Zhang, X. (1994) Multilevel Schwarz methods for the biharmonic Dirichlet problems, SIAM J. Sci. Stat. Comp., 15, pp. 621--644.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....not need the degrees of freedom associated with the mixed second derivative at the vertices. Let V H b ( Omega Gamma be the Bogner Fox Schmit space of bicubic functions (hence the subscript b) such that the mixed second derivatives at the vertices are zero; this space has been used by Zhang [118, 119], in a different context. The mappings F i now define the space V H b ( Omega Gamma ae H 2 0( Omega Gamma3 obtained by 87 Figure 5.1: The Bogner Fox Schmit element setting all the degrees of freedom on Omega to zero. The coarse space used for our algorithm is given by V H b ....

Xuejun Zhang. Multilevel Schwarz methods for the biharmonic Dirichlet problem. SIAM J. Sci. Comput., 15(3):621--644, 1994. 141

....energy bounds are available for that case. The part of this paper dealing with second order problems is based on [15] The algorithm for fourth order problems is new. For more details and theory for the second order case, see [15] For other multigrid approaches to the biharmonic equation, see [5, 9, 16, 8]. For a multigrid theory for the biharmonic equation with non nested finite element spaces, see [2] 1.1. Basic Multigrid Algorithm. For reference, we state the basic multigrid algorithm for the solution of the system of linear algebraic equations Ax = b. First, a preprocessing stage creates full ....

X. Zhang, Multilevel Schwarz methods for the biharmonic Dirichlet problem, SIAM J. Sci. Comput. , 15 (1994), pp. 621--644. 15

....to the paper [1] where two non overlapping additive Schwarz methods were developed for second order elliptic problems with discontinuous coefficients. For earlier works on two level overlapping additive Schwarz methods using nonconforming plate elements, for the biharmonic equation, we refer to [2, 4, 7] and the references therein. The paper is organized as follows. In Section 2, the biharmonic problem and its nonconforming Morley finite element approximation are recalled. In Section 3, the non overlapping Schwarz method is proposed and analyzed for the Morley finite element. The construction ....

X. Zhang, Multilevel Schwarz methods for the biharmonic Dirichlet problem SIAM J. Sci. Comput, (15), 1994, pp. 621--644.

....confirm that the new variant of the method is superior to the old one for the biharmonic equation and for elasticity, particularly for shells. For another approach to multigrid on unstructured meshes, see [7] and references therein. For other multigrid approaches to the biharmonic equation, see [6, 12, 21, 11]. For a multigrid theory for the biharmonic equation with non nested finite element spaces, see [2] 2. Basic Multigrid Algorithm. For reference, we state the basic multigrid algorithm for the solution of a system of linear algebraic equations A 1 x = b. First, a preprocessing stage creates full ....

X. Zhang, Multilevel Schwarz methods for the biharmonic Dirichlet problem, SIAM J. Sci. Comput. , 15 (1994), pp. 621--644. Fig. 6. Jet engine, 2d elasticity. (Courtesy of Charbel Farhat, Center for Aerospace Engineering, University of Colorado, Boulder) G D Fig. 7. Spherical shell with Dirichlet values prescribed on \Gamma D

....Zhang [20] In [6] Brenner studied the W cycle for the Morley elements and simplified the algorithm and analysis of [17] Hanisch [11, 12] considered the multigrid for mixed formulation as well as Morley element. Oswald [15] studied some additive multilevel methods for bicubic element. X. Zhang [21] studied additive multilevel methods and V cycle multigrid for bicubic elements. All these papers considered the cases when the multilevel spaces are defined by the same finite element and none of them discussed nonnested meshes. This paper is organized as follows. In x2, we briefly describe the ....

....above, except the BFS and PS elements, are nonnested even when the triangulations fT k g are nested. For the BFS and PS elements defined with respect to a family of nested triangulations fT k g, a uniformly convergent theory for multigrid V cycle can be established along the line of [2] cf. [21] for more details. We will denote by k Delta k s;p;D and k Delta k s;D the standard norm on Sobolev spaces W s;p (D) and H s (D) W s;2 (D) and by j Delta j s;p;D and j Delta j s;D the semi norms. We will make the following standard assumption on the finite element spaces V k . The ....

X. ZHANG, Multilevel Schwarz methods for the biharmonic Dirichlet problem, SIAM J. Sci. Comput., 15:3 (1994), pp. 621--644.

No context found.

Zhang, X. (1994) Multilevel Schwarz methods for the biharmonic Dirichlet problems, SIAM J. Sci. Stat. Comp., 15, pp. 621--644.

No context found.

Zhang, X. (1994) Multilevel Schwarz methods for the biharmonic Dirichlet problems, SIAM J. Sci. Stat. Comp., 15, pp. 621--644.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC