously published numerical results. These examples
prove the robustness of the proposed solution even for high wavenumbers, in contrast to the previous attempts
which implemented extensive investigations to find out the optimum place of the sources outside the domain
producing minimum errors. Furthermore, no fictitious eigenfrequency problem is observed for exterior acoustic
problems."
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Keywords
"Indirect BEM,
Acoustics,
Isogeometric analysis,
Collocation,
Continuous sources,
Meshless solution"