Two major issues affecting the solution of Boundary Integral Equations via collocation methods (such as the Boundary Element Method) are the high memory requirement/usage for large problems resulting, \textit{e.g.}, in high frequency acoustics, and the need for regularisation due to the non-uniqueness of the solution for the so-called spurious frequencies for exterior problems. The first problem can be effectively mitigated introducing methods such as the Adaptive-Cross-Approximation technique, which builds a hierarchical block-wise approximation of the matrix arising from the discretisation of the BIE, with a combination of low-rank approximated and fully populated blocks, reducing the storage requirement. Typical strategies to address the regularisation of the solution are the CHIEF points and the Burton \&amp; Miller methods. More recently, the Dual Surface method has been introduced and adapted for acoustics. The Dual Surface method is a regularization technique that does not increase the problem size and avoids the evaluation of hyper--singular integrals, combining the advantages of the Burton \&amp; Miller and CHIEF methods, requiring, however, the evaluation of an increased number of integrals for each matrix entry. This drawback is partially compensated when using the ACA partial pivoting algorithm, which limits the number of entries to be evaluated when building the system matrix. In this paper, the implementation of the Dual Surface method will be discussed for the classic Kirchhoff-Helmholtz integral equation and for a BIE for the sound scattered by moving bodies based on the Ffowcs Williams \&amp; Hawkings equation.

Palma, G., Burghignoli, L., Marchese, V., Iemma, U. (2022). IMPLEMENTATION OF A DUAL SURFACE REGULARIZATION TECHNIQUE IN ACA-BASED BEM SOLVER. In Proceedings of the 28th International Congress on Sound and Vibration. ICSV28 Local Committee in Singapore.

### IMPLEMENTATION OF A DUAL SURFACE REGULARIZATION TECHNIQUE IN ACA-BASED BEM SOLVER

#### Abstract

Two major issues affecting the solution of Boundary Integral Equations via collocation methods (such as the Boundary Element Method) are the high memory requirement/usage for large problems resulting, \textit{e.g.}, in high frequency acoustics, and the need for regularisation due to the non-uniqueness of the solution for the so-called spurious frequencies for exterior problems. The first problem can be effectively mitigated introducing methods such as the Adaptive-Cross-Approximation technique, which builds a hierarchical block-wise approximation of the matrix arising from the discretisation of the BIE, with a combination of low-rank approximated and fully populated blocks, reducing the storage requirement. Typical strategies to address the regularisation of the solution are the CHIEF points and the Burton \& Miller methods. More recently, the Dual Surface method has been introduced and adapted for acoustics. The Dual Surface method is a regularization technique that does not increase the problem size and avoids the evaluation of hyper--singular integrals, combining the advantages of the Burton \& Miller and CHIEF methods, requiring, however, the evaluation of an increased number of integrals for each matrix entry. This drawback is partially compensated when using the ACA partial pivoting algorithm, which limits the number of entries to be evaluated when building the system matrix. In this paper, the implementation of the Dual Surface method will be discussed for the classic Kirchhoff-Helmholtz integral equation and for a BIE for the sound scattered by moving bodies based on the Ffowcs Williams \& Hawkings equation.
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Palma, G., Burghignoli, L., Marchese, V., Iemma, U. (2022). IMPLEMENTATION OF A DUAL SURFACE REGULARIZATION TECHNIQUE IN ACA-BASED BEM SOLVER. In Proceedings of the 28th International Congress on Sound and Vibration. ICSV28 Local Committee in Singapore.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/426912
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