Finite element methods for Maxwell's equations.

Dense matrix factorizations, such as LU, Cholesky and QR, are widely used for scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This paper proposes a new hybrid approach, based on Algorithm-Based Fault Tolerance (ABFT), to help matrix factorizations algorithms survive fail-stop failures. We consider extreme conditions, such as the absence of any reliable component and the possibility of loosing both data and checksum from a single failure. We will present a generic solution for protecting the right factor, where the updates are applied, of all above mentioned factorizations. For the left factor, where the panel has been applied, we propose a scalable checkpointing algorithm. This algorithm features high degree of checkpointing parallelism and cooperatively utilizes the checksum storage leftover from the right factor protection. The fault-tolerant algorithms derived from this hybrid solution is applicable to a wide range of dense matrix factorizations, with minor modifications. Theoretical analysis shows that the fault tolerance overhead sharply decreases with the scaling in the number of computing units and the problem size. Experimental results of LU and QR factorization on the Kraken (Cray XT5) supercomputer validate the theoretical evaluation and confirm negligible overhead, with- and without-errors.

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Algorithm-based fault tolerance for dense matrix factorizations

Communication is one of the most essential activities of mankind and there is no doubt that satellite communications have made a tremendous stride in this matter. The goal has been to create uninterrupted, seamless, high throughput connectivity no matter where. The fact that this is all possible is because of the existence of electromagnetic waves: Antennas play a pivotal role in advanced functionality, efficient usage of the bandwidth, and cost effective deployment of this technology. The trends of the technological development of antennas for a wide range of commercial satellite communication services and the challenges faced in their development are chronologically reviewed. Various antenna concepts are summarized and future challenges are projected. A rather comprehensive list of references is included to assist the reader with further reading beyond this paper.

Technology Trends and Challenges of Antennas for Satellite Communication Systems

This paper proposes a new sparse matrix storage format which allows an e-cient implementation of a sparse matrix vector product on a Fermi Graphics Processing Unit (GPU). Unlike previous formats it has both low memory footprint and good throughput. The new format, which we call Sliced ELLR-T has been designed speciflcally for accelerating the iterative solution of a large sparse and complex-valued system of linear equations arising in computational electromagnetics. Numerical tests have shown that the performance of the new implementation reaches 69 GFLOPS in complex single precision arithmetic. Compared to the optimized six core Central Processing Unit (CPU) (Intel Xeon 5680) this performance implies a speedup by a factor of six. In terms of speed the new format is as fast as the best format published so far and at the same time it does not introduce redundant zero elements which have to be stored to ensure fast memory access. Compared to previously published solutions, signiflcantly larger problems can be handled using low cost commodity GPUs with limited amount of on-board memory.

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A Memory Efficient and Fast Sparse Matrix Vector Product on a GPU

A multi-GPU implementation of the multilevel fast multipole algorithm (MLFMA) based on the hybrid OpenMPCUDA parallel programming model (OpenMP-CUDA-MLFMA) is presented for computing electromagnetic scattering of a three-dimensional conducting object. The proposed hierarchical parallelization strategy ensures a high computational throughput for the GPU calculation. The resulting OpenMP-based multi-GPU implementation is capable of solving real-life problems with over one million unknowns with a remarkable speed-up. The radar cross sections of a few benchmark objects are calculated to demonstrate the accuracy of the solution. The results are compared with those from the CPU-based MLFMA and measurements. The capability and efficiency of the presented method are analyzed through the examples of a sphere, an aerocraft, and a missile-like object. Compared with the 8-threaded CPU-based MLFMA, the OpenMP-CUDA-MLFMA method can achieve from 5 to 20 total speed-up ratios.

