Date:

Monday, December 10, 2007,
11:00 am - 12:00 pm.

Place:

Mathematics Conference Room 626, UCD Building, 1250 14th St., Denver.

Speaker:

Jakub Šístek.

Affiliation:

Department of Mathematics, Faculty of Mechanical Engineering, Czech Technical University in Prague.

Title:

On parallel implementation of BDDC using multifrontal solver MUMPS.

Abstract:

The presentation covers an ongoing effort to efficiently implement the Balancing Domain Decomposition with Constraints method (BDDC) for solving large systems of equations arising from linear elasticity analyses. The BDDC method is seen as a preconditioner in PCG method. Within this framework, solution to an inexact problem is found by a direct solver. In our latest formulation of the method, decomposition of the domain just gives us a way to construct the inexact problem. It is done by relaxing most (but not all) the continuity requirements on the solution among subdomains and thus "inflating" the space where the problem is defined. We end up with a larger matrix than the one of the original problem, which is then solved exactly. However, the simple structure of this matrix makes the solution by a direct method easy and thus possible to use it for preconditioning. In finite element terminology, the larger problem is constructed by so called "partial assembly", a process that does not assemble the matrix at most of the interface nodes among subdomains. The current version of the implementation is based on the Multifrontal Massively Parallel Solver (MUMPS), an interesting open source package for solving linear equations that will be in short introduced.

Short Bio:

Jakub has visited us since September and will be leaving and the end of December. He has mainly collaborated with Jan Mandel and Bedrich Sousedík on domain decomposition methods. In 2005, Jakub obtained his M.S. from the Faculty of Mechanical Engineering CTU (in Prague, CZ) in Mathematical Modeling in Technology. His master thesis was entitled "Stabilization of finite element method for solving incompressible viscous flows" and his advisor was Prof. Pavel Burda. His M.S thesis has been awarded second position for the 2005 Babuska prize. He is pursuing a Ph.D. under Prof Pavel Burda's advisory since 2005 and hopes to propose a thesis next year. Some other info might be found on Jakub's personal web page at CTU: http://marian.fsik.cvut.cz/~jsistek