有限音線積分法による室内音場の計算

Several space-time grids with 2D-space are examined for electromagnetic field computation using finite integration (FI) method, where time-step is locally refined. Two-types of space-time grids are proposed to decrease the unphysical reflection of electromagnetic wave. A preliminary stability analysis is also carried out for stable explicit time-marching.

Summary form only given. Numerical analysis of electromagnetic scattering has been widely studied in the past. The method of moments (MoM) is suitable to simulate scattering from an object in an open region. In order to solve problems with complicated geometries and materials, the finite element method (FEM) is preferred. However, when solving unbounded problems with FEM, the use of absorbing boundary conditions or perfectly matched layers will result in truncation errors. To combine the advantages of both MoM and FEM, the finite element-boundary integral (FE-BI) method was developed and widely used (J. M. Jin, The Finite Element Method in Electromagnetics, Second Edition. New York: Wiley, 2002). This algorithm is not only able to deal with highly complicated geometry and material, but also able to eliminate the truncation error. However, since the MoM has O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2)</sup> computational and storage complexities, the computational cost of the BI-related algorithm is still prohibitively high when solving large-scale scattering problems. To alleviate this problem, the multilevel fast multipole algorithm (MLFMA) has been incorporated into the FE-BI method (J. Liu and J. M. Jin, IEEE Trans. Antennas Propag., vol. 51, pp.1157-1167, Jun. 2003). Another important technique to accelerate the computation is to resort to parallel computers. Recently, the graphics processing unit (GPU), as one of many-core computing systems, has received intensive attention from the scientific computing community due to its low price, a massive number of processors, and the resulting high computational efficiency. In this work, we discuss the GPU implementation of the FE-BI algorithm for solving electromagnetic scattering problems. First, the assembly of the BI-related matrix is parallelized on GPU by NVIDIA's compute unified device architecture (CUDA). A massive number of threads are assigned to carry out the assembly, and each thread computes one element in the BI-related matrix. Second, both the direct and iterative solvers are implemented on GPU. For the direct solver, the Intel's math kernel library (MKL) is used for LU decomposition, and the CUSPARSE (a set of basic linear algebra subroutines used for handling sparse matrices) is employed to speedup forward and backward substitutions. For the iterative solver, the high performance CUDA Basic Linear Algebra Subprograms (BLAS) is utilized for the matrix-vector multiplication and the vector-vector multiplication. Extensive numerical experiments are conducted to validate the implementation and demonstrate the achievable computational speedup.

Thrombin is a serine protease involved in blood coagulation. Since thrombin inhibitors appear to be effective in the treatment and prevention of thrombotic and embolic disorders, considerable attention has been focused on the structure and interactions of the enzyme. In this work, we calculated the relative free energies of hydration of the new thrombin inhibitor candidates, p‐substituted derivatives of benzamidine, a well‐known noncovalent thrombin inhibitor. We used molecular dynamics and the finite difference thermodynamic integration (FDTI) algorithm within the Discover program of MSI. We have shown that the orthogonality problem that occurs in the calculation of intraperturbed‐group contributions to the free energy is treated adequately by the FDTI method. We have also shown that problems of singularity and convergence in free energy calculations can be properly solved using this method. To conclude, the calculated free energies of hydration gave the following order of solvation for the candidates: p‐(2‐oxo‐1‐propyl)benzamidine &gt; p‐methylbenzamidine &gt; p‐ethylbenzamidine &gt; p‐(1‐propyl)benzamidine &gt; benzamidine. © 2001 John Wiley &amp; Sons, Inc. Int J Quantum Chem, 2001

This paper introduces a new algorithm for the automatic synthesis of SPICE-ready equivalent circuits of complex multiport lumped interconnect structures. The method is named time-domain vector fitting (TD-VF) due to its analogy to the well-known vector fitting algorithm, which operates in the frequency domain. The TD-VF computes a rational approximation of the transfer matrix for the structure under modeling using as raw data its transient port responses to suitable excitations. These include, e.g., the case of transient port scattering responses as typically obtained by full-wave electromagnetic solvers based on the finite-differences time-domain (FDTD) or finite integration (FIT) methods. The TD-VF algorithm works entirely in the time domain, without requiring any knowledge of the frequency-domain responses. This allows direct processing of possibly truncated transient responses, therefore allowing for short full-wave simulations. This paper shows that the accuracy level achievable by TD-VF is excellent. Hence, passivity can be enforced a posteriori using the spectral properties of associated Hamiltonian matrices. Several examples of package, connectors, and discontinuities are provided as illustration.

