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A gradient-based method for shape optimization problems constrained by theacoustic wave equation is presented. The method makes use of high-orderaccurate finite differences with summation-by-parts properties on multiblockcurvilinear grids to discretize in space. Representing the design domainthrough a coordinate mapping from a reference domain, the design shape isobtained by inversion of the discretized coordinate map. The adjoint stateframework is employed to efficiently compute the gradient of the lossfunctional. Using the summation-by-parts properties of the finite differencediscretization, we prove stability and dual consistency for the semi-discreteforward and adjoint problems. Numerical experiments verify the accuracy of thefinite difference scheme and demonstrate the capabilities of the shapeoptimization method on two model problems with real-world relevance.

Acoustic shape optimization using energy stable curvilinear finite differences