Sparse Equation-Eigen Solvers for Symmetric/Unsymmetric Positive-Negative-Indefinite Matrices with Finite Element and Linear Programming Applications

Vectorized sparse solvers for direct solutions of positive-negative-indefinite symmetric systems of linear equations and eigen-equations are developed. Sparse storage schemes, re-ordering, symbolic factorization and numerical factorization algorithms are discussed. Loop unrolling techniques are also incorporated in the coding to enhance the vector speed. In the indefinite solver, which employs various pivoting strategies, a simple rotation matrix is introduced to simplify the computer implementation. Efficient usage of the incore memory is accomplished by the proposed restart memory management schemes. A sparse version of the Interior Point Method, IPM, has also been implemented that incorporates the developed indefinite sparse solver for linear programming applications. Numerical performance of the developed software is conducted by performing the static analysis and eigen-analysis of several practical finite elements models, such as the EXXON Offshore Structure, the High Speed Civil Transport (HSCT) Aircraft, and the Space Shuttle Solid Rocket Booster (SRB). The results have been compared to benchmark results provided by the Computational Structural Branch at NASA Langley Research Center. Small to medium-scale linear programming examples have also been used to demonstrate the robustness of the proposed sparse IPM