Large-Scale Domain Decomposition for a Scalable, Three-dimensional Brick Finite Element Based Rotor Dynamic Analysis
ELORET CORP MOFFETT FIELD CA NASA AMES RESEARCH CENTER
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This paper implements and analyzes a dual-primal iterative substructuring method for the parallel and scalable solution of a three-dimensional finite element based dynamic analysis of helicopter rotor blades. Scalability and solution times are studied using two prototype problems -- one for steady hover symmetric and one for transient forward flight non-symmetric -- carried out on up to 128 processors. Several problem sizes of up to 0.48 million degrees of freedom are considered. A linear speed-up is observed with number of processors up to the point of substructure optimality. Substructure optimality and hence linear speed-up are shown to depend dramatically on the corner based global coarse problem selection. A minimal selection is implemented in this paper consisting only of corner nodes that lie on substructure vertices while the remaining corner nodes on substructure edges are treated as interface nodes with multiple dual variables. The key conclusion is that this minimal selection is key to extending linear speed-up to as high a processor number as possible, and minimizing the solution time for a fixed problem size. It is therefore an essential requirement for the efficient solution of a large-scale 3-D FEM problem.
- Numerical Mathematics