Article
Automatically Matched Layer: Implementation and Evaluation (en)
* Presenting author
Abstract:
The Finite Element (FE) method is a common approach for numerically solving partial differential equations of physics, e.g. acoustic sound generation and radiation. A main challenge for this numerical method is to deal with free radiation. Currently, the most general and effective approach is the so-called Perfectly Matched Layer (PML) method, i.e., artificial layers with damping properties that match the wave impedance between the physical radiation domain and the non-physical damping domain. These layers can be realized for arbitrarily-shaped but convex boundaries by applying a complex coordinate stretch to the domain's outwards-normal direction, exploiting curvilinear coordinates. The coordinate transformation requires knowledge of geometric properties only retrievable from a sufficiently regular boundary. The so-called Automatically Matched Layer (AML) attaches the layer automatically by extruding the domain mesh at the finite-element solver level, extracting the geometric parameters using an empirically determined convention. We have implemented this approach in our in-house research software openCFS (www.opencfs.org). Here, we provide details of the formulation and its implementation in FEM. In addition, we investigated the implementation numerically, comparing simulations to analytical solutions in spherical-, cylindrical-, and cuboidal-shaped domains.