Adaptive methods for high-dimensional eigenvalue problems and their computational complexity (C09#)

• Subject Area: Mathematics
• Term: from 2018 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 211504053

The subject of this project are numerical solvers for high-dimensional eigenvalue problems that combine adaptive discretisations with low-rank representations of coefficient sequences. A main objective is to establish optimality properties concerning discretisation cardinalities, arising tensor ranks, and total computational complexity. This requires in particular new techniques for a posteriori error estimation and for preconditioning with low-rank tensor decompositions. As a particular application, Schrödinger equations in occupation number representation are considered.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1060: The Mathematics of Emergent Effects
• Applicant Institution: Rheinische Friedrich-Wilhelms-Universität Bonn
• Project Head: Professor Dr. Markus Bachmayr