5 papers
Numerical Approximation of the logarithmic Laplacian via sinc-basis
Patrick Dondl, Ludwig Striet
In recent works, the authors of this chapter have shown with co-authors how a basis consisting of dilated and shifted -functions can be used to solve fractional partia…
Convex-concave splitting for the Allen-Cahn equation leads to -slow movement of interfaces
Patrick Dondl, Akwum Onwunta, Ludwig Striet +1
The convex-concave splitting discretization of the Allen-Cahn is easy to implement and guaranteed to be energy decreasing even for large time-steps. We analyze the time-stepping sc…
Arbitrary precision computation of hydrodynamic stability eigenvalues
Patrick Dondl, Ludwig Striet, Brian Straughan
We show that by using higher order precision arithmetic, i.e., using floating point types with more significant bits than standard double precision numbers, one may accurately comp…
Analysis of a sinc-Galerkin Method for the Fractional Laplacian
Harbir Antil, Patrick Dondl, Ludwig Striet
We provide the convergence analysis for a sinc-Galerkin method to solve the fractional Dirichlet problem. This can be understood as a follow-up of an earlier article by the same au…
Approximation of Integral Fractional Laplacian and Fractional PDEs via sinc-Basis
Harbir Antil, Patrick Dondl, Ludwig Striet
Fueled by many applications in random processes, imaging science, geophysics, etc., fractional Laplacians have recently received significant attention. The key driving force behind…