Friday, March 10, 2023 - 09:45 in H2
A sinc-function based numerical method for the Dirichlet problem with fractional Laplacian
A talk in the Nonlocal Equations: Analysis and Numerics 2023 series by
Patrick Dondl from Freiburg
| Abstract: |
We introduce a spectral method to approximate the fractional Laplacian with zero exterior condition. Our approach is based on interpolation by tensor products of sinc-functions, which combine a simple representation in Fourier-space with fast enough decay to suitably approximate the bounded support of solutions to the Dirichlet problem. This yields a numerical complexity of $\mathcal{O}(N \log N)$ for the application of the operator to a discretization with $N$ degrees of freedom. Iterative methods can then be employed to solve the fractional partial differential equations with exterior Dirichlet condition. We show a number of example applications and prove a convergence rate that is in line with rates for finite element based approaches. This is joint work with Ludwig Striet (Freiburg) and Harbir Antil (Fairfax, VA)
Within the CRC this talk is associated to the project(s): A7 |
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