Parallelizing iterative solvers for sparse systems of equations and eigenproblems on distributed-memory machines [electronic resource].
- Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 1994.
- Physical Description:
- pages 5, Paper 13 : digital, PDF file
- Additional Creators:
- National Science Foundation (U.S.) and United States. Department of Energy. Office of Scientific and Technical Information
- Restrictions on Access:
- Free-to-read Unrestricted online access
- For the solution of discretized ordinary or partial differential equations it is necessary to solve systems of equations or eigenproblems with coefficient matrices of different sparsity pattern, depending on the discretization method; using the finite element method (FE) results in largely unstructured systems of equations. Sparse eigenproblems play particularly important roles in the analysis of elastic solids and structures. In the corresponding FE models, the natural frequencies and mode shapes of free vibration are determined as are buckling loads and modes. Another class of problems is related to stability analysis, e.g. of electrical networks. Moreover, approximations of extreme eigenvalues are useful for solving sets of linear equations, e.g. for determining condition numbers of symmetric positive definite matrices or for conjugate gradients methods with polynomial preconditioning. Iterative methods for solving linear systems and eigenproblems mainly consist of matrix-vector products and vector-vector operations; the main work in each iteration is usually the computation of matrix-vector products. Therein, accessing the vector is determined by the sparsity pattern and the storage scheme of the matrix.
- Published through SciTech Connect., 12/31/1994., "conf-9404305--vol.2", "DE96005736", Colorado conference on iterative methods, Breckenridge, CO (United States), 5-9 Apr 1994., Basermann, A., Front Range Scientific Computations, Inc., Boulder, CO (United States), and USDOE, Washington, DC (United States)
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