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Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions. The model is formulated as a boundary value problem for the Helmholtz equation with a transparent boundary condition. Based on a duality argument technique, an a posteriori error estimate is derived for the finite element method with the truncated Dirichlet-to-Neumann boundary operator. The a posteriori error estimate...
A uniaxial perfectly matched layer (UPML) method is proposed for solving three-dimensional Helmholtz equation with multiple scatterers. The exterior domain is truncated to enclose each scatterer by a bounded domain individually. Based on reliable a posteriori error estimate, an efficient adaptive finite element algorithm is proposed to solve the multiple scattering problem. The efficiency of the adaptive...
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