A DOMAIN DECOMPOSITION SOLVER FOR LARGE SCALE TIME-HARMONIC FLOW ACOUSTICS PROBLEMS

This article is devoted to the numerical resolution of high frequency time-harmonic flow acoustic problems. We use a substructured optimized nonoverlapping Schwarz domain decomposition method as a solver in order to significantly reduce the memory footprint required by such problems. To accelerate the convergence of the iterative solver we develop suitable transmission conditions based on local approximations of the Dirichlet-to-Neumann operator, taking into account convection by strongly nonuniform mean flows. The development relies on the construction of absorbing boundary conditions through microlocal analysis and pseudodifferential calculus. We analyze the potential of the method in academic settings and subsequently propose a robust domain decomposition methodology for problems of industrial relevance modeled by the Pierce linearized acoustic operator. The algorithm is implemented in an open-source high-order finite element library. It allows solving challenging three-dimensional problems with more than one billion high-order unknowns, by taking full advantage of modern computer architectures.