Construction of higher-order curl-conforming finite elements and its assembly

Different choices are available when constructing vector finite element bases in real coordinates. In this communication, two different designs of higher-order curl-conforming basis functions are introduced and explained, showing the particularities of its assembly. Tetrahedra and hexahedra are used as element shapes to assess the effect of triangular and quadrilateral faces on the two considered constructions of basis functions. A comparison of their robustness in terms of the condition number of the finite element matrices for a number of distortions is includedMinisterio de Ciencia y Tecnología, Grant/Award Numbers: TEC2013- 47753-C3, TEC2016-80386-P; Ministerio de Educación, Cultura y Deporte, Grant/Award Number: FPU14/0374

Experimental insight into the domain decomposition method for a finite element method code

The use of Domain Decomposition Methods (DDM) for a Finite Element Method (FEM) framework was a hot topic in the past decade, leading to very powerful results in terms of scalability and widening the problems that could be full-wave simulated with the FEM, [1–3]. However, despite the promising results shown in these references, it seems not to be a widespread use of the DDM in commercial FEM softwares or publications, whereas the common research topics (adaptivity, higher-order basis functions, different element shapes) in FEM have not been explored together with DDM. In this communication, we share experimental details with different non-overlapping DDM within FEM. We explore the use of different finite element shapes with up to fourth-order basis functions. We propose a propagation problem through a rectangular waveguide as a benchmark, and we show the different implementation choices available and their impact in the performance of the code

Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method

The adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. The adaptive process consists of three steps: error estimation, marking, and refinement. We adapt techniques already applied for other shapes to the triangular prisms, showing the differences here in detail. We use five different marking strategies, comparing the results obtained with different parameters. We adapt these strategies to a conformation process necessary to avoid hanging nodes in the resulting mesh. We have also applied two special rules to ensure the quality of the refined mesh. We show the effect of these rules with the Method of Manufactured Solutions and numerical results to validate the implementation introduced.This work has been financially supported by TEC2016-80386-

Mejoramiento de imágenes de tomografía axial computarizada del corazón empleando filtrado de difusión anisotrópica /

El presente proyecto consiste del procesamiento de imágenes de tomografía computarizada empleando el método de filtrado por difusión anisotrópica, para obtener resultados de alta resolución y calidad. En las imágenes de tomografía axial computarizada se observa en general una buena relación señal a ruido debido a la naturaleza del procedimiento y los estándares de calidad aceptables en las imágenes obtenidas, lo cual es una ventaja para el análisis médico. Sin embargo, en el análisis de ciertas estructuras de tamaño muy reducido y alta densidad, como lo son las calcificaciones en las arterias ubicadas en el corazón, la calidad de la imagen no es suficiente. Para mejorar la resolución comúnmente se emplea la deconvolución, pero como efecto se tiene un incremento del ruido de alta frecuencia. En este trabajo se propone el uso de filtrado anisotrópico para reducir ruido sin afectar la resolución. Al procesar las imágenes se logró mejorar la relación señal a ruido, lo cual se demuestra al comparar los resultados obtenidos con las imágenes originales empleando una evaluación cuantitativa del mejoramiento de la imagen.Incluye referencias bibliográfica

Test-Driven Development of a Substructuring Technique for the Analysis of Electromagnetic Finite Periodic Structures

In this paper, we follow the Test-Driven Development (TDD) paradigm in the development of an in-house code to allow for the finite element analysis of finite periodic type electromagnetic structures (e.g., antenna arrays, metamaterials, and several relevant electromagnetic problems). We use unit and integration tests, system tests (using the Method of Manufactured Solutions—MMS), and application tests (smoke, performance, and validation tests) to increase the reliability of the code and to shorten its development cycle. We apply substructuring techniques based on the definition of a unit cell to benefit from the repeatability of the problem and speed up the computations. Specifically, we propose an approach to model the problem using only one type of Schur complement which has advantages concerning other substructuring techniques.This work has been financially supported by TEC2016-80386-P and PID2019-109984RB-C41

Second-Order Nedelec Curl-Conforming Prismatic Element for Computational Electromagnetics

A systematic approach to obtaining mixed-order curl-conforming basis functions for a triangular prism is presented; focus is made on the second-order case. Space of functions for the prism is given. Basis functions are obtained as the dual basis with respect to suitably discretized Nedelec degrees of freedom functionals acting on elements of the space. Thus, the linear independence of the basis functions is assured while the belonging of the basis to the a priori given space of functions is guaranteed. Different strategies for the finite element assembly of the basis are discussed. Numerical results showing the verification procedure of the correctness of the implemented basis functions are given. Numerical results about sensibility of the condition number of the basis obtained concerning the quality of the elements of the mesh are also shown. Comparison with other representative sets of basis functions for prisms is included.This work was supported by "DiDaCTIC: Desarrollo de un sistema de comunicaciones inalambrico en rango THz integrado de alta tasa de datos"; TEC2013-47753-C3, CAM S2013/ICE-3004 "DIFRAGEOS" projects and "Ayudas para contratos predoctorales de Formación del Profesorado Universitario FPU

Meshing strategies for 3d geo-electromagnetic modeling in the presence of metallic infrastructure

In 3D geo-electromagnetic modeling, an adequate discretisation of the modeling domain is crucial to obtain accurate forward responses and reliable inversion results while reducing the computational cost. This paper investigates the mesh design for subsurface models, including steel-cased wells, which is relevant for many exploration settings but still remains a numerically challenging task. Applying a goal-oriented mesh refinement technique and subsequent calculations with the high-order edge finite element method, simulations of 3D controlled-source electromagnetic models in the presence of metallic infrastructure are performed. Two test models are considered, each needing a distinct version of approximation methods to incorporate the conductive steel casings of the included wells. The influence of mesh quality, goal-oriented meshing, and high-order approximations on problem sizes, computational cost, and accuracy of electromagnetic responses is investigated. The main insights of our work are: (a) the applied numerical schemes can mitigate the computational burden of geo-electromagnetic modeling in the presence of steel artifacts; (b) investigating the processes driving the meshing of models with embedded metallic infrastructures can lead to adequate strategies to deal with the inversion of such electromagnetic data sets. Based on the modeling results and analyses conducted, general recommendations for modeling strategies are proposed when performing simulations for challenging steel infrastructure scenarios.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The work of O.C-R. has received funding from the Ministerio de Educación y Ciencia (Spain) under Project TED2021-131882B-C42.The code development of P.R. has been financed by the Smart Exploration project. Smart Exploration has received funding from the European Union’s Horizon 2020 Framework Programme under grant agreement N∘ 775971. The computations were enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC) at UPPMAX partially funded by the Swedish Research Council through grant agreement N∘ SNIC 2021/22-883.Peer ReviewedPostprint (published version

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.Funding for open access charge: CRUE-Universitat Jaume

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.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work has been supported by the Spanish Government PID2020-113656RB-C21, PID2019-106455GB-C21 and by the Valencian Regional Government through PROMETEO/2019/109, as well as the Regional Government of Madrid throughout the project MIMACUHSPACE-CM-UC3M

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.This work was supported in part by the Spanish Government under Grant TEC2016-80386-P, Grant TIN2017-82972-R, and Grant ESP2015-68245-C4-1-P, and in part by the Valencian Regional Government under Grant PROMETEO/2019/109