Mesh Free Frontier-Based Formulation (Mf3) for High Frequency Helmholtz Problems

Abstract eng:
We propose a new solution methodology for solving efficiently Helmholtz problems. The main features of the proposed method are (a) the method is a boundary type formulation, and (b) the approximation of the method does not require the use of mesh. For this reason, the method is named Mesh Free Frontier-based Formulation (MF3). The MF3 method distinguishes itself from existing methods by (a) the integral formulation does not incur any singular integrals, (b) Bessel-type functions are used to approximate locally the sought after field, and (c) the computational effort is mainly in the evaluation of integrals of Bessel-type functions on a boundary. Consequently, the resulting algebraic linear system incurs a dense matrix whose size however is very small compared to a finite element system. Numerical examples performed in the case of two-dimensional Helmholtz problems –wave-guide and scattering problems-- will be presented to illustrate the potential of the MF3 method for solving efficiently high frequency wave problems. These results reveal that the MF3 method does not exhibit any pollution effect.

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