Central Library

Mathematical theory of subdivision : (Record no. 71504)

000 -LEADER
fixed length control field 07244cam a2200625Ki 4500
001 - CONTROL NUMBER
control field 9781315168265
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20220711212530.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 190711s2019 flu ob 001 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9781315168265
-- (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 131516826X
-- (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9780429679247
-- (electronic bk. : Mobipocket)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 0429679246
-- (electronic bk. : Mobipocket)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 0429679416
-- (electronic bk. : EPUB)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9781351685443
-- (electronic bk. : PDF)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 1351685449
-- (electronic bk. : PDF)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9780429679414
-- (electronic bk.)
082 04 - CLASSIFICATION NUMBER
Call Number 530.15/1825
100 1# - AUTHOR NAME
Author Kumar, Sandeep
245 10 - TITLE STATEMENT
Title Mathematical theory of subdivision :
Sub Title finite element and wavelet methods /
300 ## - PHYSICAL DESCRIPTION
Number of Pages 1 online resource.
520 ## - SUMMARY, ETC.
Summary, etc This book provides good coverage of the powerful numerical techniques namely, finite element and wavelets, for the solution of partial differential equation to the scientists and engineers with a modest mathematical background. The objective of the book is to provide the necessary mathematical foundation for the advanced level applications of these numerical techniques. The book begins with the description of the steps involved in finite element and wavelets-Galerkin methods. The knowledge of Hilbert and Sobolev spaces is needed to understand the theory of finite element and wavelet-based methods. Therefore, an overview of essential content such as vector spaces, norm, inner product, linear operators, spectral theory, dual space, and distribution theory, etc. with relevant theorems are presented in a coherent and accessible manner. For the graduate students and researchers with diverse educational background, the authors have focused on the applications of numerical techniques which are developed in the last few decades. This includes the wavelet-Galerkin method, lifting scheme, and error estimation technique, etc. Features: Computer programs in Mathematica/Matlab are incorporated for easy understanding of wavelets. Presents a range of workout examples for better comprehension of spaces and operators. Algorithms are presented to facilitate computer programming. Contains the error estimation techniques necessary for adaptive finite element method. This book is structured to transform in step by step manner the students without any knowledge of finite element, wavelet and functional analysis to the students of strong theoretical understanding who will be ready to take many challenging research problems in this area.
505 0# - FORMATTED CONTENTS NOTE
Remark 2 <P>Preface</P><P>About the authors</P><OL><B><P></P></OL><P>1. Overview of finite element method</P><OL><P></P><OL></B><P><LI>Some common governing differential equations </LI><P></P><P><LI>Basic steps of finite element method </LI><P></P><P><LI>Element stiffness matrix for a bar </LI><P></P><P><LI>Element stiffness matrix for single variable 2d element </LI><P></P><P><LI>Element stiffness matrix for a beam element</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>2. Wavelets</P><OL><P></P></OL><OL><OL></B><P><LI>Wavelet basis functions</LI><P></P><P><LI>Wavelet-Galerkin method </LI><P></P><P><LI>Daubechies wavelets for boundary and initial value problems </LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>3. Fundamentals of vector spaces </P><OL><P></P></OL><OL><OL></B><P><LI>Introduction</LI><P></P><P><LI>Vector spaces </LI><P></P><P><LI>Normed linear spaces </LI><P></P><P><LI>Inner product spaces </LI><P></P><P><LI>Banach spaces </LI><P></P><P><LI>Hilbert spaces </LI><P></P><P><LI>Projection on finite dimensional spaces</LI><P></P><P><LI>Change of basis -- Gram-Schmidt othogonalization process</LI><P></P><P><LI>Riesz bases and frame conditions</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>4. Operators</P><OL><P></P></OL><OL><OL></B><P><LI>Mapping of sets, general concept of functions</LI><P></P><P><LI>Operators</LI><P></P><P><LI>Linear and adjoint operators</LI><P></P><P><LI>Functionals and dual space</LI><P></P><P><LI>Spectrum of bounded linear self-adjoint operator </LI><P></P><P><LI>Classification of differential operators</LI><P></P><P><LI>Existence, uniqueness and regularity of solution</LI><P></P><P><LI>References</LI><P></P></OL></OL><OL><B><P></P></OL><P>5. Theoretical foundations of the finite element method</B> </P><OL><P></P></OL><OL><OL><P><LI>Distribution theory</LI><P></P><P><LI>Sobolev spaces</LI><P></P><P><LI>Variational Method</LI><P></P><P><LI>Nonconforming elements and patch test</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>6. Wavelet- based methods for differential equations</P><OL><P></P></OL><OL><OL></B><P><LI>Fundamentals of continuous and discrete wavelets</LI><P></P><P><LI>Multiscaling</LI><P></P><P><LI>Classification of wavelet basis functions </LI><P></P><P><LI>Discrete wavelet transform </LI><P></P><P><LI>Lifting scheme for discrete wavelet transform </LI><P></P><P><LI>Lifting scheme to customize wavelets </LI><P></P><P><LI>Non-standard form of matrix and its solution </LI><P></P><P><LI>Multigrid method</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><OL><B><P></P></OL><P>7. Error -- estimation</B></P><OL><P></P><OL><P><LI>Introduction</LI><P></P><I><P><LI>A-priori</I> error estimation</LI><P></P><P><LI>Recovery based error estimators </LI><P></P><P><LI>Residual based error estimators </LI><P></P><P><LI>Goal oriented error estimators</LI><P></P><P><LI>Hierarchical & wavelet based error estimator</LI><P></P><P><LI>References for further reading</LI><P></P></OL></OL><B><P>Appendix</B><I><I></P></I></I>
700 1# - AUTHOR 2
Author 2 Pathak, Ashish,
700 1# - AUTHOR 2
Author 2 Khan, Debasish,
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier https://www.taylorfrancis.com/books/9781315168265
856 42 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type eBooks
264 #1 -
-- Boca Raton, Florida :
-- CRC Press,
-- [2019]
336 ## -
-- text
-- txt
-- rdacontent
337 ## -
-- computer
-- c
-- rdamedia
338 ## -
-- online resource
-- cr
-- rdacarrier
588 ## -
-- OCLC-licensed vendor bibliographic record.
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Finite element method.
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Wavelets (Mathematics)
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Numerical analysis.
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Harmonic analysis.
650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1
-- Generalized spaces.
650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1
-- MATHEMATICS / General
650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1
-- MATHEMATICS / Applied
650 #7 - SUBJECT ADDED ENTRY--SUBJECT 1
-- MATHEMATICS / Number Systems

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