05462cam a2200829 i 4500 vtls000079403 MTX m eo d cr cn |||m|||a 160715s2014 nyua foab 001 0 eng d 9781606506066 electronic 1606506064 electronic 9781606506042 print 1606506048 print 10.5643/9781606506066 doi (CaPaEBR)10841488 (OCoLC)870904465 (CaBNvSL)swl00403208 201607151145 staff 201605041228 admin CaBNVSL eng rda CaBNVSL CaBNVSL QC20 .F473 2014 511.6 23 Ebook Ferretti, Elena., author. 115951 The cell method : a purely algebraic computational method in physics and engineering / Elena Ferretti. New York, [New York] (222 East 46th Street, New York, NY 10017) : Momentum Press, 2014. 1 online resource (xii, 230 pages) : illustrations. text rdacontent computer rdamedia online resource rdacarrier Includes bibliographical references (pages 215-226) and index. 1. A comparison between algebraic and differential formulations under the geometrical and topological viewpoints -- 1.1 Relationship between how to compute limits and numerical formulations in computational physics -- 1.2 Field and global variables -- 1.3 Set functions in physics -- 1.4 A comparison between the cell method and the discrete methods -- 2. Algebra and the geometric interpretation of vector spaces -- 2.1 The exterior algebra -- 2.2 The geometric algebra -- 3. Algebraic topology as a tool for treating global variables with the CM -- 3.1 Some notions of algebraic topology -- 3.2 Simplices and simplicial complexes -- 3.3 Faces and cofaces -- 3.4 Some notions of the graph theory -- 3.5 Boundaries, coboundaries, and the incidence matrices -- 3.6 Chains and cochains complexes, boundary and coboundary processes -- 3.7 Discrete p-forms -- 3.8 Inner and outer orientations of time elements -- 4. Classification of the global variables and their relationships -- 4.1 Configuration, source, and energetic variables -- 4.2 The mathematical structure of the classification diagram -- 4.3 The incidence matrices of the two cell complexes in space domain -- 4.4 Primal and dual cell complexes in space/time domain and their incidence matrices -- 5. The structure of the governing equations in the cell method -- 5.1 The role of the coboundary process in the algebraic formulation -- 5.2 How to compose the fundamental equation of a physical theory -- 5.3 Analogies in physics -- 5.4 Physical theories with reversible constitutive laws -- 5.5 The choice of primal and dual cell complexes in computation -- 6. The problem of the spurious solutions in computational physics -- 6.1 Stability and instability of the numerical solution -- 6.2 The need for non-local models in quantum physics -- 6.3 Non-local computational models in differential formulation -- 6.3.1 Continuum mechanics -- 6.4 Algebraic non-locality of the CM -- References -- Index. Restricted to libraries which purchase an unrestricted PDF download via an IP. The cell method (CM) is a computational tool that maintains critical multidimensional attributes of physical phenomena in analysis. This information is neglected in the differential formulations of the classical approaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilities and spurious results. This book highlights the central theoretical concepts of the CM that preserve a more accurate and precise representation of the geometric and topological features of variables for practical problem solving. Important applications occur in fields such as electromagnetics, electrodynamics, solid mechanics and fluids. CM addresses non-locality in continuum mechanics, an especially important circumstance in modeling heterogeneous materials. Also available in print. Mode of access: World Wide Web. System requirements: Adobe Acrobat reader. Title from PDF title page (viewed on March 9, 2014). Mathematical physics. 42233 Engineering mathematics. 26640 Cell method heterogeneous materials non-local models non-standard analysis bialgebra Clifford algebra discrete formulations fracture mechanics electromagnetics electrodynamics solid mechanics fluid mechanics space-time continuum numerical instabilities topological features of variables graph theory coboundary process finite element method boundary element method finite volume method finite difference method Print version: 1606506048 9781606506042 http://portal.igpublish.com/iglibrary/search/MPB0000092.html 10 75952 75952