A Three-Dimensional Finite Element Mesh Generator with Built-In Pre- and Post-Processing Facilities
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Arxiv:1911.09220V2 [Cs.MS] 13 Jul 2020
MFEM: A MODULAR FINITE ELEMENT METHODS LIBRARY ROBERT ANDERSON, JULIAN ANDREJ, ANDREW BARKER, JAMIE BRAMWELL, JEAN- SYLVAIN CAMIER, JAKUB CERVENY, VESELIN DOBREV, YOHANN DUDOUIT, AARON FISHER, TZANIO KOLEV, WILL PAZNER, MARK STOWELL, VLADIMIR TOMOV Lawrence Livermore National Laboratory, Livermore, USA IDO AKKERMAN Delft University of Technology, Netherlands JOHANN DAHM IBM Research { Almaden, Almaden, USA DAVID MEDINA Occalytics, LLC, Houston, USA STEFANO ZAMPINI King Abdullah University of Science and Technology, Thuwal, Saudi Arabia Abstract. MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of dis- cretization approaches and emphasis on usability, portability, and high-performance computing efficiency. MFEM's goal is to provide application scientists with access to cutting-edge algorithms for high-order finite element mesh- ing, discretizations and linear solvers, while enabling researchers to quickly and easily develop and test new algorithms in very general, fully unstructured, high-order, parallel and GPU-accelerated settings. In this paper we describe the underlying algorithms and finite element abstractions provided by MFEM, discuss the software implementation, and illustrate various applications of the library. arXiv:1911.09220v2 [cs.MS] 13 Jul 2020 1. Introduction The Finite Element Method (FEM) is a powerful discretization technique that uses general unstructured grids to approximate the solutions of many partial differential equations (PDEs). It has been exhaustively studied, both theoretically and in practice, in the past several decades [1, 2, 3, 4, 5, 6, 7, 8]. MFEM is an open-source, lightweight, modular and scalable software library for finite elements, featuring arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing (HPC) efficiency [9]. -
Meshing for the Finite Element Method
Meshing for the Finite Element Method Summer Seminar ISC5939 .......... John Burkardt Department of Scientific Computing Florida State University http://people.sc.fsu.edu/∼jburkardt/presentations/. mesh 2012 fsu.pdf 10/12 July 2012 1 / 119 FEM Meshing Meshing Computer Representations The Delaunay Triangulation TRIANGLE DISTMESH MESH2D Files and Graphics 1 2 2 D Problems 3D Problems Conclusion 2 / 119 MESHING: The finite element method begins by looking at a complicated region, and thinking of it as a mesh of smaller, simpler subregions. The subregions are simple, (perhaps triangles) so we understand their geometry; they are small because when we approximate the differential equations, our errors will be related to the size of the subregions. More, smaller subregions usually mean less total error. After we compute our solution, it is described in terms of the mesh. The simplest description uses piecewise linear functions, which we might expect to be a crude approximation. However, excellent results can be obtained as long as the mesh is small enough in places where the solution changes rapidly. 3 / 119 MESHING: Thus, even though the hard part of the finite element method involves considering abstract approximation spaces, sequences of approximating functions, the issue of boundary conditions, weak forms and so on, ...it all starts with a very simple idea: Given a geometric shape, break it into smaller, simpler shapes; fit the boundary, and be small in some places. Since this is such a simple idea, you might think there's no reason to worry about it much! 4 / 119 MESHING: Indeed, if we start by thinking of a 1D problem, such as modeling the temperature along a thin strand of wire that extends from A to B, our meshing problem is trivial: Choose N, the number of subregions or elements; Insert N-1 equally spaced nodes between A and B; Create N elements, the intervals between successive nodes. -
Using the ELECTRIC VLSI Design System Version 9.07
