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A Locally Modified Second Order Finite Element Method For Interface Problems And Its Implementation In 2 Dimensions
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Book Synopsis A Locally Modified Second-order Finite Element Method for Interface Problems and Its Implementation in 2 Dimensions by : Stefan Frei
Download or read book A Locally Modified Second-order Finite Element Method for Interface Problems and Its Implementation in 2 Dimensions written by Stefan Frei and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Methods for Interface Problems with Locally Modified Triangulations by :
Download or read book Finite Element Methods for Interface Problems with Locally Modified Triangulations written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Interface problems arise in many applications such as heat conduction in different materials. The partial differential equations (PDEs) that describe these applications have domains that consist of different subdomains. The different subdomains can have complicated shapes or can have different properties. For instance, different subdomains can represent different phases of the same material, such as water and ice. The coefficients of the PDEs can be discontinuous across the interfaces of the subdomains, and the source terms can be singular. Due to these irregularities, the solutions to the PDEs can be nonsmooth or even discontinuous. Here we restrict ourselves to interface problems that do not depend on time and can be expressed in terms of elliptic or elasticity PDEs. We present finite element methods (FEMs) for elliptic and elasticity problems with interfaces. The FEMs are based on body-fitted meshes with a locally modified triangulation. A FEM based on a body-fitted mesh uses a triangulation that is aligned with the interfaces. However, for complicated interfaces it can be difficult and expensive to generate such triangulations. That is why we use a locally modified triangulation based on Cartesian meshes. We first form a Cartesian mesh, then move the grid points near the interfaces to the interfaces. This leads to a locally modified triangulation. We use the standard FEM with the locally modified triangulation to solve the elliptic and elasticity problems with interfaces. By FEM theory, the method is second order accurate in the infinity norm for piecewise smooth solutions. We present some numerical examples to show the second order accuracy of the method. We also present a new second order finite difference method that does not require to compute the curvature. At points away from the interface we can approximate the PDE by using the standard 5-point scheme. At points where the interface crosses the 5-point scheme, we still use the 5-point scheme by introducing.
Book Synopsis Finite Element Methods for Interface Problems with Locally Modified Triangulations by : Hui Xie
Download or read book Finite Element Methods for Interface Problems with Locally Modified Triangulations written by Hui Xie and published by . This book was released on 2009 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: elliptic and elasticity interface problems, FEPG, body-fitted mesh, Cartesian mesh, locally modified triangulations, finite element methods.
Book Synopsis Computational Biomechanics for Medicine by : Grand R. Joldes
Download or read book Computational Biomechanics for Medicine written by Grand R. Joldes and published by Springer. This book was released on 2016-06-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Computational Biomechanics for Medicine titles provide an opportunity for specialists in computational biomechanics to present their latest methodologies and advancements. This volume comprises eighteen of the newest approaches and applications of computational biomechanics, from researchers in Australia, New Zealand, USA, UK, Switzerland, Scotland, France and Russia. Some of the interesting topics discussed are: tailored computational models; traumatic brain injury; soft-tissue mechanics; medical image analysis; and clinically-relevant simulations. One of the greatest challenges facing the computational engineering community is to extend the success of computational mechanics to fields outside traditional engineering, in particular to biology, the biomedical sciences, and medicine. We hope the research presented within this book series will contribute to overcoming this grand challenge.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis The Virtual Element Method and its Applications by : Paola F. Antonietti
Download or read book The Virtual Element Method and its Applications written by Paola F. Antonietti and published by Springer Nature. This book was released on 2022-10-08 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present the current state of the art of the Virtual Element Method (VEM) by collecting contributions from many of the most active researchers in this field and covering a broad range of topics: from the mathematical foundation to real life computational applications. The book is naturally divided into three parts. The first part of the book presents recent advances in theoretical and computational aspects of VEMs, discussing the generality of the meshes suitable to the VEM, the implementation of the VEM for linear and nonlinear PDEs, and the construction of discrete hessian complexes. The second part of the volume discusses Virtual Element discretization of paradigmatic linear and non-linear partial differential problems from computational mechanics, fluid dynamics, and wave propagation phenomena. Finally, the third part contains challenging applications such as the modeling of materials with fractures, magneto-hydrodynamics phenomena and contact solid mechanics. The book is intended for graduate students and researchers in mathematics and engineering fields, interested in learning novel numerical techniques for the solution of partial differential equations. It may as well serve as useful reference material for numerical analysts practitioners of the field.
