INITIAL VALUE TECHNIQUES FOR THE HELMHOLTZ AND MAXWELL EQUATIONS

We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging.     

Incorporating the Havriliak–Negami dielectric model in the FD-TD method

We derive and analyze an efficient algorithm to incorporate the anomalously dispersive Havriliak–Negami dielectric model of induced polarization in the Finite-difference time-domain (FD-TD) method. Our algorithm implements this dielectric model, which in the time-domain involves fractional derivatives and fractional differential operators, with a preset error over the desired computational time interval [0,T_comp] and correctly takes into account the singularity at t = 0⁺ of the corresponding time-domain dielectric susceptibility. The overall algorithm is shown to be second-order accurate in space and time, and to obey the standard FD-TD stability condition. Numerical experiments confirm our analysis.     

几种家用加热电器的工作原理

本文主要介绍了电饭锅、微波炉和电磁灶3种家用加热电器的工作原理，旨在教学中将理论知识与实际生活相结合，有助于加深对知识的理解，也激发了学生们的兴趣和求知欲．     

Fast evaluation of Helmholtz potential on graphics processing units (GPUs)

This paper presents a parallel algorithm implemented on graphics processing units (GPUs) for rapidly evaluating spatial convolutions between the Helmholtz potential and a large-scale source distribution. The algorithm implements a non-uniform grid interpolation method (NGIM), which uses amplitude and phase compensation and spatial interpolation from a sparse grid to compute the field outside a source domain. NGIM reduces the computational time cost of the direct field evaluation at N observers due to N co-located sources from O(N²) to O(N) in the static and low-frequency regimes, to O(N log N) in the high-frequency regime, and between these costs in the mixed-frequency regime. Memory requirements scale as O(N) in all frequency regimes. Several important differences between CPU and GPU implementations of the NGIM are required to result in optimal performance on respective platforms. In particular, in the CPU implementations all operations, where possible, are pre-computed and stored in memory in a preprocessing stage. This reduces the computational time but significantly increases the memory consumption. In the GPU implementations, where handling memory often is a critical bottle neck, several special memory handling techniques are used to accelerate the computations. A significant latency of the GPU global memory access is hidden by implementing coalesced reading, which requires arranging many array elements in contiguous parts of memory. Contrary to the CPU version, most of the steps in the GPU implementations are executed on-fly and only necessary arrays are kept in memory. This results in significantly reduced memory consumption, increased problem size N that can be handled, and reduced computational time on GPUs. The obtained GPU–CPU speed-up ratios are from 150 to 400 depending on the required accuracy and problem size. The presented method and its CPU and GPU implementations can find important applications in various fields of physics and engineering.     

Non-reflecting boundary conditions for waveguides

New non-reflecting boundary conditions are introduced for the solution of the Helmholtz equation in a waveguide. These boundary conditions are perfectly transparent for all propagating modes. They do not require the determination of these propagating modes but only their propagation constants. A quasi-local form of these boundary conditions is well suited as terminating boundary condition beyond finite element meshes. Related convergence properties to the exact solution and optimal error estimates are established.

     

关于电磁学与电动力学打通的设想

从教材可行性、教材体系结构和教材内容三方面着手,提出了打通适合师范类教学的电磁学与电动力学教材的设想     

计算电磁学及其在复杂电磁环境数值模拟中的应用和发展趋势

概述计算电磁学的发展历程及其数值方法,并从学术研究、商业软件以及专用软件三个层次论述国内外研究的最新进展.结合复杂电磁环境的应用介绍复杂电磁环境数值模拟平台的研究现状,最后提出未来发展趋势的几点设想.     

Analysis of a FEM–BEM model posed on the conducting domain for the time-dependent eddy current problem

The three-dimensional eddy current time-dependent problem is considered. We formulate it in terms of two variables, one lying only on the conducting domain and the other on its boundary. We combine finite elements (FEM) and boundary elements (BEM) to obtain a FEM–BEM coupled variational formulation. We establish the existence and uniqueness of the solution in the continuous and the fully discrete case. Finally, we investigate the convergence order of the fully discrete scheme.     

时域全波电磁计算程序JEMS-FDTD在复杂电磁环境研究中的应用

将自主研发的大规模并行三维全波电磁场时域求解程序JEMS-FDTD应用于复杂电磁环境问题,计算并分析了楼宇内电波传播特性和飞行器瞬态电磁特性。对楼宇内电波传播特性的计算获得了建筑物内任意位置的电磁场分布和电磁脉冲在建筑物内的时域传播过程,其结果可用于无线通信和电磁环境安全研究;对飞行器瞬态电磁特性的计算获得了飞行器舱内外瞬态电磁近场分布,其结果可用于飞行器强辐射场防护等研究。     

Efficient evaluation of Casimir force in arbitrary three-dimensional geometries by integral equation methods

In this Letter, we generalized the surface integral equation method for the evaluation of Casimir force in arbitrary three-dimensional geometries. Similar to the two-dimensional case, the evaluation of the mean Maxwell stress tensor is cast into solving a series of three-dimensional scattering problems. The formulation and solution of the three-dimensional scattering problems are well-studied in classical computational electromagnetics. This Letter demonstrates that this quantum electrodynamic phenomenon can be studied using the knowledge and techniques of classical electrodynamics.