Effect of Ordering for Iterative Solvers in Structural Mechanics Problems
Direct solvers are commonly used in implicit finite element codes for structural mechanics problems. This study explores an alternative approach to solving the resulting linear systems by using the Conjugate Gradient algorithm. Pre-conditioning is applied by using the incomplete Cholesky factorization. The effect of ordering is investigated for the Reverse Cuthill–McKee scheme and the Approximate Minimum Degree Method. The solution time and the required storage space are reported for two test problems involving thin shell finite elements and hexahedral solid elements.
The author would like to express his gratitude to Professor Ahmed Sameh and Dr. Faisal Saied of Purdue University for the insight they provided into the fascinating world of iterative solvers. Concrete foundations of this study were laid out at the Computing Research Institute under the provision of Professor Ahmed Sameh. The test matrices were provided by Dr. Roger Grimes of the Livermore Software Technology Company of Livermore, California. The generous support of the Bogazici University Research Fund through contract number 07HT102 is gratefully acknowledged.