Speaker: Hyea Hyun Kim
Abstract
Mortar discretizations have been developed for coupling different approximations in different subdomains, that can arise from engineering applications in complicated structures with highly non-uniform materials.
The complexity of the discretizations requires fast algorithms for solving the resulting linear systems. We focus on extension of several domain decomposition algorithms, that have been successfully applied to conforming finite element discretizations, to solving such linear systems. They are overlapping Schwarz methods, FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) methods, and BDDC (Balancing Domain Decomposition by Constraints) methods.
The main contribution is that complete analysis, providing the optimal condition number estimate, has been done for geometrically non-conforming subdomain partitions and for problems with discontinuous coefficients. These algorithms are further extended to the two-dimensional Stokes and three-dimensional elasticity. In addition, an exact solver for the coarse problem has been developed, especially in the three dimensions.
Numerical computations present the performance of the suggested algorithms for the geometrically non-conforming partitions and for the problems with discontinuous coefficients. Performance of the algorithms equipped with an inexact coarse problem will also be presented.
*This work has been carried out under collaborations with Professor Maksymilian Dryja, in Warsaw University, Poland, Professor Chang-Ock Lee, in KAIST, Korea, Professor Olof B. Widlund, and Doctor Xuemin Tu, at Courant Institute, USA.
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