Using the ELECTRIC VLSI Design System Version 9.07 Steven M. Rubin Author's affiliation: Static Free Software ISBN 0−9727514−3−2 Published by R.L. Ranch Press, 2016. Copyright (c) 2016 Static Free Software Permission is granted to make and distribute verbatim copies of this book provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this book under the conditions for verbatim copying, provided also that they are labeled prominently as modified versions, that the authors' names and title from this version are unchanged (though subtitles and additional authors' names may be added), and that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Permission is granted to copy and distribute translations of this book into another language, under the above conditions for modified versions. Electric is distributed by Static Free Software (staticfreesoft.com), a division of RuLabinsky Enterprises, Incorporated. Table of Contents Chapter 1: Introduction.....................................................................................................................................1 1−1: Welcome.........................................................................................................................................1 1−2: About Electric.................................................................................................................................2 1−3: Running -
Reference Manual Ii
GiD The universal, adaptative and user friendly pre and postprocessing system for computer analysis in science and engineering Reference Manual ii Table of Contents Chapters Pag. 1 INTRODUCTION 1 1.1 What's GiD 1 1.2 GiD Manuals 1 2 GENERAL ASPECTS 3 2.1 GiD Basics 3 2.2 Invoking GiD 4 2.2.1 First start 4 2.2.2 Command line flags 5 2.2.3 Command line extra file 6 2.2.4 Settings 6 2.3 User Interface 7 2.3.1 Top menu 9 2.3.2 Toolbars 9 2.3.3 Command line 12 2.3.4 Status and Information 13 2.3.5 Right buttons 13 2.3.6 Mouse operations 13 2.3.7 Classic GiD theme 14 2.4 User Basics 16 2.4.1 Point definition 16 2.4.1.1 Picking in the graphical window 17 2.4.1.2 Entering points by coordinates 17 2.4.1.2.1 Local-global coordinates 17 2.4.1.2.2 Cylindrical coordinates 18 2.4.1.2.3 Spherical coordinates 18 2.4.1.3 Base 19 2.4.1.4 Selecting an existing point 19 2.4.1.5 Point in line 19 2.4.1.6 Point in surface 19 2.4.1.7 Tangent in line 19 2.4.1.8 Normal in surface 19 2.4.1.9 Arc center 19 2.4.1.10 Grid 20 2.4.2 Entity selection 20 2.4.3 Escape 21 2.5 Files Menu 22 2.5.1 New 22 2.5.2 Open 22 2.5.3 Open multiple.. -
MFEM: a Modular Finite Element Methods Library
MFEM: A Modular Finite Element Methods Library Robert Anderson1, Andrew Barker1, Jamie Bramwell1, Jakub Cerveny2, Johann Dahm3, Veselin Dobrev1,YohannDudouit1, Aaron Fisher1,TzanioKolev1,MarkStowell1,and Vladimir Tomov1 1Lawrence Livermore National Laboratory 2University of West Bohemia 3IBM Research July 2, 2018 Abstract MFEM is a free, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing efficiency. Its mission is to provide application scientists with access to cutting-edge algorithms for high-order finite element meshing, discretizations and linear solvers. MFEM also enables researchers to quickly and easily develop and test new algorithms in very general, fully unstructured, high-order, parallel settings. In this paper we describe the underlying algorithms and finite element abstractions provided by MFEM, discuss the software implementation, and illustrate various applications of the library. Contents 1 Introduction 3 2 Overview of the Finite Element Method 4 3Meshes 9 3.1 Conforming Meshes . 10 3.2 Non-Conforming Meshes . 11 3.3 NURBS Meshes . 12 3.4 Parallel Meshes . 12 3.5 Supported Input and Output Formats . 13 1 4 Finite Element Spaces 13 4.1 FiniteElements....................................... 14 4.2 DiscretedeRhamComplex ................................ 16 4.3 High-OrderSpaces ..................................... 17 4.4 Visualization . 18 5 Finite Element Operators 18 5.1 DiscretizationMethods................................... 18 5.2 FiniteElementLinearSystems . 19 5.3 Operator Decomposition . 23 5.4 High-Order Partial Assembly . 25 6 High-Performance Computing 27 6.1 Parallel Meshes, Spaces, and Operators . 27 6.2 Scalable Linear Solvers . -
