Multigrid in Hierarchical Low Rank Tensor Formats

Explore a 29-minute conference talk on multigrid methods in hierarchical low rank tensor formats presented by Lars Grasedyck from RWTH Aachen University. Delve into the application of tensor methods for solving high-dimensional problems in physical and data sciences. Learn about the representation of high-dimensional tensors using hierarchical low rank formats and their role in solving systems of equations. Discover how classical multigrid convergence theory is adapted to work with low rank tensor formats, including the development of compatible smoothers and prolongation/restriction operators. Gain insights into the challenges of analyzing convergence rates for these methods and the potential benefits of combining multigrid techniques with tensor-based approaches. The talk covers topics such as the multigrid method, high-dimensional parametric dependency, model problems, nestedness, approximation techniques, and open questions in the field.

Intro
The Multigrid Method
High dimensional parametric dependency
Model problem
Model example
Solution
Preview
Nestedness
Approximation
Open Questions
Conclusion