High-order 2D mesh curving methods with a piecewise linear target and application to Helmholtz problems. (December 2018) - Ziel, V.S.; Bériot, H.; Atak, O.; Gabard, G.
Abstract: High-order simulation techniques typically require high-quality curvilinear meshes. In most cases, mesh curving methods assume that the exact geometry is known. However, in some situations only a fine linear FEM mesh is available and the connection to the CAD geometry is lost. In other applications, the geometry may be represented as a set of scanned points. In this paper, two curving methods are described that take a piecewise fine linear mesh as input: a least squares approach and a continuous optimization in the H 1 -seminorm. Hierarchic, modal shape functions are used as basis for the geometric approximation. This approach allows to create very high-order curvilinear meshes efficiently ( q > 4 ) without having to optimize the location of non-vertex nodes. The methods are compared on two test geometries and then used to solve a Helmholtz problem at various input frequencies. Finally, the main steps for the extension to 3D are outlined. Highlights: The effect of geometric inaccuracy on numerical error is assessed for Helmholtz scattering problems. The importance of high order boundary representation for Helmholtz simulations is shown. Nodal and modal curving methods are compared for linear target meshes. Modally curved meshes look advantageous for Helmholtz scattering simulations.