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Computer implementation of the finite element method / by J. Alan George

Auteur principal : George, John Alan, 1943-, AuteurAuteur secondaire collectivité : Stanford University, Etablissement de soutenanceType de document : ThèseLangue : anglais.Pays : Etats Unis.Mention d'édition: Reprod. en fac-sim.Éditeur : Ann Arbor (Mich.) : University Microfilm International, 1971Description : 1 vol. (V-222 f.) : fig. ; 21 cmBibliographie : Bibliogr. f. 154-161.Sujet MSC : 65F50, Numerical linear algebra, Computational methods for sparse matrices
65K05, Numerical analysis, Numerical mathematical programming methods
65M50, Numerical analysis, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
68Q25, Computer science - Theory of computing, Analysis of algorithms and problem complexity
97-02, Research exposition (monographs, survey articles) pertaining to mathematics education
Note de thèse: Thèse de doctorat, informatique, 1971, Stanford UniversityEn-ligne : PDF
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Bibliogr. f. 154-161

Thèse de doctorat informatique 1971 Stanford University

A detailed study of the implementation of finite element methods for solving two-dimensional elliptic partial differential equations is presented. Generation and storage schemes for triangular meshes are considered, and the use of irregular meshes for finite element methods is shown to be relatively inexpensive in terms of storage. The report demonstrates that much of the manipulation of the basis functions necessary in the derivation of the approximation equations can be done semi-symbolically rather than numerically as is usually done. Ordering algorithms, compact storage schemes, and efficient implementation of elimination methods are studied in connection with sparse systems of finite element equations. A Fortran code is included for the finite element solution of a class of elliptic boundary value problems, and numerical solutions of several problems are presented. Comparisons among different finite element methods, and between finite element methods and their competitors are included

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