Polynomial basis functions are the ubiquitous workhorse of high-order finite element methods, but their generality comes at a price of high computational cost and fragility in the face of underresolution. In this paper, a method is presented for constructing a posteriori tailored, generally nonpolynomial, basis functions for approximating a solution and computing outputs of a system of equations. This method is similar to solution-based adaptation, in which elements of the computational mesh are sized and oriented based on characteristics of the solution. The method takes advantage of existing infrastructure in high-order methods: the reference-to-global mapping used in constructing curved elements. By optimizing this mapping, elements are warped to make them ideally suited for representing a target solution or computing a scalar output from the solution. Guidelines on generating a good initial guess and choosing a generalized set of optimization parameters are provided to minimize tuning time and to introduce automation into the process. For scalar advection–diffusion and Navier–Stokes problems, it is shown that warped elements can offer significant accuracy benefits without increasing the degrees of freedom in the system.
Improving High-Order Finite Element Approximation Through Geometrical Warping
2016
Article (Journal)
English
Improving High-Order Finite Element Approximation Through Geometrical Warping
Online Contents | 2016
|Improving High-Order Finite Element Approximation Through Geometrical Warping
Online Contents | 2016
|