Seminar

We introduce a spectral method to approximate PDEs involving 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 O(NlogN) for the application of the operator to a discretization with N degrees of freedom.

High order methods are known to be unstable when applied to nonlinear conservation laws whose solutions exhibit shocks and turbulence. Entropy stable schemes address this instability by ensuring that physically relevant solutions satisfy a semi-discrete entropy inequality independently of numerical resolution or solution regularization and shock capturing.

Zoom Meeting ID: 973 0230 7263

Zoom Meeting ID: 973 0230 7263