Setembro 2019 vol. 6 num. 1 - X Encontro Científico de Física Aplicada

Artigo completo - Open Access.

# Acoplamento do Método de Integração Radial com a Técnica de Elementos de Contorno por Interpolação Direta na solução de problemas de Helmholtz

### Serafim, L. D. B.; Loeffler, C. F.; Pinheiro, V. P.;

##### Artigo completo:

This paper shows the combination of two boundary element techniques whose the principal aim is the transformation of domain integrals into boundary integrals: the radial integration method (RIM) and the direct integration with radial basis method (DIBEM). Rim performs this transformation using a suitably change of variables. When is used in problems with unknown variables, the RIM usually requires the radial basis functions as auxiliary resource, following a similar procedure to the Dual Reciprocity model, in which the primal variable is interpolated. Concerning DIBEM, its main feature is to interpolate the complete kernel of the domain integral, including not only the primal variable but the fundamental solution as well. Here, the RIM is used to substitute the primitive auxiliary interpolation function employed exclusively to transform the domain integral into boundary integral in the DIBEM approach. Evaluation of the efficacy of the proposed composition is done solving the Helmholtz Equation, including the direct frequency response and the eigenvalue problem. The expected advantages are confirmed by numerical tests performed: the computational cost is strongly reduced and the increase in accuracy is meaningful improved, particularly if simpler meshes are used.

##### Artigo completo:

This paper shows the combination of two boundary element techniques whose the principal aim is the transformation of domain integrals into boundary integrals: the radial integration method (RIM) and the direct integration with radial basis method (DIBEM). Rim performs this transformation using a suitably change of variables. When is used in problems with unknown variables, the RIM usually requires the radial basis functions as auxiliary resource, following a similar procedure to the Dual Reciprocity model, in which the primal variable is interpolated. Concerning DIBEM, its main feature is to interpolate the complete kernel of the domain integral, including not only the primal variable but the fundamental solution as well. Here, the RIM is used to substitute the primitive auxiliary interpolation function employed exclusively to transform the domain integral into boundary integral in the DIBEM approach. Evaluation of the efficacy of the proposed composition is done solving the Helmholtz Equation, including the direct frequency response and the eigenvalue problem. The expected advantages are confirmed by numerical tests performed: the computational cost is strongly reduced and the increase in accuracy is meaningful improved, particularly if simpler meshes are used.

Palavras-chave: Helmholtz Equation; Eigenvalue Problems; Boundary Element Method; Radial Integration; Direct Tnterpolation,

Palavras-chave: Helmholtz Equation; Eigenvalue Problems; Boundary Element Method; Radial Integration; Direct Tnterpolation,

DOI: 10.5151/ecfa2019-17

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##### Como citar:

Serafim, L. D. B.; Loeffler, C. F.; Pinheiro, V. P.; "Acoplamento do Método de Integração Radial com a Técnica de Elementos de Contorno por Interpolação Direta na solução de problemas de Helmholtz", p. 74-79 . In: Anais do X Encontro Científico de Física Aplicada. São Paulo: Blucher, 2019.
ISSN 2358-2359, DOI 10.5151/ecfa2019-17

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