Multilevel Spectral Domain Decomposition

Multilevel Balancing Domain Decomposition at Extreme Scales

In this talk we will summarize the steps we have followed towards highly scalable solver codes tailored for Finite Element (FE) analysis in our simulation software FEMPAR. In the first part of the talk, we will introduce the Balancing Domain Decomposition by Constraints (BDDC) preconditioning approach and some of the salient properties that make it highly suitable for extreme scale solver desig...

Multilevel domain decomposition for electronic structure calculations

We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and Density Functional Theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of domain decomposition methods. Using this approach, calculations have been successfully performed on several linear polymer chains con...

Domain Decomposition and Multilevel Methods In

Protein domain decomposition using spectral graph partitioning

Proteins usually consist of several structural domains which play an important role in the classification and analysis of them. As the number of known protein structures grows at an exponential rate, a computer-aided domain decomposition of proteins becomes desirable. We present three different decomposition methods in this report. They are based on a graph representation of the proteins. These...

A Multilevel Preconditioner for Domain Decomposition Boundary Systems

In this note, we consider multilevel preconditioning of the reduced boundary systems which arise in non-overlapping domain decomposition methods. It will be shown that the resulting preconditioned systems have condition numbers which are bounded in the case of multilevel spaces on the whole domain and grow at most proportional to the number of levels in the case of multilevel boundary spaces wi...