عنوان
پدید آورنده
موضوع
رده
QA316
QA316
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
3030237885
(Number (ISBN
3030237893
(Number (ISBN
3030237907
(Number (ISBN
9783030237882
(Number (ISBN
9783030237899
(Number (ISBN
9783030237905
Erroneous ISBN
3030237877
Erroneous ISBN
9783030237875
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Introduction to numerical methods for variational problems /
General Material Designation
[Book]
First Statement of Responsibility
Hans Petter Langtangen, Kent-Andre Mardal.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Cham :
Name of Publisher, Distributor, etc.
Springer,
Date of Publication, Distribution, etc.
2019.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
SERIES
Series Title
Texts in computational science and engineering ;
Volume Designation
21
CONTENTS NOTE
Text of Note
Intro; Preface; Second Preface; Contents; List of Exercises and Problems; 1 Quick Overview of the Finite Element Method; 2 Function Approximation by Global Functions; 2.1 Approximation of Vectors; 2.1.1 Approximation of Planar Vectors; 2.1.2 Approximation of General Vectors; 2.2 Approximation Principles; 2.2.1 The Least Squares Method; 2.2.2 The Projection (or Galerkin) Method; 2.2.3 Example of Linear Approximation; 2.2.4 Implementation of the Least Squares Method; 2.2.5 Perfect Approximation; 2.2.6 The Regression Method; 2.3 Orthogonal Basis Functions; 2.3.1 Ill-Conditioning
Text of Note
2.3.2 Fourier Series2.3.3 Orthogonal Basis Functions; 2.3.4 Numerical Computations; 2.4 Interpolation; 2.4.1 The Interpolation (or Collocation) Principle; 2.4.2 Lagrange Polynomials; 2.4.3 Bernstein Polynomials; 2.5 Approximation Properties and Convergence Rates; 2.6 Approximation of Functions in Higher Dimensions; 2.6.1 2D Basis Functions as Tensor Products of 1D Functions; 2.6.2 Example on Polynomial Basis in 2D; 2.6.3 Implementation; 2.6.4 Extension to 3D; 2.7 Exercises; Problem 2.1: Linear Algebra Refresher; Problem 2.2: Approximate a Three-Dimensional Vector in a Plane
Text of Note
3.1.1 Elements and Nodes3.1.2 The Basis Functions; 3.1.3 Example on Quadratic Finite Element Functions; 3.1.4 Example on Linear Finite Element Functions; 3.1.5 Example on Cubic Finite Element Functions; 3.1.6 Calculating the Linear System; 3.1.7 Assembly of Elementwise Computations; 3.1.8 Mapping to a Reference Element; 3.1.9 Example on Integration over a Reference Element; 3.2 Implementation; 3.2.1 Integration; 3.2.2 Linear System Assembly and Solution; 3.2.3 Example on Computing Symbolic Approximations; 3.2.4 Using Interpolation Instead of Least Squares
Text of Note
3.2.5 Example on Computing Numerical Approximations3.2.6 The Structure of the Coefficient Matrix; 3.2.7 Applications; 3.2.8 Sparse Matrix Storage and Solution; 3.3 Comparison of Finite Elements and Finite Differences; 3.3.1 Finite Difference Approximation of Given Functions; 3.3.2 Interpretation of a Finite Element Approximation in Terms of Finite Difference Operators; 3.3.3 Making Finite Elements Behave as Finite Differences; 3.4 A Generalized Element Concept; 3.4.1 Cells, Vertices, and Degrees of Freedom; 3.4.2 Extended Finite Element Concept; 3.4.3 Implementation
Text of Note
Problem 2.3: Approximate a Parabola by a SineProblem 2.4: Approximate the Exponential Function by Power Functions; Problem 2.5: Approximate the Sine Function by Power Functions; Problem 2.6: Approximate a Steep Function by Sines; Problem 2.7: Approximate a Steep Function by Sines with Boundary Adjustment; Exercise 2.8: Fourier Series as a Least Squares Approximation; Problem 2.9: Approximate a Steep Function by Lagrange Polynomials; Problem 2.10: Approximate a Steep Function by Lagrange Polynomials and Regression; 3 Function Approximation by Finite Elements; 3.1 Finite Element Basis Functions
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SUMMARY OR ABSTRACT
Text of Note
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.
ACQUISITION INFORMATION NOTE
Source for Acquisition/Subscription Address
Springer Nature
Stock Number
com.springer.onix.9783030237882
OTHER EDITION IN ANOTHER MEDIUM
Title
Introduction to numerical methods for variational problems.
International Standard Book Number
9783030237875
TOPICAL NAME USED AS SUBJECT
Finite element method.
Variational inequalities (Mathematics)
Finite element method.
Variational inequalities (Mathematics)
(SUBJECT CATEGORY (Provisional
MAT006000
PBKS
PBKS
DEWEY DECIMAL CLASSIFICATION
Number
515/
.
64
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA316
PERSONAL NAME - PRIMARY RESPONSIBILITY
Langtangen, Hans Petter,1962-
PERSONAL NAME - ALTERNATIVE RESPONSIBILITY
Mardal, Kent-Andre.
ORIGINATING SOURCE
Date of Transaction
20200823093000.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
