Fast Parallel Iterative Aggregation Methods for Simulation of Dynamical Systems

A novel iterative aggregation algorithm for numerical simulations of dynamic systems is proposed and analyzed. The algorithm exploits the special structures of the linear equation problem resulting from the discretization of the dynamic system, and of the aggregation/disaggregation procedures. The algorithm has a time complexity of (I(q)+2M(q)+3)logN time complexity in solving linear systems with q states for N discrete time instants, using O(qN) processors, where I(q) is the parallel time complexity for inverting a q×q matrix, M(q) is the parallel time complexity for matrix multiplication of two q×q matrices. The competing parallel cyclic reduction method for the same problem have a time complexity of (I(q)+3M(q)+4)log N. Thus, the proposed algorithm has a definite speed advantage over the cyclic reduction method.