Analysis of a Finite Element Method: PDE/PROTRANSpringer Science & Business Media, 6 dic 2012 - 154 pagine 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. |
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Pagina vii
... . Although PDE / PROTRAN solves systems of PDEs , and the notation reflects this throughout the text , this need not confuse the reader who finds it easier to think in terms of a single PDE . The formulas are always vii.
... . Although PDE / PROTRAN solves systems of PDEs , and the notation reflects this throughout the text , this need not confuse the reader who finds it easier to think in terms of a single PDE . The formulas are always vii.
Pagina viii
PDE/PROTRAN Granville Sewell. terms of a single PDE . The formulas are always written in such a way that this can be done simply by ignoring the vector ( boldface ) and matrix notation . There are examples and exercises involving PDE ...
PDE/PROTRAN Granville Sewell. terms of a single PDE . The formulas are always written in such a way that this can be done simply by ignoring the vector ( boldface ) and matrix notation . There are examples and exercises involving PDE ...
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Sommario
1 | |
10 | |
Elliptic ProblemsForming the Algebraic Equations | 22 |
Elliptic ProblemsSolving the Algebraic Equations | 50 |
Parabolic Problems | 77 |
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A.UX algorithm approximating assumed backward difference method band solver basis functions boundary conditions BOUNDARY FORCE calculated components conjugate gradient method convergence Crank-Nicolson Crank-Nicolson method cubic curved D3EST Default defined in GLOBAL derivatives diagonal dimensional discretization discretization error DISPLACEMENTS DOUBLE PRECISION Expression dxdy eigenfunction eigenvalue problem elastic error evaluated Expression involving constants ƏR₁ Figure filename finite difference method finite element formula FORTRAN frontal method frontal solver Galerkin given grid hyperbolic problems iarcI initial triangulation integration inverse power method Jacobian matrix keyword Lanczos Iteration Lanczos method linear system Newton iteration Newton's method nonlinear nonzero normalized triangle NOUPDATE output PDE/PROTRAN PDE2D piecewise polynomial plot Pn+1 positive definite PRECISION Expression involving PRECISION MATRIX quadratic quartic elements REAL or DOUBLE satisfies Section shown solution solve specified step Structure symmetric updated UPRINT values variables defined vector velocity VERTICES VSOL XGRID xk+1 zero