Takeshi Iwashita

Convergence Acceleration of Time-Periodic Electromagnetic Field Analysis by the Singularity Decomposition-Explicit Error Correction Method

This paper proposes a novel method for the improvement of the convergence to a steady state in time-periodic transient nonlinear eddy-current analyses. The proposed method, which is based on the time-periodic finite element method and the singularity decomposition-explicit error correction method, can extract poorly converged error components corresponding to the large time constants of an analyzed system. The correction of the extracted error components efficiently accelerates the convergence to a steady state. Numerical results verify the effectiveness of the proposed method.

Similarities Between Implicit Correction Multigrid Method and A-phi Formulation in Electromagnetic Field Analysis

This paper proposes an implicit error correction method that corresponds to the explicit error correction methods, such as Hiptmairs hybrid smoother and the conventional multigrid method. The A-phi method can be seen as the implicit error correction method corresponding to the hybrid smoother. Numerical tests confirm that the A-phi method produces a similar correction effect on the error belonging to the kernel of the discrete curl operator as that of the hybrid smoother. Furthermore, this paper introduces an implicit correction multigrid method, which is the implicit error correction version of the conventional multigrid method. In this method, linear systems on all levels in a multigrid method are combined into a large linear system. This linear system is solved by an iterative solver, and any preconditioning techniques can be used. Numerical tests show that the proposed method involves coarse grid correction effects and achieves a convergence rate independent of the grid-size, thus confirming the effectiveness of the implicit error correction method.

Algebraic Block Multi-Color Ordering Method for Parallel Multi-Threaded Sparse Triangular Solver in ICCG Method

This paper covers the multi-threaded parallel processing of a sparse triangular solver for a linear system with a sparse coefficient matrix, focusing on its application to a parallel ICCG solver. We propose algebraic block multi-color ordering, which is an enhanced version of block multi-color ordering for general unstructured analysis. We present blocking and coloring strategies that achieve a high cache hit ratio and fast convergence. Five numerical tests on a shared memory parallel computer verify that the computation time of the proposed method is between 1.7 and 2.6 times faster than that of the conventional multi-color ordering method.

Algebraic multicolor ordering for parallelized ICCG solver in finite-element analyses

Proposes a new black-box-type parallel processing method for the incomplete Cholesky conjugate gradient (ICCG) solver. The new method is based on a multicolor ordering concept and an automatic reordering process in the solver. Parallel performance is evaluated in the context of three-dimensional finite edge-element eddy-current analysis. The proposed method attains high parallelism with a small increase in CG iterations and achieves high parallel performance.

Comparison Criteria for Parallel Orderings in ILU Preconditioning

This paper introduces block red-black ordering in a general three-dimensional form for parallel incomplete LU (ILU) preconditioning. This parallel ordering method is designed to attain fast convergence with reduced synchronization among processors in parallelized forward and backward substitutions. In this method, the grid-nodes are divided into blocks and red-black ordering is applied to them. Since blocks with identical colors never have a data-dependency, the blocks in each color can be processed in parallel. Moreover, in order to compare parallel orderings, we propose a new tool for investigating orderings on convergence. The analytic index for convergence, which is based on the remainder matrix, is easily computed and has a unique value for a fixed ordering. Nodes are classified into seven groups, and the effect of each group on convergence is estimated. Numerical tests using a three-dimensional problem confirm the validity of both proposed parallel ordering and analytic convergence comparison methods.

Block Red-Black Ordering: A New Ordering Strategy for Parallelization of ICCG Method

A parallel ordering technique is a typical strategy for parallelization of the ICCG method. This paper proposes a new parallel ordering method to develop a parallel ICCG solver utilizing fewer synchronization points and achieving a high convergence rate. The new parallel ordering is called “block red-black ordering.” In this method, nodes in an analyzed grid are divided into several or many blocks, and red-black ordering is applied to the blocks. Since the blocks with an identical color are independent of each other, forward and backward substitutions in the ICCG iteration can be parallelized in each color. The new method has the advantage that only one synchronization point exists in each parallelized substitution. In order to evaluate the convergence and the parallel speed-up of the method, we carried out an analytical investigation using the ordering graph theory and numerical tests on a scalar parallel computer. The analytical study shows that the convergence rate is improved by an increase in the number of nodes of one block and that an optimal block size for getting the best convergence rate is easily set. The numerical tests show that the new method achieves a high parallel speed-up rate due to fast convergence, small synchronization costs, and effective utilization of the data cache on a scalar parallel computer.

Convergence Acceleration in Steady State Analysis of Synchronous Machines Using Time-Periodic Explicit Error Correction Method

This paper develops the time-periodic explicit error correction (TP-EEC) method for the convergence acceleration to a steady state in transient analysis of synchronous machines. The methods to deal with the movement of the rotor and different time-periodicity in the fixed and moving parts of the mesh are investigated. Furthermore, we propose the novel TP-EEC method based on the polyphase time periodic condition. Numerical results verify the effectiveness of the developed methods.

Parallel Time-Periodic Finite-Element Method for Steady-State Analysis of Rotating Machines

This paper investigates the parallelization of the time-periodic finite-element method in nonlinear magnetic field analyses of rotating machines. The developed method, which can obtain the steady state solutions directly, provides large granularity even in the small-scale problems compared with the ordinary parallel FEM based on the domain decomposition approach. Furthermore, we apply the parallel TPFEM to analyses of induction motors which have different time periodicities in stator and rotor regions due to the slip. Numerical results verify the effectiveness of the developed method.

Algebraic block red-black ordering method for parallelized ICCG solver with fast convergence and low communication costs

Proposes a new parallelized incomplete Cholesky conjugate gradient (ICCG) solver effective on a small-scale multiprocessor system. The new method is based on a new reordering technique, namely the block red-black ordering method. Its parallel performance is evaluated in a finite edge-element eddy-current analysis. A numerical test shows that the proposed method is effective on a small number of processors due to fast convergence and low communication costs.

A fast solver for FEM analyses using the parallelized algebraic multigrid method

The algebraic multigrid (AMG) method is an effi- cient solver for linear systems arising in finite element analyses. The AMG method is applicable at a matrix level, different from the geometric multigrid solvers. This paper proposes a combination of the parallel processing technique and the AMG method as a fast solver for electromagnetic field analyses. While the AMG method consists of a setup phase and a solution phase, parallel processing of the former phase is difficult. We present the use of long-range interpolation instead of the conventional direct interpolation for improvement of the parallel efficiency of the AMG setup phase. A magnetostatic analysis and an eddy-current analysis show the solver performance. The numerical results show that parallelized AMG is a fast solver and has sufficient scalability, as compared with the conventional solver.