Coupling of finite element method with boundary algebraic equations
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Recently, a combined approach of CFIE--BAE has been proposed by authors for solving external scattering problems in acoustics. CFIE stands for combined-field integral equations, and BAE is the method of boundary algebraical equation. The combined method is, essentially, a discrete analogue of the boundary element method (BEM), having none of its disadvantages. Namely, due to the discrete nature of BAE one should not compute quadratures of oversingular integrals. Moreover, due to CFIE formulation, the method does not possess spurious resonances. However, the CFIE--BAE method has an important drawback. Since the modelling is performed in a regular discrete space, the shape of the obstacle should be assembled of elementary "bricks", so smooth scatterers (like spheres, cylinders, etc) are approximated with a poor accuracy. This loss of accuracy becomes the bottleneck of the method. Here this disadvantage is overcome. The CFIE--BAE method developed for regular meshing of the outer space is coupled in a standard way with a relatively small irregular mesh enabling one to describe the shape of the obstacle accurately enough.
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