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In this paper we describe the history, performance, and design concepts of direct solvers for algebraic systems resulting from Galerkin discretizations of partial differential equations. Popular direct solver implementations of Gaussian elimination (also known as LU factorization) are introduced and briefly analyzed. We discuss three of the most relevant aspects influencing the performance of direct...
The paper presents a parallel direct solver for multi-physics problems. The solver is dedicated for solving problems resulting from adaptive Finite Element Method computations. The concept of finite element is actually replaced by the concept of the node. The computational mesh consists of several nodes, related to element vertices, edges, faces and interiors. The ordering of unknowns in the solver...
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