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Locally Modified Finite Element Method for Two-phase Flow Problems by : Gozel Judakova
Download or read book A Locally Modified Finite Element Method for Two-phase Flow Problems written by Gozel Judakova and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book LocModFE written by Stefan Frei and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Automated Solution of Differential Equations by the Finite Element Method by : Anders Logg
Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Book Synopsis A Hierarchical Interface-enriched Finite Element Method for the Simulation of Problems with Complex Morphologies by : Jorge Luis Barrera Cruz
Download or read book A Hierarchical Interface-enriched Finite Element Method for the Simulation of Problems with Complex Morphologies written by Jorge Luis Barrera Cruz and published by . This book was released on 2015 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades, the finite element method (FEM) has become one of the most important computational tools for the simulation of engineering problems. Due to the increasing popularity of this method, a heavy body of research has focused its attention to the development of advanced FEM-based techniques for the treatment of complex phenomena, including intricate morphologies. This thesis introduces a hierarchical interface-enriched finite element method (HIFEM) for the mesh-independent treatment of the mentioned type of problems. The HIFEM provides a general, and yet easy-to-implement algorithm for evaluating appropriate enrichment in elements cut by multiple interfaces. In the automated framework provided by this method, the construction of enrichment functions is independent of the number and sequence of the geometries introduced to nonconforming finite element meshes. Consequently, the HIFEM algorithm eliminates the need to modify/remove existing enrichment every time a new geometry is added to the domain. The proposed hierarchical enrichment technique can accurately capture gradient discontinuities along material interfaces that are in close proximity, in contact, or intersecting with one another using nonconforming finite element meshes for discretizing the problem. The main contribution of this thesis is the development and implementation of the two-dimensional higher-order HIFEM, and in particular the development of a new hierarchical enrichment scheme for six-note triangular elements. Furthermore, this manuscript presents a new enrichment scheme to simulate strong discontinuities (cracks) in linear elastic fracture mechanics problems. Special attention is given to the available strategies to improve the level of precision and efficiency of the simulations. A detailed convergence study for the enrichment technique that yields the highest precision and the lowest computational cost is also presented. Finally, the author illustrates the application of the higher-order HIFEM for simulating the thermal and deformation responses of a variety of engineering problems with complex geometries, including porous media, fiber-reinforced composites, and quasi- static cracks in a heterogeneous domain.
Book Synopsis The Immersed Interface Method by : Zhilin Li
Download or read book The Immersed Interface Method written by Zhilin Li and published by SIAM. This book was released on 2006-07-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book will be a useful resource for mathematicians, numerical analysts, engineers, graduate students, and anyone who uses numerical methods to solve computational problems, particularly problems with fixed and moving interfaces, free boundary problems, and problems on regular domains."--BOOK JACKET.
Book Synopsis Electrical & Electronics Abstracts by :
Download or read book Electrical & Electronics Abstracts written by and published by . This book was released on 1997 with total page 2304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Notices of the American Mathematical Society by : American Mathematical Society
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1994 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Scaled Boundary Finite Element Method by : Chongmin Song
Download or read book The Scaled Boundary Finite Element Method written by Chongmin Song and published by John Wiley & Sons. This book was released on 2018-06-19 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1989 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modeling and Simulation Based Engineering by : Satya N. Atluri
Download or read book Modeling and Simulation Based Engineering written by Satya N. Atluri and published by . This book was released on 1998 with total page 1056 pages. Available in PDF, EPUB and Kindle. Book excerpt:
