Unstructured Meshing Technologies
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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]. -
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 . -
FELICITY: a MATLAB/C++ TOOLBOX for DEVELOPING FINITE ELEMENT METHODS and SIMULATION MODELING\Ast
SIAM J. SCI.COMPUT. \bigcircc 2018 Society for Industrial and Applied Mathematics Vol. 40, No. 2, pp. C234{C257 FELICITY: A MATLAB/C++ TOOLBOX FOR DEVELOPING FINITE ELEMENT METHODS AND SIMULATION MODELING\ast SHAWN W. WALKERy Abstract. This paper describes a MATLAB/C++ finite element toolbox, called FELICITY, for simulating various types of systems of partial differential equations (e.g., coupled elliptic/parabolic problems) using the finite element method. It uses MATLAB in an object-oriented way for high-level manipulation of data structures in finite element codes, while utilizing a domain-specific language (DSL) and code generation to automate low-level tasks such as matrix assembly (via the MATLAB mex interface). We describe the fundamental functionality of the toolbox's MATLAB interface, such as using higher order Lagrange (simplicial) meshes, defining finite element spaces, allocating degrees- of-freedom, assembling discrete bilinear and linear forms, and interpolation over meshes. Moreover, we describe in-depth how automatic code generation is implemented in FELICITY. Two example problems and their implementation are provided to demonstrate the ability of FELICITY to solve coupled problems with interacting subdomains of different co-dimension. Future improvements are also discussed. Key words. finite elements, coupled systems, geometric flows, code generation, MATLAB, open source software AMS subject \bfc \bfl \bfa \bfs \bfifi\bfc\bfa\bft\bfo\bfn. 68N30, 65N30, 65M60, 68N19, 68N20 DOI. 10.1137/17M1128745 1. Introduction. The development of numerical methods to solve partial dif- ferential equations (PDEs) continues to advance to address new domain areas and problems of increasing complexity. With this, the number of software packages has increased to address the needs for researching new methods and simulating large prob- lems. -
Mofem: an Open Source, Parallel Finite Element Library
MoFEM: An open source, parallel finite element library Kaczmarczyk, Ł., Ullah, Z., Lewandowski, K., Meng, X., Zhou, X-Y., Athanasiadis, I., Nguyen, H., Chalons- Mouriesse, C-A., Richardson, E. J., Miur, E., Shvarts, A. G., Wakeni, M., & Pearce, C. J. (2020). MoFEM: An open source, parallel finite element library. The Journal of Open Source Software, 5(45). https://doi.org/doi.org/10.21105/joss.01441 Published in: The Journal of Open Source Software Document Version: Publisher's PDF, also known as Version of record Queen's University Belfast - Research Portal: Link to publication record in Queen's University Belfast Research Portal Publisher rights © 2020 The Authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited. General rights Copyright for the publications made accessible via the Queen's University Belfast Research Portal is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The Research Portal is Queen's institutional repository that provides access to Queen's research output. Every effort has been made to ensure that content in the Research Portal does not infringe any person's rights, or applicable UK laws. If you discover content in the Research Portal that you believe breaches copyright or violates any law, please contact [email protected]. Download date:06. -
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). -
Aparallel Implementation of a Femsolver in Scilab
powered by A PARALLEL IMPLEMENTATION OF A FEM SOLVER IN SCILAB Author: Massimiliano Margonari Keywords. Scilab; Open source software; Parallel computing; Mesh partitioning, Heat transfer equation. Abstract: In this paper we describe a parallel application in Scilab to solve 3D stationary heat transfer problems using the finite element method. Two benchmarks have been done: we compare the results with reference solutions and we report the speedup to measure the effectiveness of the approach. Contacts [email protected] This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. EnginSoft SpA - Via della Stazione, 27 - 38123 Mattarello di Trento | P.I. e C.F. IT00599320223 A parallel FEM solver in Scilab 1. Introduction Nowadays many simulation software have the possibility to take advantage of multi- processors/cores computers in the attempt to reduce the solution time of a given task. This not only reduces the annoying delays typical in the past, but allows the user to evaluate larger problems and to do more detailed analyses and to analyze a greater number of scenarios. Engineers and scientists who are involved in simulation activities are generally familiar with the terms “high performance computing” (HPC). These terms have been coined to indicate the ability to use a powerful machine to efficiently solve hard computational problems. One of the most important keywords related to the HPC is certainly parallelism. The total execution time can be reduced if the original problem can be divided into a given number of subtasks. Total time is reduced because these subtasks can be tackled concurrently, that means in parallel, by a certain number of machines or cores. -
