Keywords: HFETI, domain decomposition, high performance computing, large-scale problem, singular matrices, advection-diffusion.

The main goal of the paper is to show how to effectively solve non-symmetric problems, taking possibly full utilization of currently the most powerful supercomputers in the world. To achieve this, we utilize Hybrid Total Finite Element Tearing and Interconnecting (HTFETI) method for solving large linear systems arising from finite element approximations of scalar advection-diffusion problems. A lot of physical and environmental processes (e.g. heat transfer, air and water pollution transport etc.) can be modeled as advection-diffusion problems. The linear system arising from Galerkin method is in our case non-symmetric. Although HTFETI method is originally conceived for solving symmetric linear systems, it can be also effectively used for non-symmetric linear systems. However, utilization of this method for nonsymmetric problems is not straightforward. Therefore, the paper describes challenges that must be handled differently in the non-symmetric case, for example, corners and kernel strategy for assembly cluster constraints, efficient method for kernel detection and influence of the different type of iterative solvers or preconditioners to scalability results. We have performed both weak and strong scalability tests on the Salomon supercomputer.

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