the Institute for Theoretical and Engineering Science
Department of Mathematics

University of Houston

Scientific Computing Seminar

Professor Jin-Fa Lee
ElectroScience Lab., ECE Department
The Ohio State University

A Non-Overlapping and Non-Conforming Domain Decomposition Technique
for Solving Large Electromagnetic Problems

Thursday, April 7, 2005
3:00 PM- 4:00 PM
Room 634 S&R1

Abstract: In this talk, I will discuss a recently developed domain decomposition (DD) methodology for solving large electromagnetic problems. Domain decomposition methods have been very popular in applied mathematics community, mainly due to their parallel processing attributes. In this work, the DD will be used in conjunction with a sub-domain solver, which employs hierarchical ${\bf H}(curl)$ conforming basis functions in the frequency domain. The DDM presented herein is a non-overlapping and non-conforming approach. Particularly, the FEM mesh on each of the sub-domains can be created independently. It is through the ``Cement'' element technique that sub-domains with dis-similar meshes will be ``glued'' together. Specific topics to be addressed in the talk are:

• Babuška-Brezzi inf-sup condition for the sub-domain solver with hierarchical ${\bf H}(curl)$ basis functions in-conjunction with tree-cotree splitting.
• Krylov method with $p$-type multiplicative Schwarz (pMUS) preconditioner for the sub-domain solver.
• Fourier analyses of the transmission conditions - 1st and 2nd order transmission conditions.
• ``Cement'' element technique for non-conforming domain decomposition method - exact integration through the union mesh and unconventional Lagrange multipliers.

Future talks in Scientific Computing Seminar $\bullet$ April 28 : Gene H Golub, Department of Computer Science, Stanford University.

This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.