Understanding the Relationships Between Aesthetic Properties Of
Understanding the relationships between aesthetic properties of shapes and geometric quantities of free-form curves and surfaces using Machine Learning Techniques Aleksandar Petrov To cite this version: Aleksandar Petrov. Understanding the relationships between aesthetic properties of shapes and ge- ometric quantities of free-form curves and surfaces using Machine Learning Techniques. Mechanical engineering [physics.class-ph]. Ecole nationale supérieure d’arts et métiers - ENSAM, 2016. English. NNT : 2016ENAM0007. tel-01344873 HAL Id: tel-01344873 https://pastel.archives-ouvertes.fr/tel-01344873 Submitted on 12 Jul 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. N°: 2009 ENAM XXXX 2016-ENAM-0007 PhD THESIS in cotutelle To obtain the degree of Docteur de l’Arts et Métiers ParisTech Spécialité “Mécanique – Conception” École doctorale n° 432: “Science des Métiers de l’ingénieur” and Dottore di Ricerca della Università degli Studi di Genova Specialità “Ingeneria Meccanica” Scuola di Dottorato: “Scienze e tecnologie per l’ingegneria” ciclo XXVI Presented and defended publicly by Aleksandar PETROV January 25th, 2016 Understanding the relationships between aesthetic properties of shapes and geometric quantities of free-form curves and surfaces using Machine Learning Techniques Director of thesis: Philippe VÉRON Co-director of thesis: Franca GIANNINI T Co-supervisors of the thesis: Jean-Philippe PERNOT, Bianca FALCIDIENO H È Jury M. -
Octave Package, User's Guide
Octave package, User’s Guide∗ version 0.1.0 François Cuveliery March 24, 2019 Abstract This Octave package make it possible to generate mesh files from .geo files by using gmsh. It’s also possible with the ooGmsh2 and ooGmsh4 classes to read the mesh file (respectively for MSH file format version 2.2 and version 4.x) and to store its contains in more user-friendly form. This package must be regarded as a very simple interface between gmsh files and Octave. So you are free to create any data structures or objects you want from an ooGmsh2 object or an ooGmsh4 object. 0 Contents 1 Introduction 2 2 Installation 3 2.1 Installation automatic, all in one (recommanded) . .3 3 gmsh interface 4 3.1 function fc_oogmsh.gmsh.buildmesh2d ............................4 3.2 function fc_oogmsh.gmsh.buildmesh3d ............................6 3.3 function fc_oogmsh.gmsh.buildmesh3ds ...........................6 3.4 function fc_oogmsh.gmsh.buildpartmesh2d .........................6 3.5 function fc_oogmsh.gmsh.buildpartmesh3d .........................8 3.6 function fc_oogmsh.gmsh.buildpartmesh3ds .........................8 3.7 function fc_oogmsh.gmsh.buildPartRectangle .......................8 4 ooGmsh4 class (version 4.x) 9 4.1 Methods . 10 4.1.1 ooGms4 constructor . 10 4.1.2 info method . 10 ∗LATEX manual, revision 0.1.0.a, compiled with Octave 5.1.0, and packages fc-oogmsh[0.1.0], fc-tools[0.0.27], fc-meshtools[0.1.0], fc-graphics4mesh[0.0.4], and using gmsh 4.2.2 yLAGA, UMR 7539, CNRS, Université Paris 13 - Sorbonne Paris Cité, Université Paris 8, 99 Avenue J-B Clément, F-93430 Villetaneuse, France, [email protected]. -
High-Performance High-Order Simulation of Wave and Plasma Phenomena
High-Performance High-Order Simulation of Wave and Plasma Phenomena by Andreas Klockner¨ Dipl.-Math. techn., Universitat¨ Karlsruhe (TH); Karlsruhe, Germany, 2005 M.S., Brown University; Providence, RI, 2006 A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Division of Applied Mathematics at Brown University PROVIDENCE, RHODE ISLAND May 2010 c Copyright 2010 by Andreas Klockner¨ This dissertation by Andreas Klockner¨ is accepted in its present form by The Division of Applied Mathematics as satisfying the dissertation requirement for the degree of Doctor of Philosophy. Date Jan Sickmann Hesthaven, Ph.D., Advisor Recommended to the Graduate Council Date Johnny Guzman,´ Ph.D., Reader Date Chi-Wang Shu, Ph.D., Reader Approved by the Graduate Council Date Sheila Bonde, Dean of the Graduate School iii Vitae Biographical Information Birth August 5th, 1977 Konstanz, Germany Education 2005 – 2010 Ph.D. in Applied Mathematics (in progress) Division of Applied Mathematics, Brown University, Providence, RI Advisor: Jan Hesthaven 2005 Diplom degree in Applied Mathematics (Technomathematik) Institut fur¨ Angewandte Mathematik, Universitat¨ Karlsruhe, Ger- many Advisor: Willy Dorfler¨ 2001 – 2002 Exchange Student, Department of Mathematics University of North Carolina at Charlotte, Charlotte, NC 2000 Vordiplom in Computer Science, Universitat¨ Karlsruhe, Germany Experience 6/2006 – 9/2006 J. Wallace Givens Research Associate Mathematics and Computer Science Div., Argonne Nat’l Laboratory, -
Quality Tetrahedral Mesh Generation with HXT and the Growing SPR Operation
Received: Added at production Revised: Added at production Accepted: Added at production DOI: xxx/xxxx ARTICLE TYPE Quality tetrahedral mesh generation with HXT Célestin Marot* | Jean-François Remacle 1 Institute of Mechanics, Materials and Civil Engineering, Université catholique de Summary Louvain, Louvain-la-Neuve, Belgium We proposed, in a recent paper 1, a fast 3D parallel Delaunay kernel for tetrahedral Correspondence mesh generation. This kernel was however incomplete in the sense that it lacked Célestin Marot, Institute of Mechanics, the necessary mesh improvement tools. The present paper builds on that previous Materials and Civil Engineering, Université catholique de Louvain, work and proposes a fast parallel mesh improvement stage that delivers high-quality Avenue Georges Lemaitre 4, bte L4.05.02, tetrahedral meshes compared to alternative open-source mesh generators. Our mesh 1348 Louvain-la-Neuve, Belgium. Email: [email protected] improvement toolkit includes edge removal and improved Laplacian smoothing as well as a brand new operator called the Growing SPR Cavity, which can be regarded Funding Information as the mother of all flips. The paper describes the workflow of the new mesh improve- This research was supported by the ment schedule, as well as the details of the implementation. The result of this research European Union’s Horizon 2020 research is a series of open-source scalable software components, called HXT, whose overall and innovation programme, ERC-2015AdG-694020. efficiency is demonstrated on practical examples by means of a detailed comparative benchmark with two open-source mesh generators: Gmsh and TetGen. KEYWORDS: HXT, Growing SPR Cavity, quality, tetrahedral, mesh, improvement 1 INTRODUCTION Tetrahedral meshes are the geometrical support for most finite element discretizations. -
Large Scale Finite Element Mesh Generation with Gmsh
Towards (very) large scale finite element mesh generation with Gmsh Christophe Geuzaine Universit´e de Li`ege ELEMENT workshop, October 20, 2020 1 Some background • I am a professor at the University of Li`ege in Belgium, where I lead a team of about 15 people in the Montefiore Institute (EECS Dept.), at the intersection of applied math, scientific computing and engineering physics • Our research interests include modeling, analysis, algorithm development, and simulation for problems arising in various areas of engineering and science • Current applications: low- and high-frequency electromagnetics, geophysics, biomedical problems • We write quite a lot of codes, some released as open source software: http://gmsh.info, http://getdp.info, http://onelab.info 2 What is Gmsh? • Gmsh (http://gmsh.info) is an open source 3D finite element mesh generator with a built-in CAD engine and post-processor • Includes a graphical user interface (GUI) and can drive any simulation code through ONELAB • Today, Gmsh represents about 500k lines of C++ code • still same 2 core developers (Jean-Francois Remacle from UCLouvain and myself); about 100 with ≥ 1 commit • about 1,000 people on mailing lists • about 10,000 downloads per month (70% Windows) • about 500 citations per year – the main Gmsh paper is cited about 4,500 times • Gmsh has probably become one of the most popular (open source) finite element mesh generators? 3 ∼ 20 years of Gmsh development in 1 minute A warm thank you to all the contributors! A little bit of history • Gmsh was started in 1996, as -
Unstructured WW3
WW3 Tutorial 5.1: Unstructured WW3 1. Purpose In this tutorial exercise, we will construct a hindcast simulation using WW3’s unstructured grid mode. Topics covered are the generation of unstructured meshes and the setting up of the unstructured model run, including the specification of offshore wave boundary conditions for coastal applications. 2. Input files At the start of this tutorial exercise, you will find the following files in the directory day_5/tutorial_unstructured/ : ww3_grid.inp (ww3 grid preprocessor input file) ww3_bound.inp (ww3 boundary condition preprocessor input file) ww3_shel.inp (ww3 main model input file) ww3_ounf.inp (ww3 field output postprocessor input file, NetCDF format) hawaii_v5.msh (unstructured computational mesh) mww3.?????????.spec (Various boundary condition input files) plot_gmsh.m (Matlab script for visualizing the unstructured mesh) plot_ounf_unstr.m (Matlab script for visualizing unstructured output, from NetCDF) 2.1 Unstructured mesh definition The main difference in this model configuration relative to the regular grid option is the presence of the unstructured mesh file *.msh . Since this mesh does not have a regular structure as in the case of a regular grid, the grid points (called nodes ) and their connections (called elements ) need to be explicitly defined. The unstructured meshes used by WW3 comprise of triangular elements, but in general unstructured grids can also feature quadrilateral, pentagonal, hexagonal, etc. elements. The construction of a good unstructured mesh is a time-consuming process, and we will only discuss the general principles here. There are a number of grid generation programs available to build meshes, either relatively simple open source systems such as Gmsh 1 , Triangle 2 , BatTri 3 , or more sophisticated proprietary software such as SMS 4.