000 07244cam a2200625Ki 4500
001 9781315168265
003 FlBoTFG
005 20220711212530.0
006 m o d
007 cr cnu---unuuu
008 190711s2019 flu ob 001 0 eng d
040 _aOCoLC-P
_beng
_erda
_epn
_cOCoLC-P
020 _a9781315168265
_q(electronic bk.)
020 _a131516826X
_q(electronic bk.)
020 _a9780429679247
_q(electronic bk. : Mobipocket)
020 _a0429679246
_q(electronic bk. : Mobipocket)
020 _a0429679416
_q(electronic bk. : EPUB)
020 _a9781351685443
_q(electronic bk. : PDF)
020 _a1351685449
_q(electronic bk. : PDF)
020 _a9780429679414
_q(electronic bk.)
020 _z9781138051584
020 _z1138051586
024 8 _a10.1201/9781315168265
_2doi
035 _a(OCoLC)1107880840
035 _a(OCoLC-P)1107880840
050 4 _aQC20.7.F56
_bK85 2019eb
072 7 _aMAT
_x000000
_2bisacsh
072 7 _aMAT
_x003000
_2bisacsh
072 7 _aMAT
_x021000
_2bisacsh
072 7 _aUB
_2bicssc
082 0 4 _a530.15/1825
_223
100 1 _aKumar, Sandeep
_c(Professor of mechanical engineering),
_eauthor.
_917351
245 1 0 _aMathematical theory of subdivision :
_bfinite element and wavelet methods /
_cSandeep Kumar, Ashish Pathak, Debasish Khan.
264 1 _aBoca Raton, Florida :
_bCRC Press,
_c[2019]
300 _a1 online resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
520 _aThis 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 _a<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>
588 _aOCLC-licensed vendor bibliographic record.
650 0 _aFinite element method.
_917352
650 0 _aWavelets (Mathematics)
_910807
650 0 _aNumerical analysis.
_94603
650 0 _aHarmonic analysis.
_914381
650 0 _aGeneralized spaces.
_917353
650 7 _aMATHEMATICS / General
_2bisacsh
_917354
650 7 _aMATHEMATICS / Applied
_2bisacsh
_96859
650 7 _aMATHEMATICS / Number Systems
_2bisacsh
_917355
700 1 _aPathak, Ashish,
_eauthor.
_917356
700 1 _aKhan, Debasish,
_eauthor.
_917357
856 4 0 _3Taylor & Francis
_uhttps://www.taylorfrancis.com/books/9781315168265
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942 _cEBK
999 _c71504
_d71504