New Development in Freefem++
J. Numer. Math., Vol. 20, No. 3-4, pp. 251–265 (2012) DOI 10.1515/jnum-2012-0013 c de Gruyter 2012 New development in freefem++ F. HECHT∗ Received July 2, 2012 Abstract — This is a short presentation of the freefem++ software. In Section 1, we recall most of the characteristics of the software, In Section 2, we recall how to to build the weak form of a partial differential equation (PDE) from the strong form. In the 3 last sections, we present different examples and tools to illustrated the power of the software. First we deal with mesh adaptation for problems in two and three dimension, second, we solve numerically a problem with phase change and natural convection, and the finally to show the possibilities for HPC we solve a Laplace equation by a Schwarz domain decomposition problem on parallel computer. Keywords: finite element, mesh adaptation, Schwarz domain decomposition, parallel comput- ing, freefem++ 1. Introduction This paper intends to give a small presentation of the software freefem++. A partial differential equation is a relation between a function of several variables and its (partial) derivatives. Many problems in physics, engineering, mathematics and even banking are modeled by one or several partial differen- tial equations. Freefem++ is a software to solve these equations numerically in dimen- sions two or three. As its name implies, it is a free software based on the Finite Element Method; it is not a package, it is an integrated product with its own high level programming language; it runs on most UNIX, WINDOWS and MacOs computers. -
Calculix USER's MANUAL
CalculiX USER’S MANUAL - CalculiX GraphiX, Version 2.7 - Klaus Wittig February 18, 2014 Figure 1: A complex model made from scratch using second order brick elements 1 Contents 1 Introduction 7 2 Concept 7 3 File Formats 8 4 Getting Started 9 5 Program Parameters 13 6 Input Devices 14 6.1 Mouse ................................. 14 6.2 Keyboard ............................... 15 7 Menu 16 7.1 Datasets................................ 16 7.1.1 Entity ............................. 17 7.2 Viewing ................................ 17 7.2.1 ShowElementsWithLight . 17 7.2.2 ShowBadElements . 17 7.2.3 Fill............................... 17 7.2.4 Lines.............................. 17 7.2.5 Dots.............................. 18 7.2.6 ToggleCullingBack/Front . 18 7.2.7 ToggleModelEdges . 18 7.2.8 ToggleElementEdges . 18 7.2.9 ToggleSurfaces/Volumes . 18 7.2.10 Toggle Move-Z/Zoom . 18 7.2.11 Toggle Background Color . 19 7.2.12 ToggleVector-Plot . 19 7.2.13 ToggleAdd-Displacement . 19 7.3 Animate................................ 19 7.3.1 Start.............................. 19 7.3.2 Tune-Value .......................... 19 7.3.3 StepsperPeriod ....................... 20 7.3.4 TimeperPeriod ....................... 20 7.3.5 ToggleRealDisplacements . 20 7.3.6 ToggleDatasetSequence. 20 7.4 Frame ................................. 20 7.5 Zoom ................................. 20 7.6 Center................................. 20 7.7 Enquire ................................ 21 7.8 Cut .................................. 21 7.9 Graph ................................. 21 7.10Orientation .............................. 21 2 7.10.1 +xView............................ 21 7.10.2 -xView ............................ 21 7.10.3 +yView............................ 21 7.10.4 -yView ............................ 21 7.10.5 +zView............................ 21 7.10.6 -zView ............................ 22 7.11Hardcopy ............................... 22 7.11.1 Tga-Hardcopy ........................ 22 7.11.2 Ps-Hardcopy ......................... 22 7.11.3 Gif-Hardcopy . -
An XFEM Based Fixed-Grid Approach to Fluid-Structure Interaction
