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In this paper, we extend the reduced-basis methods developed earlier for waveequations to goal-oriented wave equations with affine parameter dependence. Theessential new ingredient is the dual (or adjoint) problem and the use of itssolution in a sampling procedure to pick up "goal-orientedly" parametersamples. First, we introduce the reduced-basis recipe --- Galerkin projectiononto a space $Y_N$ spanned by the reduced basis functions which are constructedfrom the solutions of the governing partial differential equation at severalselected points in parameter space. Second, we propose a new "goal-oriented"Proper Orthogonal Decomposition (POD)--Greedy sampling procedure to constructthese associated basis functions. Third, based on the assumption of affineparameter dependence, we use the offline-online computational proceduresdeveloped earlier to split the computational procedure into offline and onlinestages. We verify the proposed computational procedure by applying it to athree-dimensional simulation dental implant problem. The good numerical resultsshow that our proposed procedure performs better than the standard POD--Greedyprocedure in terms of the accuracy of output functionals.

A goal-oriented reduced basis method for the wave equation in inverse analysis