Tomonori Tsuburaya

Improvement of the Preconditioned MRTR Method With Eisenstat's Technique in Real Symmetric Sparse Matrices

The Incomplete Cholesky Conjugate Gradient (ICCG) method is widely used to solve indefinite algebraic equations obtained using an edge-based finite element method. However, when a linear solver based on the minimum residual is used, there is a possibility of reducing the elapsed time for a linear system. This paper shows the performance of the preconditioned minimized residual method based on the three-term recurrence formula of the CG-type (MRTR) method by comparing the MRTR method with the ICCG method for real symmetric sparse matrices. Furthermore, we intend to reduce computational costs by using Eisenstats technique, and achieve more speed-up by applying a preconditioned residual to the convergence criterion.

Parallelization of Preconditioned MRTR Method With Eisenstat’s Technique by Means of Algebraic Multicolor Ordering

The performance of preconditioned Minimized Residual method based on the Three-term Recurrence formula of the conjugate gradient CG-type (MRTR) method has been demonstrated on various symmetric linear systems based on 3-D FEM. The symmetric Gauss-Seidel-preconditioned MRTR method with Eisenstats technique (MESGS-MRTR) has higher validity for reducing the elapsed time when a conventional PC is used. However, MESGS-MRTR cannot be parallelized, when a block preconditioner is adopted. Therefore, we propose a parallelized MESGS-MRTR method supported by algebraic multicolor ordering in the 3-D low-frequency electromagnetic problems. We present a performance comparison of the proposed method with block preconditioner using reverse Cuthill-McKee ordering.

Parallelized ICCG method using block-multicolor orderings in real symmetric linear system derived from voltage-driven FEM in time domain

Purpose – The purpose of this paper is to improve the performance of block-multicolor (BMC) ordering for the parallelized incomplete-Cholesky-preconditioned conjugate gradient (ICCG) method. Then, the BMC ordering based on level structure arising in reverse Cuthill-McKee RCM ordering is newly proposed. The name of proposed method is abbreviated as “RBMC”. This paper shows the validity of proposed method by comparison with greedy-based multicolor (MC) and conventional BMC on the real symmetric linear system derived from the voltage-driven finite element method in time domain. Design/methodology/approach – In RBMC, the blocking and coloring is performed level by level. The number of synchronizations in forward and backward substitution is reduced so that all blocks can be colored with two colors. However, the load-balance in forward and backward substitution might deteriorate because the irregular block matrices are distributed around diagonal. To uniformize load-balance in forward and backward substitution...

Performance of Preconditioned Linear Solvers Based on Minimum Residual for Complex Symmetric Linear Systems

Fast computation of linear systems is essential for reducing the elapsed time when using finite element analysis. The incomplete Cholesky conjugate orthogonal conjugate gradient method is widely used as a linear solver for complex symmetric systems derived from the edge-based FEM in the frequency domain. On the other hand, the performance of the preconditioned minimized residual method based on the three-term recurrence (MRTR) formula of the conjugate gradient-type method has been demonstrated on various symmetric sparse linear systems obtained from edge-based FEM formulated in the magnetostatic and time domain. This paper shows for the first time the performance of the preconditioned conjugate orthogonal MRTR method applied to complex symmetric linear systems.

Fast nonlinear finite element analysis using Newton-Raphson method implemented by Krylov subspace method with relaxed convergence criterion

Purpose – The purpose of this paper is the realization of Fast nonlinear finite element analysis (FEA). Design/methodology/approach – Nonlinear magnetic field analysis is achieved by using Newton-Raphson method implemented by relaxed convergence criterion of Krylov subspace method. Findings – This paper mathematically analyzes the reason why nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed. Research limitations/implications – The proposed method is essential to reduce the elapsed time in nonlinear magnetic field analysis of quasi-stationary field. Practical implications – The proposed method is able to be extended to not only static field but also time domain FEA strongly coupled with circuit equation. Social implications – Because the speedup of performance evaluation of electrical machines would be achieved using proposed method, the work efficiency in manufacturing would be accelerated. Originality/value – It can be seen that the nonlinear convergenc...

Improvement of Torque Characteristics For a Synchronous Reluctance Motor Using MMA-based Topology Optimization Method

Because a synchronous reluctance motor (SynRM) does not require permanent magnets, its industrial applications focus on lowering manufacturing costs. However, the SynRM has disadvantages. It experiences a lower average torque and oscillations derived from torque ripple compared to a permanent magnet-based motor. Therefore, the improvement of torque characteristics is investigated using topology optimization (TO) method which allows a greater variety of rotor structure than the shape optimization technique and does not require the concrete initial structure. Although the level set method is well known among TO methods, the smoothed-heaviside-function-based TO implemented by method of moving asymptotes is more suitable due to the feasibility of implementing the physical structure and the convergence speed. In this paper, the reasonable structure of rotor core in SynRM is investigated using TO method to improve the torque characteristic.

Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation

Abstract It is very important to design electrical machineries with high efficiency from the point of view of saving energy. Therefore, topology optimization (TO) is occasionally used as a design method for improving the performance of electrical machinery under the reasonable constraints. Because TO can achieve a design with much higher degree of freedom in terms of structure, there is a possibility for deriving the novel structure which would be quite different from the conventional structure. In this paper, topology optimization using sequential linear programming using move limit based on adaptive relaxation is applied to two models. The magnetic shielding, in which there are many local minima, is firstly employed as firstly benchmarking for the performance evaluation among several mathematical programming methods. Secondly, induction heating model is defined in 2-D axisymmetric field. In this model, the magnetic energy stored in the magnetic body is maximized under the constraint on the volume of magnetic body. Furthermore, the influence of the location of the design domain on the solutions is investigated.

Topology optimization of IH-equipment using heaviside function in 2-D axisymmetric electromagnetic field

Topology optimization is one of the mathematical methods for finding the optimal structure of electrical machinery. Because topology optimization can make a design with much higher degree of freedom in terms of structure than other optimization methods, there is a possibility for achieving a completely new shape that is not limited to the conventional model. The optimized structure is strongly dependent on the characteristic function which is an explicit function with respect to the design variable. To identify the practical topology in which the gray scale elements do not exist as much as possible, Heaviside function is suitable to suppress the generation of gray scale. In this paper, Heaviside function is applied to the IH equipment problem, and both influences of the difference between single and multiple design domain and the difference of the constraint value of the magnetic body volume on optimal solution are particularly investigated.

Parallelization performance of robust incomplete factorization preconditioner for real symmetric linear systems arising in magnetic field analyses

This paper investigates the parallelization performance of robust-incomplete-factorization-preconditioned conjugate gradient (RIF-CG) method for linear systems arising in magnetic field analyses using finite element method. A blocked strategy of coefficient matrix is applied to the parallelization of RIF preconditioner. Consequently, it can be seen that the scalability of block RIF is superior to that of block incomplete-Cholesky (IC) preconditioner.