PERFORMANCE ANALYSYS OF THE DIRECT INTEGRATION TECHNIQUE FOR SOLVING EIGENVALUE PROBLEMS WITH NON- REGULAR DOMAINS

carlos friedrich loeffler¹; hercules de melo barcelos¹

¹ ufes

doi:10.20906/CPS/CILAMCE2017-0775

Resumo

The aim of this work is evaluate the performance of the Direct Interpolation Boundary Element Formulation (DIBEM) in the solution of Helmholtz problems that present non regular geometric shapes. Using the radial basis functions, the DIBEM approximates the non-self adjoint kernel of the domain integral equations, which appear in many partial differential equations of the mathematical, physics and engineering. Modeling the Helmholtz Equation, the DIBEM approximates the inertia term by a sequence of radial basis functions. The technique has been successfully used previously in Poisson and Helmholtz problems, considering regular geometries and taking analytical solutions as reference for performance evaluation. In this paper, the effects of slenderness of the domain and the introduction of grooves in the boundary are evaluated. Reference solutions are generated through simulation with the Finite Element Method using a fine mesh.

Palavras-chave: Boundary elements; Helmholtz's equation; Irregular geometric conformation