Abstract. The FETI methods blend iterative and direct solvers. The dual problem is solved iteratively using e.g. CG method; in each iteration, the auxiliary problems related to the application of an unassembled system matrix (subdomain problems' solutions and projector application in dual operator) are solved directly. The paper deals with the comparison of the direct solvers available in PETSc on the Cray XE6 machine HECToR (PETSc, MUMPS, SuperLU) regarding their performance in the two most time consuming actions in TFETI -the pseudoinverse application and the coarse problem solution. For the numerical experiments, our novel TFETI implementation in FLLOP (FETI Light Layer on top of PETSc) library was used.

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We propose a method of a parallel distribution of densely populated matrices arising in boundary element discretizations of partial differential equations. In our method the underlying boundary element mesh consisting of n elements is decomposed into N submeshes. The related N ×N submatrices are assigned to N concurrent processes to be assembled. Additionally we require each process to hold exactly one diagonal submatrix, since its assembling is typically most time consuming when applying fast boundary elements. We obtain a class of such optimal parallel distributions of the submeshes and corresponding submatrices by cyclic decompositions of undirected complete graphs. It results in a method the theoretical complexity of which is O((n/ √ N) log(n/ √ N)) in terms of time for the setup, assembling, matrix action, as well as memory consumption per process. Nevertheless, numerical experiments up to n = 2744832 and N = 273 on a real-world geometry document that the method exhibits superior parallel scalability O((n/N) log n) of the overall time, while the memory consumption scales accordingly to the theoretical estimate.

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