TECHNISCHE UNIVERSITAT¨ MUNCHEN¨ Lehrstuhl fur¨ Numerische Mechanik An XFEM based fixed-grid approach to fluid-structure interaction Axel Gerstenberger Vollstandiger¨ Abdruck der von der Fakultat¨ fur¨ Maschinenwesen der Techni- schen Universitat¨ Munchen¨ zur Erlangung des akademischen Grades eines Doktor-Ingenieurs (Dr.-Ing.) genehmigten Dissertation. Vorsitzender: Univ.-Prof. Dr.-Ing. habil. Nikolaus A. Adams Prufer¨ der Dissertation: 1. Univ.-Prof. Dr.-Ing. Wolfgang A. Wall 2. Prof. Peter Hansbo, Ph.D. University of Gothenburg / Sweden Die Dissertation wurde am 14. 4. 2010 bei der Technischen Universitat¨ Munchen¨ eingereicht und durch die Fakultat¨ fur¨ Maschinenwesen am 21. 6. 2010 ange- nommen. Zusammenfassung Die vorliegende Arbeit behandelt ein Finite Elemente (FE) basiertes Festgit- terverfahren zur Simulation von dreidimensionaler Fluid-Struktur-Interak- tion (FSI) unter Berucksichtigung¨ großer Strukturdeformationen. FSI ist ein oberflachengekoppeltes¨ Mehrfeldproblem, bei welchem Stuktur- und Fluid- gebiete eine gemeinsame Oberflache¨ teilen. In dem vorgeschlagenen Festgit- terverfahren wird die Stromung¨ durch eine Eulersche Betrachtungsweise be- schrieben, wahrend¨ die Struktur wie ublich¨ in Lagrangscher Betrachtungs- weise formuliert wird. Die Fluid-Struktur-Grenzflache¨ kann sich dabei un- abhangig¨ von dem ortsfesten Fluidnetz bewegen, so dass keine Fluidnetzver- formungen auftreten und beliebige Grenzflachenbewegungen¨ moglich¨ sind. Durch die unveranderte¨ Lagrangsche Strukturformulierung liegt der Schwer- punkt der Arbeit -
Getting Started in High Performance Electronic Design
Getting started in high performance electronic design Wojtek Skulski Department of Physics and Astronomy University of Rochester Rochester, NY 14627-0171 skulski _at_ pas.rochester.edu First presented May/23/2002 Updated for the web July/03/2004 Wojtek Skulski May/2002 Department of Physics and Astronomy, University of Rochester Getting started with High performance electronic design • 3-hour class • Designing high performance surface mount and multilayer boards. • What tools and resources are available? • How to get my design manufactured and assembled? • Board design with OrCAD Capture and Layout. • When and where: • Thursday, May/23/2002, 9-12am, Bausch&Lomb room 106 (1st floor). • Slides updated for the web July/03/2004. • Reserve your handout. • Send e-mail to [email protected] if you plan to attend. • Walk-ins are invited, but there may be no handouts if you do not register. • See you there! Wojtek Skulski May/2002 Department of Physics and Astronomy, University of Rochester The goal and outline of this class • Goal: • Describe the tools available to us for designing high performance electronic instruments. • Outline • Why do we need surface mount and multilayer boards? • What tools and resources are available? • How to get my PCB manufactured? • How to get my board assembled? • Designing with OrCAD Capture and OrCAD Layout. • The audience • You know the basics of electronics. • … and you need to get going quickly with your design. Wojtek Skulski May/2002 Department of Physics and Astronomy, University of Rochester Disclaimer • I am describing tools and methods which work for me. • I do not claim that this information is complete. -
Open-Source Automatic Nonuniform Mesh Generation for FDTD Simulation
This is a repository copy of Structured Mesh Generation : Open-source automatic nonuniform mesh generation for FDTD simulation. White Rose Research Online URL for this paper: https://eprints.whiterose.ac.uk/100155/ Version: Accepted Version Article: Berens, Michael, Flintoft, Ian David orcid.org/0000-0003-3153-8447 and Dawson, John Frederick orcid.org/0000-0003-4537-9977 (2016) Structured Mesh Generation : Open- source automatic nonuniform mesh generation for FDTD simulation. IEEE Antennas and Propagation Magazine. pp. 45-55. ISSN 1045-9243 https://doi.org/10.1109/MAP.2016.2541606 Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ 1 Open Source Automatic Non-uniform Mesh Generation for FDTD Simulation Michael K. Berens, Ian D. Flintoft, Senior Member, IEEE, and John F. Dawson, Member, IEEE, Abstract—This article describes a cuboid structured mesh generator suitable for 3D numerical modelling using techniques such as finite-difference time-domain (FDTD) and transmission-line matrix (TLM). -
