We present a perturbed formulation of the BDDC method where the invertibility of the global coarse matrix is automatically guaranteed and positive direct solvers can be used without corner constraints or a change of basis. The perturbed method has the same polylogarithmic bounds for the precondition number and is weakly scalable. It is suitable for large scale simulations as small coarse spaces associated with only edge or/and face constraints can be used. In addition, it offers extra robustness when there are disconnected subdomains or in other situations where constraints fails to fix a small number of rigid body modes.
|Title of host publication
|Domain Decomposition Methods in Science and Engineering XXIII
|Hyea Hyun Kim, Axel Klawonn, Eun-Jae Park, Chang-Ock Lee, Olof B. Widlund, Xiao-Chuan Cai, David E. Keyes
|Place of Publication
|Springer-Verlag London Ltd.
|Number of pages
|Published - 1 Jan 2017
|International Conference on Domain Decomposition Methods 2015 - International Convention Center Jeju, Jeju Island, Korea, South
Duration: 6 Jul 2015 → 10 Jul 2015
Conference number: 23rd
|Lecture Notes in Computational Science and Engineering
|Springer International Publishing
|International Conference on Domain Decomposition Methods 2015
|6/07/15 → 10/07/15
|The main technical content of the DD conference series has always been mathematical, but the principal motivation was and is to make efficient use of distributed memory computers for complex applications arising in science and engineering. As we approach the dawn of exascale computing, where we will command 1018 floating-point operations per second, clearly efficient and mathematically well-founded methods for the solution of large-scale systems become more and more important—as does their sound realization in the framework of modern HPC architectures. In fact, the massive parallelism, which makes exascale computing possible, requires the development of new solution methods, which are capable of efficiently exploiting this large number of cores as the connected hierarchies for memory access. Ongoing developments such as parallelization in time asynchronous iterative methods or nonlinear domain decomposition methods show that this massive parallelism does not only demand for new solution and discretization methods but also allows to foster the development of new approaches.