## ＜電子ブック＞Analysis of a Finite Element Method : PDE/PROTRAN

責任表示 by Granville Sewell Sewell, Granville SpringerLink (Online service) English (英語) Springer US 1985- New York, NY, United States This text can be used for two quite different purposes. It can be used as a reference book for the PDElPROTRAN user· who wishes to know more about the methods employed by PDE/PROTRAN Edition 1 (or its... predecessor, TWODEPEP) in solving two-dimensional partial differential equations. However, because PDE/PROTRAN solves such a wide class of problems, an outline of the algorithms contained in PDElPROTRAN is also quite suitable as a text for an introductory graduate level finite element course. Algorithms which solve elliptic, parabolic, hyperbolic, and eigenvalue partial differential equation problems are pre sented, as are techniques appropriate for treatment of singularities, curved boundaries, nonsymmetric and nonlinear problems, and systems of PDEs. Direct and iterative linear equation solvers are studied. Although the text emphasizes those algorithms which are actually implemented in PDEI PROTRAN, and does not discuss in detail one- and three-dimensional problems, or collocation and least squares finite element methods, for example, many of the most commonly used techniques are studied in detail. Algorithms applicable to general problems are naturally emphasized, and not special purpose algorithms which may be more efficient for specialized problems, such as Laplace's equation. It can be argued, however, that the student will better understand the finite element method after seeing the details of one successful implementation than after seeing a broad overview of the many types of elements, linear equation solvers, and other options in existence.続きを見る 1. Partial Differential Equation Applications1.1 Energy Minimization1.2 Mass Balance1.3 Force Balance1.4 Resonance1.5 PDE/PROTRAN1.6 Exercises2. Elliptic Problems-Forming the Algebraic Equations2.1 The Galerkin Method2.2 Lagrangian Isoparametric Triangular Elements2.3 Numerical Integration2.4 Triangulation Refinement and Grading2.5 Exercises3. Elliptic Problems-Solving the Algebraic Equations3.1 The Newton-Raphson Method3.2 The Band Solver3.3 The Frontal Solver3.4 The Lanczos Solver3.5 Exercises4. Parabolic Problems4.1 The Time Discretization4.2 Stability4.3 Solving the Linear Equations4.4 Exercises5. Hyperbolic problems5.1 First Order Transport Problems5.2 Second Order Wave Problems5.3 Exercises6. Eigenvalue Problems6.1 The Rayleigh-Ritz Approximation6.2 The Inverse Power Method6.3 ExercisesAppendices1. Lanczos Iteration Properties2. The PROTRAN Preprocessor3. PDE/PROTRAN Keywords4. Postscript.続きを見る http://hdl.handle.net/2324/1001385334 Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive)

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レコードID 3110831 QA297-299.4 518 Mathematics. Numerical analysis. Mathematics. Numerical Analysis. ssj0001295825 9780387962269[0387962263](print) 9781468463316[1468463314] 2020.06.27 2021.05.09