Mesh Truncation Technique Research Articles

Strategies to parallelize a finite element mesh truncation technique on multi-core and many-core architectures

Achieving maximum parallel performance on multi-core CPUs and many-core GPUs is a challenging task depending on multiple factors. These include, for example, the number and granularity of the computations or the use of the memories of the devices. In this paper, we assess those factors by evaluating and comparing different parallelizations of the same problem on a multiprocessor containing a CPU with 40 cores and four P100 GPUs with Pascal architecture. We use, as study case, the convolutional operation behind a non-standard finite element mesh truncation technique in the context of open region electromagnetic wave propagation problems. A total of six parallel algorithms implemented using OpenMP and CUDA have been used to carry out the comparison by leveraging the same levels of parallelism on both types of platforms. Three of the algorithms are presented for the first time in this paper, including a multi-GPU method, and two others are improved versions of algorithms previously developed by some of the authors. This paper presents a thorough experimental evaluation of the parallel algorithms on a radar cross-sectional prediction problem. Results show that performance obtained on the GPU clearly overcomes those obtained in the CPU, much more so if we use multiple GPUs to distribute both data and computations. Accelerations close to 30 have been obtained on the CPU, while with the multi-GPU version accelerations larger than 250 have been achieved.

An Efficient Parallel Hybrid Method of FEM-MLFMA for Electromagnetic Radiation and Scattering Analysis of Separated Objects

In order to meet the rapidly increasing demand for accurate and efficient analysis of complex radiating or scattering structures in the presence of electrically large objects, a finite element method (FEM)-multilevel fast multipole algorithm (MLFMA) hybrid method that based on the Finite Element-Iterative Integral Equation Evaluation (FE-IIEE) mesh truncation technique is proposed in this paper. The present method makes use of FEM for the regions with small and complex features and MLFMA for the analysis of the electrically large objects, which ensure the accuracy and applicability of the method are better than most commonly adopted FEM-high frequency technique (HFT) hybrid method. The mutual interactions between regions are taken into account in a fully coupled way through iterative near filed computation process. In order to achieve an excellent performance, both algorithms have been implemented together from scratch, being able to run over multi CPU cores. An efficient parallel FEM domain decomposition method (DDM) solver with exploiting geometrical repetitions is included to drastically reduce memory requirements and computational time in the calculation of large array antenna. Also, the parallel MLFMA is adopted to expedite the near-field information exchange between regions. Through numerical example, the effect of distance between regions on the convergence of the proposed hybrid method is studied, and it is shown that the proposed method converge well even if the distance is equal to 0.05λ. Through comparisons with an in-house higher order method of moments (HOMoM) code and commercial software FEKO, the accuracy and effectiveness of the implemented parallel hybrid method are validated showing excellent performance.

GPU Acceleration of a Non-Standard Finite Element Mesh Truncation Technique for Electromagnetics

The emergence of General Purpose Graphics Processing Units (GPGPUs) provides new opportunities to accelerate applications involving a large number of regular computations. However, properly leveraging the computational resources of graphical processors is a very challenging task. In this paper, we use this kind of device to parallelize FE-IIEE (Finite Element-Iterative Integral Equation Evaluation), a non-standard finite element mesh truncation technique introduced by two of the authors. This application is computationally very demanding due to the amount, size and complexity of the data involved in the procedure. Besides, an efficient implementation becomes even more difficult if the parallelization has to maintain the complex workflow of the original code. The proposed implementation using CUDA applies different optimization techniques to improve performance. These include leveraging the fastest memories of the GPU and increasing the granularity of the computations to reduce the impact of memory access. We have applied our parallel algorithm to two real radiation and scattering problems demonstrating speedups higher than 140 on a state-of-the-art GPU.

On the use of many-core machines for the acceleration of a mesh truncation technique for FEM

Finite element method (FEM) has been used for years for radiation problems in the field of electromagnetism. To tackle problems of this kind, mesh truncation techniques are required, which may lead to the use of high computational resources. In fact, electrically large radiation problems can only be tackled using massively parallel computational resources. Different types of multi-core machines are commonly employed in diverse fields of science for accelerating a number of applications. However, properly managing their computational resources becomes a very challenging task. On the one hand, we present a hybrid message passing interface + OpenMP-based acceleration of a mesh truncation technique included in a FEM code for electromagnetism in a high-performance computing cluster equipped with 140 compute nodes. Results show that we obtain about 85% of the theoretical maximum speedup of the machine. On the other hand, a graphics processing unit has been used to accelerate one of the parts that presents high fine-grain parallelism.

Self-adaptive [formula omitted] finite element method with iterative mesh truncation technique accelerated with Adaptive Cross Approximation

To alleviate the computational bottleneck of a powerful two-dimensional self-adaptive hp finite element method (FEM) for the analysis of open region problems, which uses an iterative computation of the Integral Equation over a fictitious boundary for truncating the FEM domain, we propose the use of Adaptive Cross Approximation (ACA) to effectively accelerate the computation of the Integral Equation. It will be shown that in this context ACA exhibits a robust behavior, yields good accuracy and compression levels up to 90%, and provides a good fair control of the approximants, which is a crucial advantage for hp adaptivity. Theoretical and empirical results of performance (computational complexity) comparing the accelerated and non-accelerated versions of the method are presented. Several canonical scenarios are addressed to resemble the behavior of ACA with h, p and hp adaptive strategies, and higher order methods in general.