Development of a Coupling Approach for Multi-Physics Analyses of Fusion Reactors
Development of a coupling approach for multi-physics analyses of fusion reactors Zur Erlangung des akademischen Grades eines Doktors der Ingenieurwissenschaften (Dr.-Ing.) bei der Fakultat¨ fur¨ Maschinenbau des Karlsruher Instituts fur¨ Technologie (KIT) genehmigte DISSERTATION von Yuefeng Qiu Datum der mundlichen¨ Prufung:¨ 12. 05. 2016 Referent: Prof. Dr. Stieglitz Korreferent: Prof. Dr. Moslang¨ This document is licensed under the Creative Commons Attribution – Share Alike 3.0 DE License (CC BY-SA 3.0 DE): http://creativecommons.org/licenses/by-sa/3.0/de/ Abstract Fusion reactors are complex systems which are built of many complex components and sub-systems with irregular geometries. Their design involves many interdependent multi- physics problems which require coupled neutronic, thermal hydraulic (TH) and structural mechanical (SM) analyses. In this work, an integrated system has been developed to achieve coupled multi-physics analyses of complex fusion reactor systems. An advanced Monte Carlo (MC) modeling approach has been first developed for converting complex models to MC models with hybrid constructive solid and unstructured mesh geometries. A Tessellation-Tetrahedralization approach has been proposed for generating accurate and efficient unstructured meshes for describing MC models. For coupled multi-physics analyses, a high-fidelity coupling approach has been developed for the physical conservative data mapping from MC meshes to TH and SM meshes. Interfaces have been implemented for the MC codes MCNP5/6, TRIPOLI-4 and Geant4, the CFD codes CFX and Fluent, and the FE analysis platform ANSYS Workbench. Furthermore, these approaches have been implemented and integrated into the SALOME simulation platform. Therefore, a coupling system has been developed, which covers the entire analysis cycle of CAD design, neutronic, TH and SM analyses. -
Intel Xeon W-1200 Workstation Processors Product Brief
PRODUCT BRIEF | Intel® Xeon® W-1200 Workstation Processors PROFESSIONAL PERFORMANCE POWER AN ENTRY-LEVEL PROFESSIONAL WORKSTATION WITH AN INTEL® Xeon® W-1200 PROCESSOR Intel® Xeon® W-1200 processors (succeeding the Intel® Xeon® E-2200 processors) deliver great performance for entry workstation users with integrated processor graphics alongside the added reliability and confidence of Error Correcting Code (ECC) memory. Get outstanding performance plus best-in-class manageability features and support for ground- breaking technologies that enable you to visualize, simulate, research and work with greater accuracy than ever before. PROFESSIONAL Performance WHEN IT MATTERS • Up to 10 Cores | Up to 20 Threads • Up to 4.1 GHz Base • Up to 5.3 GHz with Intel® Thermal Velocity Boost1 • NEW Intel® Turbo Boost Max Technology 3.0 • Support for up to 128 GB DDR4-2933 ECC Memory2 • Intel® Wi-Fi AX202 (Gig+) support using CNVi³ FeaTURED TecHNOLOGIES • Intel® Hyper-Threading Technology • Up to 40 processor PCIe* lanes • Error-correcting code (ECC) memory support • Thunderbolt™ 3 support • Intel® Optane™ technology support • Intel vPro® platform support A NEW LEVEL OF Performance Designed to deliver an entry-level platform for professionals requiring a true workstation, Intel® Xeon® W-1200 processors are specially optimized for a wide range of workflows and industries such as health and life sciences, financial services, architecture, engineering and construction (AEC). IncreaseD CapaBILITY ENHANCED Performance FAST ConnecTIVITY NEW—Intel® Thermal Velocity Boost NEW—UP TO 5.3 GHz NEW—2.5G Intel® Ethernet Controller Technology i225 support4 Get up to a blazing 5.3 GHz clock speed, Even the most complex workflows won’t Network speed is essential in today’s right out of the box for fast performance.