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The Isogeometric Boundary Element Method

2019-09-21 Science
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Release : 2019-09-21
Genre : Science
Kind : eBook
Book Rating : 391/5 ( reviews)

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Book Synopsis The Isogeometric Boundary Element Method by : Gernot Beer

Download or read book The Isogeometric Boundary Element Method written by Gernot Beer. This book was released on 2019-09-21. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.

The Isogeometric Boundary Element Method

2020 Boundary element methods
Download The Isogeometric Boundary Element Method PDF Online Free

Author :
Release : 2020
Genre : Boundary element methods
Kind : eBook
Book Rating : 402/5 ( reviews)

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Book Synopsis The Isogeometric Boundary Element Method by : Gernot Beer

Download or read book The Isogeometric Boundary Element Method written by Gernot Beer. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.

Precursors of Isogeometric Analysis

2019-01-01 Science
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Release : 2019-01-01
Genre : Science
Kind : eBook
Book Rating : 890/5 ( reviews)

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Book Synopsis Precursors of Isogeometric Analysis by : Christopher G. Provatidis

Download or read book Precursors of Isogeometric Analysis written by Christopher G. Provatidis. This book was released on 2019-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book addresses the three most popular computational methods in CAE (finite elements, boundary elements, collocation methods) in a unified way, bridging the gap between CAD and CAE. It includes applications to a broad spectrum of engineering (benchmark) application problems, such as elasto-statics/dynamics and potential problems (thermal, acoustics, electrostatics). It also provides a large number of test cases, with full documentation of original sources, making it a valuable resource for any student or researcher in FEA-related areas. The book, which assumes readers have a basic knowledge of FEA, can be used as additional reading for engineering courses as well as for other interdepartmental MSc courses.

Finite Element Analysis of Acoustic Scattering

2006-03-29 Mathematics
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Release : 2006-03-29
Genre : Mathematics
Kind : eBook
Book Rating : 008/5 ( reviews)

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Book Synopsis Finite Element Analysis of Acoustic Scattering by : Frank Ihlenburg

Download or read book Finite Element Analysis of Acoustic Scattering written by Frank Ihlenburg. This book was released on 2006-03-29. Available in PDF, EPUB and Kindle. Book excerpt: A cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations, while the main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. In the final chapter, three dimensional computational simulations are presented and compared with experimental data. The author also includes broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditions, infinite elements and the perfectly matched layer. A self-contained and easily readable work.

Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism

2020-11-30 Technology & Engineering
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Release : 2020-11-30
Genre : Technology & Engineering
Kind : eBook
Book Rating : 397/5 ( reviews)

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Book Synopsis Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism by : Felix Wolf

Download or read book Analysis and Implementation of Isogeometric Boundary Elements for Electromagnetism written by Felix Wolf. This book was released on 2020-11-30. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive mathematical and computational approach for solving electromagnetic problems of practical relevance, such as electromagnetic scattering and the cavity problems. After an in-depth introduction to the mathematical foundations of isogeometric analysis, which discusses how to conduct higher-order simulations efficiently and without the introduction of geometrical errors, the book proves quasi-optimal approximation properties for all trace spaces of the de Rham sequence, and demonstrates inf-sup stability of the isogeometric discretisation of the electric field integral equation (EFIE). Theoretical properties and algorithms are described in detail. The algorithmic approach is, in turn, validated through a series of numerical experiments aimed at solving a set of electromagnetic scattering problems. In the last part of the book, the boundary element method is combined with a novel eigenvalue solver, a so-called contour integral method. An algorithm is presented, together with a set of successful numerical experiments, showing that the eigenvalue solver benefits from the high orders of convergence offered by the boundary element approach. Last, the resulting software, called BEMBEL (Boundary Element Method Based Engineering Library), is reviewed: the user interface is presented, while the underlying design considerations are explained in detail. Given its scope, this book bridges an important gap between numerical analysis and engineering design of electromagnetic devices.

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