Simplicial Partitions With Applications To The Finite Element Method

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Simplicial Partitions with Applications to the Finite Element Method

Jan Brandts,Sergey Korotov,Michal Křížek
Simplicial Partitions with Applications to the Finite Element Method Book PDF

Author : Jan Brandts,Sergey Korotov,Michal Křížek
Publisher : Springer Nature
Page : 197 pages
File Size : 45,7 Mb
Release : 2020-10-05
Category : Mathematics
ISBN : 9783030556778

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Simplicial Partitions with Applications to the Finite Element Method by Jan Brandts,Sergey Korotov,Michal Křížek Pdf

This monograph focuses on the mathematical and numerical analysis of simplicial partitions and the finite element method. This active area of research has become an essential part of physics and engineering, for example in the study of problems involving heat conduction, linear elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and gravitational fields. These problems require the simulation of various phenomena and physical fields over complicated structures in three (and higher) dimensions. Since not all structures can be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions are important. In this book an emphasis is placed on angle conditions guaranteeing the convergence of the finite element method for elliptic PDEs with given boundary conditions. It is aimed at a general mathematical audience who is assumed to be familiar with only a few basic results from linear algebra, geometry, and mathematical and numerical analysis.

Anisotropic hp-Mesh Adaptation Methods

Vít Dolejší,Georg May
Anisotropic hp Mesh Adaptation Methods Book PDF

Author : Vít Dolejší,Georg May
Publisher : Springer Nature
Page : 258 pages
File Size : 54,6 Mb
Release : 2022-06-06
Category : Mathematics
ISBN : 9783031042799

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Anisotropic hp-Mesh Adaptation Methods by Vít Dolejší,Georg May Pdf

Mesh adaptation methods can have a profound impact on the numerical solution of partial differential equations. If devised and implemented properly, adaptation significantly reduces the size of the algebraic systems resulting from the discretization, while ensuring that applicable error tolerances are met. In this monograph, drawing from many years of experience, the authors give a comprehensive presentation of metric-based anisotropic hp-mesh adaptation methods. A large part of this monograph is devoted to the derivation of computable interpolation error estimates on simplicial meshes, which take into account the geometry of mesh elements as well as the anisotropic features of the interpolated function. These estimates are then used for the optimization of corresponding finite element spaces in a variety of settings. Both steady and time dependent problems are treated, as well as goal-oriented adaptation. Practical aspects of implementation are also explored, including several algorithms. Many numerical experiments using the discontinuous Galerkin method are presented to illustrate the performance of the adaptive techniques. This monograph is intended for scientists and researchers, including doctoral and master-level students. Portions of the text can also be used as study material for advanced university lectures concerning a posteriori error analysis and mesh adaptation.

In the Tradition of Thurston II

Ken’ichi Ohshika,Athanase Papadopoulos
In the Tradition of Thurston II Book PDF

Author : Ken’ichi Ohshika,Athanase Papadopoulos
Publisher : Springer Nature
Page : 525 pages
File Size : 42,7 Mb
Release : 2022-08-02
Category : Mathematics
ISBN : 9783030975609

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In the Tradition of Thurston II by Ken’ichi Ohshika,Athanase Papadopoulos Pdf

The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.

From Great Discoveries in Number Theory to Applications

Michal Křížek,Lawrence Somer,Alena Šolcová
From Great Discoveries in Number Theory to Applications Book PDF

Author : Michal Křížek,Lawrence Somer,Alena Šolcová
Publisher : Springer Nature
Page : 342 pages
File Size : 53,6 Mb
Release : 2021-09-21
Category : Mathematics
ISBN : 9783030838997

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From Great Discoveries in Number Theory to Applications by Michal Křížek,Lawrence Somer,Alena Šolcová Pdf

This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.

Numerical Mathematics and Advanced Applications ENUMATH 2019

Fred J. Vermolen,Cornelis Vuik
Numerical Mathematics and Advanced Applications ENUMATH 2019 Book PDF

Author : Fred J. Vermolen,Cornelis Vuik
Publisher : Springer Nature
Page : 1185 pages
File Size : 41,5 Mb
Release : 2021-04-30
Category : Mathematics
ISBN : 9783030558741

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Numerical Mathematics and Advanced Applications ENUMATH 2019 by Fred J. Vermolen,Cornelis Vuik Pdf

This book gathers outstanding papers presented at the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019). The conference was organized by Delft University of Technology and was held in Egmond aan Zee, the Netherlands, from September 30 to October 4, 2019. Leading experts in the field presented the latest results and ideas regarding the design, implementation and analysis of numerical algorithms, as well as their applications to relevant societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications, all examined at the highest level of international expertise. The first ENUMATH was held in Paris in 1995, with successive installments at various sites across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), Ankara (2015) and Bergen (2017).

Partition of Unity Methods

St¿phane Bordas,Alexander Menk,Sundararajan Natarajan
Partition of Unity Methods Book PDF

Author : St¿phane Bordas,Alexander Menk,Sundararajan Natarajan
Publisher : John Wiley & Sons
Page : 373 pages
File Size : 55,9 Mb
Release : 2023-10-16
Category : Technology & Engineering
ISBN : 9780470667088

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Partition of Unity Methods by St¿phane Bordas,Alexander Menk,Sundararajan Natarajan Pdf

PARTITION OF UNITY METHODS Master the latest tool in computational mechanics with this brand-new resource from distinguished leaders in the field While it is the number one tool for computer aided design and engineering, the finite element method (FEM) has difficulties with discontinuities, singularities, and moving boundaries. Partition of unity methods addresses these challenges and is now increasingly implemented in commercially available software. Partition of Unity Methods delivers a detailed overview of its fundamentals, in particular the extended finite element method for applications in solving moving boundary problems. The distinguished academics and authors introduce the XFEM as a natural extension of the traditional finite element method (FEM), through straightforward one-dimensional examples which form the basis for the subsequent introduction of higher dimensional problems. This book allows readers to fully understand and utilize XFEM just as it becomes ever more crucial to industry practice. Partition of Unity Methods explores all essential topics on this key new technology, including: Coverage of the difficulties faced by the finite element method and the impetus behind the development of XFEM The basics of the finite element method, with discussions of finite element formulation of linear elasticity and the calculation of the force vector An introduction to the fundamentals of enrichment A revisitation of the partition of unity enrichment A description of the geometry of enrichment features, with discussions of level sets for stationary interfaces Application of XFEM to bio-film, gradient theories, and three dimensional crack propagation Perfect for researchers and postdoctoral candidates working in the field of computational mechanics, Partition of Unity Methods also has a place in the libraries of senior undergraduate and graduate students working in the field. Finite element and CFD analysts and developers in private industry will also greatly benefit from this book.

Large-Scale Scientific Computing

Ivan Lirkov,Svetozar Margenov
Large Scale Scientific Computing Book PDF

Author : Ivan Lirkov,Svetozar Margenov
Publisher : Springer Nature
Page : 557 pages
File Size : 45,5 Mb
Release : 2022-03-17
Category : Computers
ISBN : 9783030975494

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Large-Scale Scientific Computing by Ivan Lirkov,Svetozar Margenov Pdf

This book constitutes revised selected papers from the 13th International Conference on Large-Scale Scientific Computing, LSSC 23021, which was held in Sozopol, Bulgaria, during June 7-11, 2021. The 60 papers included in this book were carefully reviewed and selected from a total of 73 submissions. The volume also includes two invited talks in full paper length. The papers were organized in topical sections as follows: Fractional diffusion problems: numerical methods, algorithms and applications; large-scale models: numerical methods, parallel computations and applications; application of metaheuristics to large-scale problems; advanced discretizations and solvers for coupled systems of partial differential equations; optimal control of ODEs, PDEs and applications; tensor and matrix factorization for big-data analysis; machine learning and model order reduction for large scale predictive simulations; HPC and big data: algorithms and applications; and contributed papers.

Impact of Scientific Computing on Science and Society

Pekka Neittaanmäki,Marja-Leena Rantalainen
Impact of Scientific Computing on Science and Society Book PDF

Author : Pekka Neittaanmäki,Marja-Leena Rantalainen
Publisher : Springer Nature
Page : 451 pages
File Size : 53,7 Mb
Release : 2023-07-07
Category : Technology & Engineering
ISBN : 9783031290824

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Impact of Scientific Computing on Science and Society by Pekka Neittaanmäki,Marja-Leena Rantalainen Pdf

This book analyzes the impact of scientific computing in science and society over the coming decades. It presents advanced methods that can provide new possibilities to solve scientific problems and study important phenomena in society. The chapters cover Scientific computing as the third paradigm of science as well as the impact of scientific computing on natural sciences, environmental science, economics, social science, humanistic science, medicine, and engineering. Moreover, the book investigates scientific computing in high performance computing, quantum computing, and artificial intelligence environment and what it will be like in the 2030s and 2040s.

Numerical Analysis and Its Applications

Svetozar D. Margenov,Lubin Georgiev Vulkov,Jerzy Wasniewski
Numerical Analysis and Its Applications Book PDF

Author : Svetozar D. Margenov,Lubin Georgiev Vulkov,Jerzy Wasniewski
Publisher : Springer
Page : 646 pages
File Size : 54,5 Mb
Release : 2009-02-07
Category : Computers
ISBN : 9783642004643

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Numerical Analysis and Its Applications by Svetozar D. Margenov,Lubin Georgiev Vulkov,Jerzy Wasniewski Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Conference on Numerical Analysis and Its Applications, NAA 2008, held in Lozenetz, Bulgaria in June 2008. The 61 revised full papers presented together with 13 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address all current aspects of numerical analysis and discuss a wide range of problems concerning recent achievements in physics, chemistry, engineering, and economics. A special focus is given to numerical approximation and computational geometry, numerical linear algebra and numerical solution of transcendental equations, numerical methods for differential equations, numerical modeling, and high performance scientific computing.

Numerical Mathematics and Advanced Applications 2009

Gunilla Kreiss,Per Lötstedt,Axel Målqvist,Maya Neytcheva
Numerical Mathematics and Advanced Applications 2009 Book PDF

Author : Gunilla Kreiss,Per Lötstedt,Axel Målqvist,Maya Neytcheva
Publisher : Springer Science & Business Media
Page : 900 pages
File Size : 53,7 Mb
Release : 2010-10-19
Category : Mathematics
ISBN : 9783642117954

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Numerical Mathematics and Advanced Applications 2009 by Gunilla Kreiss,Per Lötstedt,Axel Målqvist,Maya Neytcheva Pdf

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A Simple Introduction to the Mixed Finite Element Method

Gabriel N. Gatica
A Simple Introduction to the Mixed Finite Element Method Book PDF

Author : Gabriel N. Gatica
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 43,6 Mb
Release : 2014-01-09
Category : Mathematics
ISBN : 9783319036953

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A Simple Introduction to the Mixed Finite Element Method by Gabriel N. Gatica Pdf

The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.

Numerical Mathematics and Advanced Applications ENUMATH 2017

Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop
Numerical Mathematics and Advanced Applications ENUMATH 2017 Book PDF

Author : Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop
Publisher : Springer
Page : 1070 pages
File Size : 55,5 Mb
Release : 2019-01-05
Category : Computers
ISBN : 9783319964157

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Numerical Mathematics and Advanced Applications ENUMATH 2017 by Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop Pdf

This book collects many of the presented papers, as plenary presentations, mini-symposia invited presentations, or contributed talks, from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2017. The conference was organized by the University of Bergen, Norway from September 25 to 29, 2017. Leading experts in the field presented the latest results and ideas in the designing, implementation, and analysis of numerical algorithms as well as their applications to relevant, societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications. These discussions are upheld at the highest level of international expertise. The first ENUMATH conference was held in Paris in 1995 with successive conferences being held at various locations across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), and Ankara (2015).

The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

A. K. Aziz
The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations Book PDF

Author : A. K. Aziz
Publisher : Academic Press
Page : 814 pages
File Size : 40,9 Mb
Release : 2014-05-10
Category : Technology & Engineering
ISBN : 9781483267982

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The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations by A. K. Aziz Pdf

The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations is a collection of papers presented at the 1972 Symposium by the same title, held at the University of Maryland, Baltimore County Campus. This symposium relates considerable numerical analysis involved in research in both theoretical and practical aspects of the finite element method. This text is organized into three parts encompassing 34 chapters. Part I focuses on the mathematical foundations of the finite element method, including papers on theory of approximation, variational principles, the problems of perturbations, and the eigenvalue problem. Part II covers a large number of important results of both a theoretical and a practical nature. This part discusses the piecewise analytic interpolation and approximation of triangulated polygons; the Patch test for convergence of finite elements; solutions for Dirichlet problems; variational crimes in the field; and superconvergence result for the approximate solution of the heat equation by a collocation method. Part III explores the many practical aspects of finite element method. This book will be of great value to mathematicians, engineers, and physicists.

Application and Implementation of Finite Element Methods

J. E. Akin
Application and Implementation of Finite Element Methods Book PDF

Author : J. E. Akin
Publisher : Unknown
Page : 388 pages
File Size : 43,9 Mb
Release : 1984
Category : Mathematics
ISBN : MINN:31951D002307831

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Application and Implementation of Finite Element Methods by J. E. Akin Pdf

Mathematics of Computing -- Numerical Analysis.

Finite Elements II

Alexandre Ern,Jean-Luc Guermond
Finite Elements II Book PDF

Author : Alexandre Ern,Jean-Luc Guermond
Publisher : Springer Nature
Page : 491 pages
File Size : 45,6 Mb
Release : 2021-04-22
Category : Mathematics
ISBN : 9783030569235

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Finite Elements II by Alexandre Ern,Jean-Luc Guermond Pdf

This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.