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The efficient treatment of dense matrices arising, e.g., from the finite element discretisation of integral operators requires special compression techniques. In this article, we use a hierarchical low-rank approximation, the so-called -matrix, that approximates the dense stiffness matrix in admissible blocks (corresponding to subdomains where the underlying kernel function is smooth) by low rank...
In this article, we present two new algorithms for solving given triangular systems in parallel on a shared memory architecture. Multilevel incomplete LU factorization based preconditioners, which have been very successful for solving linear systems iteratively, require these triangular solves. Hence, the algorithms presented here can be seen as parallelizing the application of these preconditioners...
In this paper, we introduce and analyze a modification of the Hermitian and skew-Hermitian splitting iteration method for solving a broad class of complex symmetric linear systems. We show that the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method is unconditionally convergent. Each iteration of this method requires the solution of two linear systems with real symmetric positive...
For the structured systems of linear equations arising from the Galerkin finite-element discretizations of the distributed control problems, we construct block-counter-diagonal and block-counter-tridiagonal preconditioning matrices to precondition the Krylov subspace methods such as GMRES. We derive explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrices...
Physarum polycephalum is an amoeba-like organism and is able to find the shortest path in a labyrinth. Inspired by P. polycephalum, recently, a mathematical model and an algorithm (Physarum Solver) was developed. There are, however, only sequential implementations of this algorithm. In this paper, a fast and efficient parallel Physarum Solver is proposed. The proposed algorithm requires the solution...
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