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Continuous Versus Discontinuous Elastic Modulus Distribution In Inverse Problems Based On Finite Element Methods
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Book Synopsis Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods by : Xuchen Liu
Download or read book Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods written by Xuchen Liu and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Elasticity imaging, which is also known as Elastography, aims to determine the elastic property distribution of non-homogeneous deformable solids such as soft tissues. This can be done non-destructively using displacement fields measured with medical imaging modalities, such as ultrasound or magnetic resonance imaging. Elasticity imaging can potentially be used to detect tumors based on the stiffness contrast between different materials. This requires the solution of an inverse problem in elasticity. This field has been growing very fast in the past decade. One of the most useful applications of elasticity imaging may be in breast cancer diagnosis, where the tumor could potentially be detected and visualized by its stiffness contrast from its surrounding tissues. In this work the inverse problem will be solved for the shear modulus which is directly related to the Young's modulus through the Poisson's ratio. The inverse problem is posed as a constrained optimization problem, where the difference between a computed (predicted) and measured displacement field is minimized. The computed displacement field satisfies the equations of equilibrium. The material is modeled as an isotropic and incompressible material. The present work focuses on assessing the solution of the inverse problem for problem domains defined with a continuous and discontinuous shear modulus distribution. In particular, two problem domains will be considered: 1) a stiff inclusion in a homogeneous background representing a stiff tumor surrounded by soft tissues, 2) a layered ring model representing an arterial wall cross-section. The hypothetical "measured" displacement field for these problem domains will be created by solving the finite element forward problem. Additionally, noise will be added to the displacement field to simulate noisy measured displacement data. According to the results of my thesis work, the potential of the elasticity imaging in the medical field is emerging. The inclusion in problem domain 1, representing a stiffer tumor in a uniform background, can be found and located in the shear modulus reconstructions. Thus, these reconstructed images can potentially be used to detect tumors in the medical field. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155332
Book Synopsis Analysis of Novel Finite Element Formulations for Iterative Solution of Elastic Inverse Problems by : Carlos Enrique Rivas Aroni
Download or read book Analysis of Novel Finite Element Formulations for Iterative Solution of Elastic Inverse Problems written by Carlos Enrique Rivas Aroni and published by . This book was released on 2009 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Inverse problems are often formulated as optimization problems. One seeks the parameter distribution which, when used in a forward model of the problem, gives the best match possible to the measured data. We consider the problem of imaging the elastic modulus distributions of soft tissues in this context. These optimization formulations are usually ill-posed and hence some form of regularization is needed in order to guarantee uniqueness and stability for the inverse solution. In this dissertation, however, we present two stabilized optimization formulations for the plane stress inverse problem without any form of regularization. These formulations include novel Galerkin Least Squares (GLS) terms. The Flux-GLS and the Bspline-GLS are formulated and analyzed in this work. These GLS terms improve the stability of the optimization formulation without upsetting consistency. We prove that these two stabilized optimization formulations are well defined under reasonable conditions on the data. We prove further that these two stabilized methods have optimal rates of convergence with mesh refinement. Finally, computational examples are presented to demonstrate the analysis described in this dissertation. These numerical results show the accuracy and stability of these two methods in different conditions. In noisy conditions, we recover unbiased reconstructions of material property distributions without regularization in the presence of high levels noise in the data.
Book Synopsis Inverse Problems in Engineering by : Nicholas Zabaras
Download or read book Inverse Problems in Engineering written by Nicholas Zabaras and published by American Society of Mechanical Engineers. This book was released on 1993 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Seismic Waves written by Masaki Kanao and published by BoD – Books on Demand. This book was released on 2012-01-25 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni.
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 The Finite Element Method: Theory, Implementation, and Applications by : Mats G. Larson
Download or read book The Finite Element Method: Theory, Implementation, and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Book Synopsis Crystal Plasticity Finite Element Methods by : Franz Roters
Download or read book Crystal Plasticity Finite Element Methods written by Franz Roters and published by John Wiley & Sons. This book was released on 2011-08-04 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.
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 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis International Aerospace Abstracts by :
Download or read book International Aerospace Abstracts written by and published by . This book was released on 1999 with total page 1042 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discontinuous Galerkin Methods by : Bernardo Cockburn
Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Book Synopsis Nodal Discontinuous Galerkin Methods by : Jan S. Hesthaven
Download or read book Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
Book Synopsis Numerical Solution of Partial Differential Equations by the Finite Element Method by : Claes Johnson
Download or read book Numerical Solution of Partial Differential Equations by the Finite Element Method written by Claes Johnson and published by Courier Corporation. This book was released on 2012-05-23 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
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.
Download or read book Physics Briefs written by and published by . This book was released on 1993 with total page 1420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Numerical Methods for Variational Problems by : Hans Petter Langtangen
Download or read book Introduction to Numerical Methods for Variational Problems written by Hans Petter Langtangen and published by Springer Nature. This book was released on 2019-09-26 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Book Synopsis Universality of Nonclassical Nonlinearity by : Pier Paolo Delsanto
Download or read book Universality of Nonclassical Nonlinearity written by Pier Paolo Delsanto and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the results of two major international research projects on phenomenology, theory and applications of Nonclassical Nonlinearity. It conveys concepts, experimental techniques and applications which were previously found in specialized journals. It also allows for an interdisciplinary audience to better understand the range of practical applications, and is timely and interesting to both researchers and professionals.
Author :United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch Publisher : ISBN 13 : Total Pages :1080 pages Book Rating :4.E/5 ( download)
Book Synopsis Japanese Science and Technology, 1983-1984 by : United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch
Download or read book Japanese Science and Technology, 1983-1984 written by United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch and published by . This book was released on 1985 with total page 1080 pages. Available in PDF, EPUB and Kindle. Book excerpt:
