A large-grained parallel algorithm for nonlinear eigenvalue problems and its implementation using OmniRPC
Takeshi Amako, Yusaku Yamamoto, Shao‐Liang Zhang · 2008
The nonlinear eigenvalue problem plays an important role in various fields such as nonlinear elasticity, electronic structure calculation and theoretical fluid dynamics. We recently proposed a new algorithm for the nonlinear eigenvalue problem, which reduces the original problem to a smaller generalized linear eigenvalue problem with Hankel coefficient matrices through complex contour integral. This algorithm has a unique feature that it can find all the eigenvalues in a closed curve on the complex plane. Moreover, it has large-grain parallelism and is suited for execution in a Grid environment. In this paper, we study the numerical properties of our algorithm theoretically. In particular, we analyze the effect of numerical integration to the computed eigenvalues and give a guideline on how to choose the size of the Hankel matrices properly. Also, we show the parallel performance of our algorithm implemented on a PC cluster using OmniRPC, a Grid RPC system. Parallel efficiency of 75% is achieved when solving a nonlinear eigenvalue problem of order 1000 using 14 processors.