An OpenMP-CUDA Implementation of Multilevel Fast Multipole Algorithm for Electromagnetic Simulation on Multi-GPU Computing Systems

In this paper, we combine and extend two of our previous works to provide a more complete solution for the GPU acceleration of the Method of Moments, using CUDA by NVIDIA. To this end, the formulations of the original 1982 Rao-Wilton-Glisson paper are revisited, and the scattering analysis of a square PEC plate is considered as a simple example. One of the primary contributions of the paper is to serve as a guide for the implementation of other GPU-accelerated computational electromagnetic routines. As such, this provides a background on general-purpose GPU computation, as well as insight into the finer details of the implementation. The results computed compared well with reference values. From a performance point of view, the GPU implementation was found to be significantly faster. The fastest measured speedup for one of the phases of the Method of Moments computations was more than a factor of 140. This translated into a speedup of about a factor of 45, when the entire Method of Moments solution process for the problem was considered.

GPU-Accelerated Method of Moments by Example: Monostatic Scattering

In the method of moments (MOM) analysis of electromagnetic phenomena, the LU decomposition is often an important and costly step in the solution process. In this reported work, the acceleration of LU decomposition using graphics processing units (GPUs) has been considered. Although existing GPU methods, such as those supplied by MAGMA, provide significant speedup over CPU-only implementations, they are limited to smaller problems by the amount of device memory available. The method now presented takes a left-looking LU decomposition as a starting point and uses an out-of-core like approach to significantly increase the size of the problems that can be solved. In addition, a hybrid implementation that utilises MAGMA as part of the solution process is presented, further improving the performance of the method. For the double precision complex variant of the LU decomposition, the number of MOM degrees of freedom that can be solved using a solver based on MAGMA and a GPU device with 1GB of memory is limited to 7936. Using the presented panel-based and hybrid approaches has already permitted problems more than four times larger to be solved with significant speedup.

GPU-based LU decomposition for large method of moments problems

This paper considers the characteristic mode analysis (CMA) of arbitrary electromagnetic structures using the comprehensive 3D electromagnetic field solver, FEKO [1]. The theory of characteristic modes, as presented in [2], is used to derive the real orthogonal current modes. These modes are obtained by solving a generalised symmetric eigenvalue problem defined by the real and imaginary parts of the Method-of-Moments (MoM) impedance matrix. The research presented in this article discusses the techniques used in FEKO to solve this generalised eigenproblem. Furthermore, paralleli-sation using both distributed and shared memory programming models, as well as GPU computation is considered within the FEKO framework to accelerate the CMA.

Characteristic mode analysis of arbitrary electromagnetic structures using FEKO

In this paper, a GPU accelerated implementation of the matrix assembly phase of the methods of moments is presented. The modelling of PEC structures using the electric field integral equation and the Rao-Wilton-Glisson basis functions introduced in [1] is considered. NVIDIA CUDA is used to do the GPU development and the double precision support offered by the GT200 architecture is used to provide a high level of accuracy. The CUDA implementation of the matrix assembly phase considered is able to attain a speedup of 65 times over the CPU implementation.

GPU acceleration of method of moments matrix assembly using Rao-Wilton-Glisson basis functions

FEniCS is a set of software tools that allows for rapid implementation of expressions associated with finite-element analysis. The main interface for FEniCS is DOLFIN, which provides both C++ and Python front ends to the software tools. The use of the Python front end, PyDOLFIN, to model various electromagnetic (EM) problems is investigated. Some elementary problems implemented in FEniCS include the scalar potential solution to closed- and open-boundary electrostatic problems, as well as the cutoff and dispersion analysis of a hollow rectangular waveguide. More advanced topics considered include the implementation of radiation from an infinitesimal dipole, and near-field-to-far-field transformations.

E. Lezar

Papers

GPU-Accelerated Method of Moments by Example: Monostatic Scattering

GPU-based LU decomposition for large method of moments problems

Characteristic mode analysis of arbitrary electromagnetic structures using FEKO

GPU acceleration of method of moments matrix assembly using Rao-Wilton-Glisson basis functions

Using the FEniCS Package for FEM Solutions in Electromagnetics