| 000 | 05462cam a2200829 i 4500 | ||
|---|---|---|---|
| 001 | vtls000079403 | ||
| 003 | MTX | ||
| 006 | m eo d | ||
| 007 | cr cn |||m|||a | ||
| 008 | 160715s2014 nyua foab 001 0 eng d | ||
| 020 |
_a9781606506066 _qelectronic |
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| 020 |
_a1606506064 _qelectronic |
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| 020 |
_z9781606506042 _qprint |
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| 020 |
_z1606506048 _qprint |
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| 024 | 7 |
_a10.5643/9781606506066 _2doi |
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| 035 | _a(CaPaEBR)10841488 | ||
| 035 | _a(OCoLC)870904465 | ||
| 035 | _a(CaBNvSL)swl00403208 | ||
| 039 | 9 |
_a201607151145 _bstaff _y201605041228 _zadmin |
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| 040 |
_aCaBNVSL _beng _erda _cCaBNVSL _dCaBNVSL |
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| 050 | 4 |
_aQC20 _b.F473 2014 |
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| 082 | 0 | 4 |
_a511.6 _223 |
| 099 | _aEbook | ||
| 100 | 1 |
_aFerretti, Elena., _eauthor. _9115951 |
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| 245 | 1 | 4 |
_aThe cell method : _ba purely algebraic computational method in physics and engineering / _cElena Ferretti. |
| 264 | 1 |
_aNew York, [New York] (222 East 46th Street, New York, NY 10017) : _bMomentum Press, _c2014. |
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| 300 |
_a1 online resource (xii, 230 pages) : _billustrations. |
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| 336 |
_atext _2rdacontent |
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| 337 |
_acomputer _2rdamedia |
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| 338 |
_aonline resource _2rdacarrier |
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| 504 | _aIncludes bibliographical references (pages 215-226) and index. | ||
| 505 | 0 | _a1. 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 -- | |
| 505 | 8 | _a2. Algebra and the geometric interpretation of vector spaces -- 2.1 The exterior algebra -- 2.2 The geometric algebra -- | |
| 505 | 8 | _a3. 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 -- | |
| 505 | 8 | _a4. 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 -- | |
| 505 | 8 | _a5. 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 -- | |
| 505 | 8 | _a6. 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 -- | |
| 505 | 8 | _aReferences -- Index. | |
| 506 | _aRestricted to libraries which purchase an unrestricted PDF download via an IP. | ||
| 520 | 3 | _aThe 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. | |
| 530 | _aAlso available in print. | ||
| 538 | _aMode of access: World Wide Web. | ||
| 538 | _aSystem requirements: Adobe Acrobat reader. | ||
| 588 | _aTitle from PDF title page (viewed on March 9, 2014). | ||
| 650 | 0 |
_aMathematical physics. _942233 |
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| 650 | 0 |
_aEngineering mathematics. _926640 |
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| 653 | _aCell method | ||
| 653 | _aheterogeneous materials | ||
| 653 | _anon-local models | ||
| 653 | _anon-standard analysis | ||
| 653 | _abialgebra | ||
| 653 | _aClifford algebra | ||
| 653 | _adiscrete formulations | ||
| 653 | _afracture mechanics | ||
| 653 | _aelectromagnetics | ||
| 653 | _aelectrodynamics | ||
| 653 | _asolid mechanics | ||
| 653 | _afluid mechanics | ||
| 653 | _aspace-time continuum | ||
| 653 | _anumerical instabilities | ||
| 653 | _atopological features of variables | ||
| 653 | _agraph theory | ||
| 653 | _acoboundary process | ||
| 653 | _afinite element method | ||
| 653 | _aboundary element method | ||
| 653 | _afinite volume method | ||
| 653 | _afinite difference method | ||
| 776 | 0 | 8 |
_iPrint version: _z1606506048 _z9781606506042 |
| 856 | 4 | 0 | _uhttp://portal.igpublish.com/iglibrary/search/MPB0000092.html |
| 942 | _c10 | ||
| 999 |
_c75952 _d75952 |
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