Seminar by Karsten Urban

Speaker

Karsten Urban (Universität Ulm)

Title

A reduced basis method for the Schrödinger equation

Date

  • March 14, 2023 16:00 CET+0100 (Europe/Rome)

  • March 14, 2023 11:00 EDT-0400 (US/Eastern)

  • March 14, 2023 10:00 CDT-0500 (US/Central)

  • March 14, 2023 08:00 PDT-0700 (US/Pacific)

Abstract

We present a well-posed ultra-weak space-time variational formulation for the time-dependent version of the linear Schrödinger equation with an instationary Hamiltonian. We prove optimal inf-sup stability and introduce a space-time Petrov-Galerkin discretization with optimal discrete inf-sup stability.

We show norm-preservation of the ultra-weak formulation. The inf-sup optimal Petrov-Galerkin discretization is shown to be asymptotically norm-preserving, where the deviation is shown to be in the order of the discretization. In addition, we introduce a Galerkin discretization, which has suboptimal inf-sup stability but exact norm-preservation.

Numerical experiments underline the performance of the ultra-weak space-time variational formulation, especially for non-smooth initial data.

Recording

Watch the recording on our YouTube channel.