An automatic perfectly matched layer for acoustic finite element simulations in convex domains of general shape

This article addresses the efficient finite element solution of exterior acoustic problems with truncated computational domains surrounded by perfectly matched layers (PMLs). The PML is a popular nonreflecting technique that combines accuracy, computational efficiency, and geometric flexibility. Unfortunately, the effective implementation of the PML for convex domains of general shape is tricky because of the geometric parameters that are required to define the PML medium. In this work, a comprehensive implementation strategy is proposed. This approach, which we call the automatically matched layer (AML) implementation, is versatile and fully automatic for the end-user. With the AML approach, the mesh of the layer is extruded, the required geometric parameters are automatically obtained during the extrusion step, and the practical implementation relies on a simple modification of the Jacobian matrix in the elementwise integrals. The AML implementation is validated and compared with other implementation strategies using numerical benchmarks in two and three dimensions, considering computational domains with regular and nonregular boundaries. A three-dimensional application with a generally shaped domain generated using a convex hull is proposed to illustrate the interest of the AML approach for realistic industrial cases.