Partitioning, Ordering, and Load Balancing in a Hierarchically Parallel Hybrid Linear Solver

Institut National Polytechnique de Toulouse, RT-APO-12-2PDSLin is a general-purpose algebraic parallel hybrid (direct/iterative) linear solver based on the Schur complement method. The most challenging step of the solver is the computation of a preconditioner based on an approximate global Schur complement. We investigate two combinatorial problems to enhance PDSLin's performance at this step. The first is a multi-constraint partitioning problem to balance the workload while computing the preconditioner in parallel. For this, we describe and evaluate a number of graph and hypergraph partitioning algorithms to satisfy our particular objective and constraints. The second problem is to reorder the sparse right-hand side vectors to improve the data access locality during the parallel solution of a sparse triangular system with multiple right-hand sides. This is to speed up the process of eliminating the unknowns associated with the interface. We study two reordering techniques: one based on a postordering of the elimination tree and the other based on a hypergraph partitioning. To demonstrate the effect of these techniques on the performance of PDSLin, we present the numerical results of solving large-scale linear systems arising from two applications of our interest: numerical simulations of modeling accelerator cavities and of modeling fusion devices

Finite element analysis of switched reluctance motor with rotor position based control

This research presents a field-circuit coupled parallel finite element model of a switched reluctance motor embedded in a simple closed loop control system. The parallel numerical model is based on the Schur-complement method coupled with an iterative solver. The used control system is the rotor position based control, which is applied to the FEM model. The results and parallel performance of the voltage driven finite element model are compared with the results from the current driven model. Moreover, the results of the start-up of the loaded motor show why the model accuracy is important in the control loop