An automatic PML for acoustic finite element simulations in convex domains of general shape

We address the efficient finite element solution of exterior acoustic problems with truncated computational domains surrounded by perfectly matched layers (PMLs). The PML is a popular non-reflecting technique, which combines accuracy, computational efficiency and geometric flexibility. Unfortunately, the effective implementation of the PML for generally-shaped convex domains 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 called 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 effective implementation relies on a simple modification of the Jacobian matrix in the element-wise integrals. The AML implementation is validated and compared to other implementation strategies using numerical benchmarks in two and three dimensions, considering computational domains with regular and non-regular 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.