Taku Itoh

Iterative Solver for Linear System Obtained by Edge Element: Variable Preconditioned Method With Mixed Precision on GPU

The variable preconditioned (VP) Krylov subspace method with mixed precision is implemented on graphics processing unit (GPU) using compute unified device architecture (CUDA), and the linear system obtained from the edge element is solved by means of the method. The VPGCR method has the sufficient condition for the convergence. This sufficient condition leads us that the residual equation for the preconditioned procedure of VPGCR can be solved in the range of single precision. To stretch the sufficient condition, we propose the hybrid scheme of VP Krylov subspace method that uses single and double precision operations. The results of computations show that VPCG with mixed precision on GPU demonstrated significant achievement than that of CPU. Especially, VPCG-JOR on GPU with mixed precision is 41.853 times faster than that of VPCG-CG on CPU.

Large-Scale Simulation of Electromagnetic Wave Propagation Using Meshless Time Domain Method With Parallel Processing

The large-scale simulation of the electromagnetic wave propagation using meshless time domain method (MTDM) is numerically investigated. Moreover, compute unified device architecture (CUDA) and OpenMP is adopted for parallelization technique to reduce the computation time. The results of computation show that the execution time of the time evolution calculation on GPU is 8.8 time faster than that of CPU. In addition, the execution time of the shape function generation procedure can be speedup about 7842 times by proposed scheme and OpenMP.

Accuracy Improvement of Extended Boundary-Node Method

The extended boundary-node method (X-BNM) has been modified for improving the accuracy degradation due to the boundary shape and its performance has been numerically investigated by comparing with the standard one. For the case where the boundary shape is strongly concave, the results of computations show that the accuracy of the modified X-BNM is always higher than that of the standard one. In addition, the speed of the modified X-BNM is almost equal to that of the standard one. Therefore, it is found that the performance of the modified X-BNM is much superior to that of the standard one.

Development of 2-D Meshless Approaches Without Using Integration Cells

The element-free Galerkin method (EFGM) and the boundary-node method (BNM) have been reformulated without integration cells. After a boundary is represented in terms of an implicit function, matrix elements are evaluated by use of the function. The results of computations show that the accuracy of the reformulated BNM is even higher than that of the dual-reciprocal boundary-element method. In addition, both the accuracy of the X-BNM and that of X-EFGM strongly depend on the support radius.

Interpolating Moving Least-Squares-Based Meshless Time-Domain Method for Stable Simulation of Electromagnetic Wave Propagation in Complex-Shaped Domain

To stabilize the electromagnetic wave propagation simulations using a meshless time-domain method (MTDM) in complex-shaped domains, the new MTDM embedding the shape functions generated by the interpolating moving least-squares method has been developed. Numerical experiments show that the new MTDM can employ a relatively large time step for the simulations in comparison with that of the conventional MTDM. In addition, the parameters for generating the shape functions of new MTDM can be chosen more flexibly than those of the conventional MTDM. Furthermore, it is found that the stability of the simulations by MTDM depends not only on the stable condition for MTDM, but also on the specific kind of shape functions used and on the number of nodes contained in their support.

Speedup of Iterative Solver for Electromagnetic Analysis Using Many Integrated Core Architecture

Speedup of Krylov subspace method for the linear system obtained from an electromagnetic analysis using Many Integrated Core (MIC) architecture is investigated. In recent years, MIC architecture appears on the scene of high-performance computing research fields. Since Xeon Phi coprocessor is x86 architecture, the ordinal numerical code can be implemented on the devices without transcribing. In this paper, the linear systems obtained by extended element-free Galerkin method and edge element are solved by mixed precision variable preconditioned (VP) Krylov subspace method, and the methods are implemented on MIC to get high performance. The results of computation show that speedup of VP generalized minimal residual on MIC is three times faster than that of sequential calculation. In addition, the speedup of VP conjugate gradient (CG) is 40.47 times faster than that of sequential CG method.

Performance Improvement of Extended Boundary Node Method

The extended boundary node method (X-BNM) with the radial point interpolation method (RPIM) shape function is proposed and its performance is numerically investigated by comparing with the dual reciprocity boundary element method (DRM). The results of computations show that the accuracy of the X-BNM is almost equal to that of the DRM. In addition, the speed of the X-BNM with the RPIM shape function is almost equal to that of the DRM. Therefore, not only the DRM but also the X-BNM with the RPIM shape function is a powerful method for solving the Poisson problem.

High-Performance Computing of Electromagnetic Wave Propagation Simulation Using Meshless Time-Domain Method on Many Integrated Core Architecture

Electromagnetic wave propagation simulations using meshless time-domain method (MTDM) have been accelerated by parallelization techniques on Many Integrated Core (MIC) architecture. Numerical experiments show that, in the symmetric mode with the appropriate number of assigned nodes for each MIC, the simulation is about 9.41 times faster than that of the serial execution on CPU. In addition, in the offload mode with the explicit optimization strategy for MIC, the simulation using MTDM on MIC is about 8.16 times faster than that of the serial execution on CPU.

Application of Extended Element-Free Galerkin Method to Nonlinear Problem

A new method has been proposed for implementing the essential boundary condition and the natural one to the Element-Free Galerkin Method (EFGM). Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that the accuracy degradation of the numerical solution can be suppressed by using the proposed method. In addition, the convergence performance of the proposed method is more stable than that of the standard EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem.

Surface reconstruction from 3D scattered points with normals using both delaunay tetrahedralization and implicit function

A robust visualization method for reconstructing surfaces from 3D scattered points with normals is proposed. The method is based on both the Delaunay tetrahedralization and the implicit function. The method enables to reduce total computational costs of the surface visualization by using the Delaunay tetrahedralization mainly. Even if some unexpected surfaces are generated in a result of the Delaunay tetrahedralization, the method can modify the result by using an implicit function. In experiments, some results are shown as examples of applying the method.