Direct methods for sparse matrices
Direct methods for sparse matrices
Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
Parallel computation in finite element method
Parallel computation in finite element method
Matrix computations (3rd ed.)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
A performance assessment of NE/Nastran's new sparse direct and iterative solvers
Advances in Engineering Software - Special issue on large-scale analysis, design and intelligent synthesis environments
High Performance Computing
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
On the efficient solution of sparse systems of linear and nonlinear equations.
On the efficient solution of sparse systems of linear and nonlinear equations.
Graph partitioning for high-performance scientific simulations
Sourcebook of parallel computing
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Accelerated subspace iteration with aggressive shift
Computers and Structures
Euro-Par'12 Proceedings of the 18th international conference on Parallel Processing
Improving eigenpairs of automated multilevel substructuring with subspace iterations
Computers and Structures
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Symmetric positive definite equation solvers play a very important role in promoting the efficiency of the finite element analyses (FEA). The focus of this paper is to describe a new storage scheme--cell-sparse storage scheme--and the corresponding algorithm of the direct symmetric positive definite equation solver in FEA. Loop-unrolling (or simply unrolling) techniques are incorporated into sparse solvers to enhance the vector speed. Sparse storage schemes, out-of-core strategy, and numerical factorization are discussed. The performance in terms of elapsed time and memory requirement of different solvers are demonstrated by finding static displacement vectors for practical engineering problems. Numerical tests indicate that the cell-sparse storage scheme and the two-level unrolling can improve the performance of symmetric positive definite equation solvers significantly.