Approximation of Periodic PDE Solutions with Anisotropic Translation Invariant Spaces
Provides a theoretical framework for FFT-based methods in computational mechanics, but the contribution is incremental.
The paper unifies FFT-based discretization methods for periodic PDEs into a common framework and extends them to anisotropic lattices, showing numerical benefits. Finite element methods are recovered as a special case.
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.