The near-field steady state scattered potential around a rigid scatterer subjected to plane incident wave is computed using the finite element method with radiation boundary dampers on a finite truncation boundary. Then the solution in the outer domain is sought in the form of an eigenfunction expansion and the expansion coefficients are obtained using the finite element solution on the truncation boundary as Dirichlet boundary condition. The scattered far-field pattern is derived from this solution for prolate spheroid and hemispherically capped cylinder problems.

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