Corner treatments for high-order local absorbing boundary conditions in high-frequency acoustic scattering

International audienceThis paper deals with the design and validation of accurate local absorbing boundary conditions set on convex polygonal and polyhedral computational domains for the finite element solution of high-frequency acoustic scattering problems. While high-order absorbing boundary conditions (HABCs) are accurate for smooth fictitious boundaries, the precision of the solution drops in the presence of corners if no specific treatment is applied. We present and analyze two strategies to preserve the accuracy of Padé-type HABCs at corners: first by using compatibility relations (derived for right angle corners) and second by regularizing the boundary at the corner. Exhaustive numerical results for two- and three-dimensional problems are reported in the paper. They show that using the compatibility relations is optimal for domains with right angles. For the other cases, the error still remains acceptable, but depends on the choice of the corner treatment according to the angle

A Symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

International audienceA general symmetric Trefftz Discontinuous Galerkin method is builtfor solving the Helmholtz equation with piecewise constant coefficients.The construction of the corresponding local solutions to the Helmholtzequation is based on a boundary element method. A series of numericalexperiments displays an excellent stability of the method relativelyto the penalty parameters, and more importantly its outstanding abilityto reduce the instabilities known as the pollution effect inthe literature on numerical simulations of long-range wave propagation