Iterative thresholding low-rank time integration for high-dimensional problems

arXiv (Cornell University)

Abstract

This work analyzes a method for time integration of high-dimensional linear Schrödinger-type problems based on hierarchical tensor approximations. In particular, this method provides a balance between error bounds and associated approximation ranks, using a scheme for iterative refinement with soft thresholding of tensors. The practical performance of the method is illustrated by numerical tests on coupled oscillators.

Authors 4

1. Markus Bachmayr Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Templer- graben 55 , 52062 Aachen , Germany

2. Tianyu Jin Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Templer- graben 55 , 52062 Aachen , Germany

3. Polina Sachsenmaier
4. Federico Vismara Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Templer- graben 55 , 52062 Aachen , Germany