In this paper, a novel wideband antenna of which shape is tears drop type is proposed by evolving the antenna combined a hemisphere with a biconical antenna element. The antenna is composed a mono-conical antenna element, which is set on a metal floor in an anechoic chamber and can generate the high power electromagnetic field above 1 GHz. Fundamental characteristics of this antenna such as the radiation directivity and the frequency response are measured. These are also calculated by the FI (Finite Integration) method. The phi direction directivity of the tears drop antenna was almost omni directional. The measured responses do not agree well to the calculated ones quantitatively. However, the measured and the calculated responses tend to degrade the electric-field strength as the height of the receiving antenna increase. The antenna has an almost flat frequency response from 1 GHz to 6 GHz within 10 dB in a case of 3 m. Therefore, it was confirmed that the tears drop antenna is suitable for the antenna for the electromagnetic field generation in wideband frequencies from 1 GHz to 6 GHz.

A finite integration method on 3D and 4D space-time grids is studied for electromagnetic wave computation, where a non-uniform time-step distribution is naturally introduced. A dual grid based on the Hodge duality and the Lorentz metric is introduced to provide a simple constitutive equation for electromagnetic variables. An improved space-time grid shape is proposed to suppress unphysical wave-reflection.

A finite volume implicit time integration method for solving the equations of ideal magnetohydrodynamics for the hyperbolic divergence cleaning approach

The description of the developed algorithms and programs, which are used for calibration of fiber-optic gyroscopes working in the conditions of heat varying during spacecraft’s motion in circumterrestrial orbit, is discussed. The mathematical statement for problem of non-stationary heat conduction for the satellite frame and on-board devices is presented.The method of numerical solution is based on the combination of Finite Element Method for boundary value problem and finite difference time integration method for initial one. The developed approach which allows use the parallel calculations in heat problems, is described. The information about developed software is presented by description of main functions written in C++ language. The temperature distribution in dependence on time in the satellite frame and directly in fiber-optic gyroscope’s shell is found by use of developed software. Found distribution makes an opportunity at first to justify demands for ground calibration of gyroscopes for obtaining the compensation models. Secondly, the use of similar models in the conditions of uncertain value of gyroscope’s temperature, which can be, for example, in the case of heat-sensing device’s failure, can be done. The mathematical model of fiber-optic gyroscope snap data is discussed. The hypothesis of the linear dependence of the drift motion from temperature is suggested. The description of calibration algorithm for temperature model of fiber-optic gyroscope is presented. It was concluded that the main influence on the errors of fiber-optic gyroscope measurements is caused by temperature gradient and influence of absolute temperature is not so significant. Thereby, the minimization of temperature error of devices, which are affiliated in orientation and navigation on-board systems, can be performed as well as fail safety of such systems can be increased by use of the presented methods and algorithms.

We present an efficient method for modeling 3-D doubly periodic structures over a wide frequency range based on hybrid finite element/boundary integral (FEBI) methods. The 3-D periodic structures can be represented as non-orthogonal lattices composed of inhomogeneous bianisotropic media with arbitrary metallic patches. Triangular prismatic volume elements were utilized to mesh the unit cell, which provided a great deal of flexibility in modeling complex planar geometries of arbitrary shape. The adaptive integral method (AIM) was applied to speed up the calculation of the matrix-vector product for the BI part within the iterative solver. Furthermore, a model-based parameter estimation (MBPE) technique was proposed for the wide-band interpolation of sparse impedance matrix elements in the BI portion for near field components that were used in the AIM. The accuracy and efficiency of the proposed algorithm is demonstrated by the presented numerical results. To demonstrate the flexibility of the proposed method in modeling arbitrarily shaped elements of frequency selective surfaces (FSS), we included simulation results for an FSS with a non-orthogonal lattice and two elliptical shaped patches embedded in bianisotropic media.

