The cell method : a purely algebraic computational method in physics and engineering /

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 analys...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ferretti, Elena
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Momentum Press, ©2014.
Temas:
Mathematical physics.
Engineering mathematics.
Physique mathématique.
Mathématiques de l'ingénieur.
SCIENCE > Energy.
SCIENCE > Mechanics > General.
SCIENCE > Physics > General.
MATHEMATICS > General.
Engineering mathematics
Mathematical physics
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
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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