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 13
Pagina 1
... force balance . 1.1 Energy Minimization If it is possible to express the ... boundary ( because PDE / PROTRAN solves two dimensional problems , only two ... boundary , then a PDE system may be derived by assuming that the steady state ...
... force balance . 1.1 Energy Minimization If it is possible to express the ... boundary ( because PDE / PROTRAN solves two dimensional problems , only two ... boundary , then a PDE system may be derived by assuming that the steady state ...
Pagina 2
... force , f ( x , y ) . ( Note that potential energy increases if u is in a ... boundary where it is attached to the frame . On the free part , by ( 1.1.2 ) ... forces is of the form : E ( u1 , u2 ) SS E1 ( € 11 , 12 , 22 , u1 , u2 ) dxdy + ...
... force , f ( x , y ) . ( Note that potential energy increases if u is in a ... boundary where it is attached to the frame . On the free part , by ( 1.1.2 ) ... forces is of the form : E ( u1 , u2 ) SS E1 ( € 11 , 12 , 22 , u1 , u2 ) dxdy + ...
Pagina 3
... force 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 ...
... force 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 ...
Pagina 4
... force . Although the appearance of second derivatives prevent the application of ( 1.1.2 ) , the same procedure may ... boundary ( clamped boundary condition ) , & and ap / an are zero there also . If u is given and V2u is zero ( simply ...
... force . Although the appearance of second derivatives prevent the application of ( 1.1.2 ) , the same procedure may ... boundary ( clamped boundary condition ) , & and ap / an are zero there also . If u is given and V2u is zero ( simply ...
Pagina 6
... boundary conditions are to specify either the value of the concentration u , or the boundary flux Jn . This latter ... Force Balance In Section 1.1 , Example 1 , 6.
... boundary conditions are to specify either the value of the concentration u , or the boundary flux Jn . This latter ... Force Balance In Section 1.1 , Example 1 , 6.
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