High-Performance Finite Elements with MFEM

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. This paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy’s Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED)

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.This work has been fnancially supported by TEC2016-80386-P, TIN2017-82972-R, CAM S2013/ICE-3004 projects and “Ayudas para contratos predoctorales de Formación del Profesorado Universitario FPU”

High Performance Computing of Complex Electromagnetic Algorithms Based on GPU/CPU Heterogeneous Platform and Its Applications to EM Scattering and Multilayered Medium Structure

The fast and accurate numerical analysis for large-scale objects and complex structures is essential to electromagnetic simulation and design. Comparing to the exploration in EM algorithms from mathematical point of view, the computer programming realization is coordinately significant while keeping up with the development of hardware architectures. Unlike the previous parallel algorithms or those implemented by means of parallel programming on multicore CPU with OpenMP or on a cluster of computers with MPI, the new type of large-scale parallel processor based on graphics processing unit (GPU) has shown impressive ability in various scenarios of supercomputing, while its application in computational electromagnetics is especially expected. This paper introduces our recent work on high performance computing based on GPU/CPU heterogeneous platform and its application to EM scattering problems and planar multilayered medium structure, including a novel realization of OpenMP-CUDA-MLFMM, a developed ACA method and a deeply optimized CG-FFT method. With fruitful numerical examples and their obvious enhancement in efficiencies, it is convincing to keep on deeply investigating and understanding the computer hardware and their operating mechanism in the future

Accelerating magnetic induction tomography‐based imaging through heterogeneous parallel computing

Magnetic Induction Tomography (MIT) is a non‐invasive imaging technique, which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters of an object from measurements made on its surface. With the exploitation of parallelism, it is possible to achieve high quality inexpensive MIT images for biomedical applications on clinically relevant time scales. In this paper we investigate the performance of different parallel implementations of the forward eddy current problem, which is the main computational component of the inverse problem through which measured voltages are converted into images. We show that a heterogeneous parallel method that exploits multiple CPUs and GPUs can provide a high level of parallel scaling, leading to considerably improved runtimes. We also show how multiple GPUs can be used in conjunction with deal.II, a widely‐used open source finite element library