Introduction to Parallel & Vector Solution of Linear Systems
Introduction to Parallel & Vector Solution of Linear Systems
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
PSBLAS: a library for parallel linear algebra computation on sparse matrices
ACM Transactions on Mathematical Software (TOMS)
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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In this paper, we present an object-oriented concept of sparse matrix and iterative linear solver for large scale parallel and sequential finite element analysis of multi-field problems. With the present concept, the partitioning and parallel solving of linear equation systems can be easily realized, and the memory usage to solve coupled multi-field problems is optimized. For the parallel computing, the present objects are tailored to the domain decomposition approach for both equation assembly and linear solver. With such approach, the assembly of a global equation system is thoroughly avoided. Parallelization is realized in the sparse matrix object by the means of (1) enable the constructor of the sparse matrix class to use domain decomposition data to establish the local domain sparse pattern and (2) introduce MPI calls into the member function of matrix-vector multiplication to collect local results and form global solutions. The performance of these objects in C++ is demonstrated by a geotechnical application of 3D thermal, hydraulic and mechanical (THM) coupled problem in parallel manner.