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. |
Dall'interno del libro
Risultati 1-5 di 31
Pagina viii
... vector ( boldface ) and matrix notation . There are examples and exercises involving PDE / PROTRAN usage , and the availability of PDE / PROTRAN would make it easy for the student to test the algorithms studied , which otherwise could ...
... vector ( boldface ) and matrix notation . There are examples and exercises involving PDE / PROTRAN usage , and the availability of PDE / PROTRAN would make it easy for the student to test the algorithms studied , which otherwise could ...
Pagina 1
... vector of state variables which must take known values u - FB ( x , y ) on the remaining portion ƏR1 of the boundary , then a PDE system may be derived by assuming that the steady state condition minimizes the energy of the system . If ...
... vector of state variables which must take known values u - FB ( x , y ) on the remaining portion ƏR1 of the boundary , then a PDE system may be derived by assuming that the steady state condition minimizes the energy of the system . If ...
Pagina 2
... vector . Now E1 / 11 is by definition 011 , the stress which opposes the strain £ 11 . That is , 011 is the rate at which potential energy increases with increasing strain £ 11 . Similarly : ǝE1 / € 12 # 012 JE1 / € 22 2.
... vector . Now E1 / 11 is by definition 011 , the stress which opposes the strain £ 11 . That is , 011 is the rate at which potential energy increases with increasing strain £ 11 . Similarly : ǝE1 / € 12 # 012 JE1 / € 22 2.
Pagina 3
... vector and ( gb1 , gb2 ) the boundary force vector . Thus ( 1.1.2 ) and ( 1.1.1 ) give : ( 1.1.3 ) and ( 011 ) x + ( 012 ) y + £ 1 = 0 in R f2 ( 012 ) x + ( 022 ) y + f2 = 0 + = 011nx 012ny gb1 + 012nx 022ny = on JR2 gb2 while on the ...
... vector and ( gb1 , gb2 ) the boundary force vector . Thus ( 1.1.2 ) and ( 1.1.1 ) give : ( 1.1.3 ) and ( 011 ) x + ( 012 ) y + £ 1 = 0 in R f2 ( 012 ) x + ( 022 ) y + f2 = 0 + = 011nx 012ny gb1 + 012nx 022ny = on JR2 gb2 while on the ...
Pagina 5
... vector , that is , a vector such that JTV gives the mass of u crossing a plane perpendicular to the unit vector v per unit area per unit time , then the net change in u per unit time in the subregion E due to mass crossing the boundary ...
... vector , that is , a vector such that JTV gives the mass of u crossing a plane perpendicular to the unit vector v per unit area per unit time , then the net change in u per unit time in the subregion E due to mass crossing the boundary ...
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