Amane Takei

Full Wave Analyses of Electromagnetic Fields With an Iterative Domain Decomposition Method

This paper describes large-scale full wave analyses of electromagnetic fields by the finite-element method with an iterative domain decomposition method (IDDM). A stationary vector wave equation for the high-frequency electromagnetic field analyses is solved taking an electric field as an unknown function. Then, to solve subdomain problems by the direct method, the direct method based on the LDLT decomposition method is introduced in subdomains. If the direct method is applied for solving subdomain problems, the computation time seems to be reduced by the improved accuracy of subdomain problems, and storing matrices that are results of the decomposition on main memory.

A numerical study of iterative substructuring method for finite element analysis of high frequency electromagnetic fields

This paper describes iterative methods for the high frequency electromagnetic analysis using the finite element method of Maxwell equations including displacement current. The conjugate orthogonal conjugate gradient method has been widely used to solve a complex symmetric system. However, the conventional method suffers from oscillating convergence histories in large-scale analysis. In this paper, to solve large-scale complex symmetric systems arising from the formulation of the E method, an iterative substructuring method like the minimal residual method is presented, and the performance of the convergence of the method is evaluated by numerical results. As the result, the proposed method shows a stable convergence behavior and a fast convergence rate compared to other iterative methods.

Performance evaluation of parallel finite element electromagnetic field analysis using numerical human models in HPCI

This paper describes large-scale full-wave analyses of electromagnetic fields using numerical human body models. This is achieved by the use of the parallel finite element method with iterative domain decomposition. The numerical human body models provided by the National Institute of Information and Communications Technology (NICT) in Japan are composed of voxel data with all sides of 2mm and include skin layers, blood vessels, bones, internal organs, etc. distinguished by material properties. By using a High Performance Computing Infrastructure (HPCI), the user can evaluate the electromagnetic filed distribution inside the whole body model.

High-Accuracy Electromagnetic Field Simulation Using Numerical Human Body Models

We have investigated a high-accuracy analysis for the electromagnetic field of numerical human body models using the finite-element method. The numerical human body models generated from computed tomography images are represented as voxel data, and composed of skin layers, blood vessels, bones, internal organs, and so on. In this paper, we propose a mesh smoothing technique to reduce the noise caused by reflection and scattering of the electric fields around material boundaries. Therefore, using a supercomputer, we successfully evaluated the electromagnetic field distribution inside the whole body model with a high accuracy.

Improved Convergence in Eddy-Current Analysis by Singular Value Decomposition of Subdomain Problem

The purpose of this study is to improve the convergence of the iterative domain decomposition method for the Interface Problem in time-harmonic eddy-current analysis. The solver applied is the \( A \)-\( \phi \) method, which consists of the magnetic vector potential \( A \) and an unknown function of the electric scalar potential \( \phi \). However, it is known that the convergence of the iterative domain decomposition method deteriorates for the interface problem in analyses with large-scale numerical models. In addition, the equation obtained by the \( A \)-\( \phi \) method is a singular linear equations. In general, iterative methods are applied to solve this equation, however it is difficult to achieve high-precision because of the truncation error. In this research, to solve this problem, a direct method using a generalized inverse matrix based on a singular value decomposition method is introduced to solve the subdomain problems. Although this increases the computational cost, high-precision arithmetic becomes possible. Here, we investigate the improvement in the convergence of the interface problem by comparing our proposed method with previous method, when applied to the standard time-harmonic eddy-current problem.

Development and Validation of Parallel Acoustic Analysis Method for the Sound Field Design of a Large Space

Recently, acoustic analysis techniques are used in the design of acoustic environments both inside and outside of rooms containing a sound source. However, when the analysis area is expanded or the frequency is increased, unknowns of a solving liner equation increase, and large-scale analyses becomes necessary. Therefore, in this study, a large-scale acoustic analysis method has been developed based on a parallel finite element method. In the proposed large-scale analysis method, an iterative method is applied to the interface problem as the iterative domain decomposition method, which is known to be an effective parallelization method. To improve the convergence of the iterative method, balancing domain decomposition has been applied as a preconditioner step, and its effectiveness in large-scale acoustic analysis is demonstrated. The acoustic analysis code is developed in this study that is shown to be capable of the large-scale analysis of finite element models on the order of tens of millions of elements with high accuracy.

Parallel full-wave electromagnetic field simulation using anatomical human body models

The authors have investigated a high-accuracy analysis for the electromagnetic field of numerical human body models using the finite element method. The numerical human body models generated from computed tomography images are represented as voxel data, and composed of skin layers, blood vessels, bones, internal organs, etc. In this paper, we propose a mesh smoothing technique to reduce the noise caused by reflection and scattering of the electric fields around material boundaries. Therefore, by using a supercomputer, we successfully evaluated the electromagnetic field distribution inside the whole body model with a high accuracy.

Parallel finite element electromagnetic field analysis using numerical human models in HPC

This paper describes large-scale full-wave analyses of electromagnetic fields using numerical human body models. Recently, medical equipment using electromagnetic fields including hyperthermia is spreading. During treatment, it is effective to focus the electromagnetic field onto the lesions inside the human body. The purpose of this research is to accurately calculate the electromagnetic field inside the human body using a numerical electromagnetic analysis method. The numerical human body model database has been released free-of-charge for researchers by NICT. This database is constructed using voxels that have 2mm edge length. The numerical human model is multi-material including skin, blood vessels, bones, internal organs etc.. The adult male model is named “TARO”, and has 44 million voxels. Over 200 million tetrahedral elements are generated from the voxel data. In general, numerical analysis using ordinary finite element codes is difficult to apply to such a numerical human model because of the very large size of the mesh. However, by using parallelization techniques based on the iterative domain decomposition method (IDDM) we were able to perform large-scale finite element full-wave analyses for electromagnetic fields. In this paper, we apply our parallel finite element code based on IDDM to the calculation of full-wave electromagnetic fields. We report analyses of the numerical human body models with more than 200 million complex DOF by using a High Performance Computing (HPC) environment. The electromagnetic field in the human body is analyzed by numerical human models. All computations are performed using 320-cores (20-nodes) of the Fujitsu FX100 supercomputer in Nagoya University. We analyzed frequencies of 1 (MHz), 8 (MHz), 70 (MHz) and 300 (MHz) using the full-wave electromagnetic field analysis based on the IDDM.

A domain decomposition method based on an algorithm of the MINRES method for high-frequency electromagnetic field analysis

This paper describes the Domain Decomposition Method (DDM) for high frequency electromagnetic field problems. As an efficient iterative method to solve a complex symmetric system arising from the formulation of the E method, a DDM based on a MINimal RESidual (MINRES)-like iterative procedure is presented. Numerical experiments are demonstrated to report a faster convergence compared to conventional methods.

PARALLEL FEM ANALYSIS OF HIGH FREQUENCY ELECTROMAGNETIC WAVE IN AN ENVIRONMENT

This paper presents a parallel finite element analysis of high frequency electro- magnetic wave in an environment. The HDDM (Hierarchical Domain Decom- position Method) is employed as a parallel solver. Nedelec element is employed. The simulation method is tested for a simple model, and the results are compared with exact solutions.