GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Coupling of Finite Elements and Boundary Elements in Electromagnetic Scattering
SIAM Journal on Numerical Analysis
Perfectly Matched Layers for the Convected Helmholtz Equation
SIAM Journal on Numerical Analysis
Regularized Combined Field Integral Equations
Numerische Mathematik
SIAM Journal on Scientific Computing
Stabilized FEM-BEM Coupling for Helmholtz Transmission Problems
SIAM Journal on Numerical Analysis
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We consider the convected Helmholtz equation modeling linear acoustic propagation at a fixed frequency in a subsonic flow around a scattering object. The flow is supposed to be uniform in the exterior domain far from the object, and potential in the interior domain close to the object. Our key idea is the reformulation of the original problem using the Prandtl-Glauert transformation on the whole flow domain, yielding (i) the classical Helmholtz equation in the exterior domain and (ii) an anisotropic diffusive PDE with skew-symmetric first-order perturbation in the interior domain such that its transmission condition at the coupling boundary naturally fits the Neumann condition from the classical Helmholtz equation. Then, efficient off-the-shelf tools can be used to perform the BEM-FEM coupling, leading to two novel variational formulations for the convected Helmholtz equation. The first formulation involves one surface unknown and can be affected by resonant frequencies, while the second formulation avoids resonant frequencies and involves two surface unknowns. Numerical simulations are presented to compare the two formulations.