Approximation of Periodic PDE Solutions with Anisotropic Translation Invariant Spaces

Abstract

We approximate the quasi-static equation of linear elasticity in translation invariant spaces on the torus. This unifies different FFT-based discretisation methods into a common framework and extends them to anisotropic lattices. We analyse the connection between the discrete solution spaces and demonstrate the numerical benefits. Finite element methods arise as a special case of periodised Box spline translates.

References in corpus (3)

• A numerical method for computing the overall response of nonlinear composites with complex microstructure
• An FFT-based Galerkin Method for Homogenization of Periodic Media
• A Framework for FFT-based Homogenization on Anisotropic Lattices