The cell method: a purely algebraic computational method in physics and engineering
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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New York, NY
Momentum Press
©2014
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| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and index The Cell Method (CM) is a computational tool that maintains criticalmultidimensional attributes of physical phenomena in analysis. Thisinformation is neglected in the differential formulations of the classicalapproaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilitiesand spurious results. This book highlights the central theoretical concepts of the CM thatpreserve a more accurate and precise representation of the geometricand topological features of variables for practical problem solving. Important applications occur in 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. |
| Beschreibung: | 1 Online-Ressource (1 volume) |
| ISBN: | 1306375274 1606506048 1606506064 9781306375276 9781606506042 9781606506066 |
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| 500 | |a Includes bibliographical references and index | ||
| 500 | |a The Cell Method (CM) is a computational tool that maintains criticalmultidimensional attributes of physical phenomena in analysis. Thisinformation is neglected in the differential formulations of the classicalapproaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilitiesand spurious results. This book highlights the central theoretical concepts of the CM thatpreserve a more accurate and precise representation of the geometricand topological features of variables for practical problem solving. Important applications occur in | ||
| 500 | |a 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 | ||
| 500 | |a 2. Algebra and the geometric interpretation of vector spaces -- 2.1 The exterior algebra -- 2.2 The geometric algebra | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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. | ||
| 650 | 4 | |a Mathematical physics | |
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| 650 | 4 | |a Engineering mathematics | |
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Datensatz im Suchindex
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| author | Ferretti, Elena |
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| dewey-ones | 530 - Physics 511 - General principles of mathematics |
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| dewey-search | 530.1/55353 511/.6 511.6 |
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| discipline | Physik Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:16:51Z |
| institution | BVB |
| isbn | 1306375274 1606506048 1606506064 9781306375276 9781606506042 9781606506066 |
| language | English |
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| publisher | Momentum Press |
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| spelling | Ferretti, Elena Verfasser aut The cell method a purely algebraic computational method in physics and engineering Elena Ferretti Purely algebraic computational method in physics and engineering New York, NY Momentum Press ©2014 1 Online-Ressource (1 volume) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and index The Cell Method (CM) is a computational tool that maintains criticalmultidimensional attributes of physical phenomena in analysis. Thisinformation is neglected in the differential formulations of the classicalapproaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilitiesand spurious results. This book highlights the central theoretical concepts of the CM thatpreserve a more accurate and precise representation of the geometricand topological features of variables for practical problem solving. Important applications occur in 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. Mathematical physics Engineering mathematics SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh MATHEMATICS / General bisacsh Engineering mathematics fast Mathematical physics fast Mathematische Physik http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=690092 Aggregator Volltext |
| spellingShingle | Ferretti, Elena The cell method a purely algebraic computational method in physics and engineering Mathematical physics Engineering mathematics SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh MATHEMATICS / General bisacsh Engineering mathematics fast Mathematical physics fast Mathematische Physik |
| title | The cell method a purely algebraic computational method in physics and engineering |
| title_alt | Purely algebraic computational method in physics and engineering |
| title_auth | The cell method a purely algebraic computational method in physics and engineering |
| title_exact_search | The cell method a purely algebraic computational method in physics and engineering |
| title_full | The cell method a purely algebraic computational method in physics and engineering Elena Ferretti |
| title_fullStr | The cell method a purely algebraic computational method in physics and engineering Elena Ferretti |
| title_full_unstemmed | The cell method a purely algebraic computational method in physics and engineering Elena Ferretti |
| title_short | The cell method |
| title_sort | the cell method a purely algebraic computational method in physics and engineering |
| title_sub | a purely algebraic computational method in physics and engineering |
| topic | Mathematical physics Engineering mathematics SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh MATHEMATICS / General bisacsh Engineering mathematics fast Mathematical physics fast Mathematische Physik |
| topic_facet | Mathematical physics Engineering mathematics SCIENCE / Energy SCIENCE / Mechanics / General SCIENCE / Physics / General MATHEMATICS / General Mathematische Physik |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=690092 |
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