Unstructured Multi-Grid method and the efficient implementation technique on parallel machines

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Efficient preconditioning for Conjugate Gradient method requires parallelization and good acceleration of convergence. These two things are often incompatible. Thus, the authors proposed the Multi-Grid preconditioning, which satisfies both of two things, and have demonstrated the efficiency of the method.In this study, we considered the problems with unstructured grids and with a big anisotropy. SA-AMG method, which is one of the multi-grid methods, calculates the smaller matrix and reaches the convergence efficiently utilizing that smaller matrix. But the SA-AMG method's efficiency deteriorates for anisotropic problems. The authors have shown that the smaller matrix creation method based on domain border information enables the method efficient convergence.We also studied the vectorization of the SA-AMG method for the implementation technique. Three matrix multiplications occupy the most calculation cost. For vectorization of this part, we tested various combinations of sparse matrix … More data structures and demonstrated the method based on the JDS and the CRS data structures is the most efficient for 3-Dimentional elastic problems. For another related study of the implementation technique, the authors created the re-distribution and re-ordering library for distributed sparse matrix. This library offers the frame work of the dynamic re-distribution and re-ordering, and enables those things easily.For other study of basic parallel implementation technique, the authors have studied the redistribution scheduling problem for finite sized multi-master divisible load problem. By identification of some parameters the authors showed that the simulation duplicates the behavior of the real system. We have also studied data distribution problem of the parallel molecular dynamics, and researched the best data distribution method in the case that the communication band-width and latency between computer nodes are not uniform. It is a challenge for the future to apply these basic techniques for parallel implementation of multi-grid method on various computer platforms. Less