We introduce the application of an arbitrary high‐order derivative (ADER) discontinuous Galerkin (DG) method to simulate earthquake rupture dynamics. The ADER‐DG method uses triangles as computational cells which simplifies the process of discretization of very complex surfaces and volumes by using external automated tools. Discontinuous Galerkin methods are well suited for solving dynamic rupture problems in the velocity‐stress formulation as the variables are naturally discontinuous at the interface between two elements. Therefore, the fault has to be honored by the computational mesh. The so‐called Riemann problem can be solved to obtain well defined values of the variables at the discontinuity itself. Fault geometries of high complexity can be modeled thanks to the flexibility of unstructured meshes, which solves a major bottleneck of other high‐order numerical methods. Additionally, element refinement and coarsening are easily controlled in the meshing process to better resolve the near‐fault area of the model. The fundamental properties of the method are shown, as well as a series of validating exercises with reference solutions and a comparison with the well‐established finite difference, boundary integral, and spectral element methods, in order to test the accuracy of our formulation. An example of dynamic rupture on a nonplanar fault based upon the Landers 1992 earthquake fault system is presented to illustrate the main potentials of the new method.

A critical study of numerical methods for the solution of nonlinear hyperbolic equations for resonance systems

A dual-polarized frequency-tunable composite left-handed slab (CLS) is proposed. The CLS consists of periodic split-ring resonators (SRRs) along with thin wires. Two orthogonal SRR/wire arrays are utilized for dual-polarization purposes. Polarization-selectivity and frequency-tuning are achieved by means of on/off switches placed between the rings of the SRR. By opening all of the switches for one array and closing them for the other, the left-handed behavior can be switched on and off, respectively. Frequency-tuning performance is then achieved by turning on/off the switches in the former array. Transmission characteristics of the composite structure are predicted using a fast periodic array simulator based on the hybrid finite element-boundary integral (FE-BI) method in conjunction with the fast spectral domain algorithm (FSDA). Numerical results demonstrate dual-polarization and frequency-tuning performance of the proposed switching configuration.

By virtue of their low operation count, the application of fast integral methods such as the fast multipole (FMM) and adaptive integral methods (AIM) result in a substantial quickening of the boundary integral portion of the hybrid finite element-boundary integral (FE-BI) method, independent of the shape of the BI contour. Recently, various versions of the FMM have been proposed, each introducing a different approximation to the implementation of the boundary integral. The main goal of this Letter is to provide a comparison of the effect of these fast integral algorithms on the boundary integral when used in conjunction with the traditional FE-BI method.

A numerical scheme, which hybridizes the element level dual field time domain finite element domain decomposition method (ELDFDD/TDFEM) and time domain boundary integral (TDBI) method to accurately and efficiently analyze open-region transient electromagnetic scattering problems, is proposed. The element level decomposition permits an efficient leapfrog-like explicit marching scheme to be used to integrate Maxwell equations in time. The hybridization with TDBI method ensures that an accurate solution can be obtained in the smallest computation domain possible. The accuracy and applicability of the proposed hybrid method is demonstrated by numerical experiments.

Electromagnetic scattering from three-dimensional chiral objects above a perfectly electric or magnetic conducting plane (PEC and PMC) is analyzed by the hybrid finite element-boundary integral (FEM-BI) method. The chiral image principle is used to transform the original single chiral target in half space into two chiral targets with the same permittivity and permeability yet conjugate chirality parameters. Numerical examples demonstrate that the FEM-BI method provides a flexible and powerful solution of multiple scattering from inhomogeneous chiral objects. Both near field distribution and radar cross section (RCS) of chiral objects illuminated by plane waves are provided to demonstrate the effectiveness of the hybrid method.