ANALYSIS OF V TRANSMISSION LINES RESPONSE TO EXTERNAL ELECTROMAGNETIC FIELDS

In the present paper the response of V transmission line to electromagnetic illumination has been obtained. Also in order to determine the VTL frequency operation band for both TE and TM modes a Gaussian pulse source has been applied to the structure. The VTL structure has received considerable attention in high frequency and microwave IC packaging. The purpose of this study is to determine high frequency design considerations in order to reduce the effects of electromagnetic interference (EMI) on the VTL structure and maintain the desired performance. It was observed that the effect of incident EM waves on the V lines performance is considerably lower than conventional microstrips, however the V lines are more sensitive to sources at close proximity. In addition, although the V lines show lower dispersion at higher frequencies, their frequency operation band is limited by a resonance like behavior which is directly related to the V groove dimensions. The full wave analysis is carried out using the Yee-cell based 2 Dimensional Finite Difference Time Domain method (2D-FDTD), while enforcing a very stable and efficient mesh truncation technique.

Concurrent complementary operators for mesh truncation in frequency-domain simulations

The concurrent complementary operators method (C-COM), when used in the finite-difference time-domain method (FDTD), achieved levels of accuracy unprecedented in any previous mesh-truncation technique. In this paper, we introduce the extension of the C-COM theory to frequency-domain (time-harmonic) simulations. A validation of the new method is demonstrated by using the finite-difference frequency domain (FDFD) method.

Application of the concurrent complementary operators method to numerically derived absorbing boundary conditions

AbstractThe concurrent complementary operators method (C–COM) has been demonstrated to be a highly effective mesh truncation technique for the simulation of electromagnetic open‐region transient or time‐harmonic problems. In previous work, the C–COM was applied to analytically derived absorbing boundary conditions (ABCs). In this work, we show that the C–COM can be applied to the wider class of highly effective and versatile numerically derived ABCs. As a demonstration of the validity of this generalization, we consider the case of a Liao ABC, and show that high accuracy can be obtained. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 272–275, 2002.

Frequency-domain complementary operators for finite-elements simulation

A new mesh-truncation technique is introduced for the frequency-domain (time-harmonic) solution of open-region radiation problems. The technique is based on the complementary operators method (COM), where two independent solutions are averaged to eliminate first-order boundary reflections. The dual complementariness in the frequency domain is achieved by introducing a discrete-domain operator that achieves the objective of /spl part//sub t/ in the original time-domain development of COM.

The complementary operators method applied to acoustic finite-difference time-domain simulations

The complementary operators method (COM) has recently been introduced as a mesh-truncation technique for open-domain radiation problems in electromagnetics. The COM entails the construction of two solutions that employ absorbing boundary conditions (ABCs) with complementary behavior, i.e., the reflection coefficients associated with the two ABCs are exactly opposite each other. The average of these solutions then yields a new solution in which the errors caused by artificial reflections from the termination of grid are nearly eliminated. In this work, COM is introduced for the finite-difference time-domain (FDTD) solution of acoustics problems. The development of COM is presented in terms of Higdon’s absorbing boundary operators, but generalization to non-Higdon operators is straightforward. The effectiveness of COM in comparison to other absorbing boundary conditions is demonstrated with numerical experiments in two and three dimensions.

Extension of the concurrent COM mesh-truncation technique to 3-D FDTD simulations

In a recent letter, a new implementation of the complementary operators method (COM) was introduced for 2-D radiation problems. Referred to as the concurrent complementary operators method (C-COM), this new implementation achieved a level of accuracy and efficiency that surpassed that achieved earlier by the classical two solution implementation of COM. This letter extends the application of the C-COM to treat 3-D radiation problems. Numerical results using the finite-difference time-domain method (FDTD) for two representative experiments are presented to demonstrate the effectiveness of this new technique. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 17: 244–247, 1998.

Dynamic analysis of V transmission lines

In this work, a dynamic analysis of the V line is presented. Previous work analyzed the performance of this structure for low frequency applications using quasistatic approximations. Here, we extend the analysis of the V line into the higher frequency range where dispersion becomes significant and where it cannot be predicted by quasistatic methods. We show that the V line provides features and advantages that are not present in the conventional microstrip structures, most notably the appreciable decrease in coupling between adjacent lines in comparison with the conventional microstrip structure. This feature makes the V line well suited for high packaging density applications. The full-wave analysis is carried out using a Yee-cell based finite-difference time-domain (FDTD) method, while enforcing a highly efficient and stable mesh truncation technique. Results are presented for a single and multiconductor structures.

Comparative study of the PML and C-COM mesh-truncation techniques

The recently developed concurrent complementary operators method (C-COM) for mesh truncation of finite-difference time-domain (FDTD) problems has been shown to produce a substantial improvement in differential equation-based absorbing boundary conditions (ABCs). In this letter, the C-COM and the perfectly matched layer (PML) approaches are compared using two-dimensional problems. Two representative geometries are considered that address the absorption of evanescent waves and waves traveling at near-grazing incidence. It is found that the C-COM yields significant improvements over the PML solution for these geometries.

A 3-D application of the Bymoment method for electromagnetic scattering

One can find various mesh truncation techniques in the literature for the finite element solution of electromagnetic scattering problems. In this paper, a mesh truncation approach referred to as the three-dimensional bymoment method is considered. This approach uses two z-directed Hertz vector potentials instead of three Cartesian field components to formulate the relevant boundary conditions. The pertaining FEM field solutions are calculated by treating the scattering problem as an interior region problem. The FEM field solutions are then numerically coupled on a second boundary surface that is conformal to the first one and completely enclosed by it. The coupling procedure yields a set of expansion coefficients, with the help of which the total field solution is written as an appropriate linear combination of the interior region FEM field solutions.