R. H. W. HOPPE, Y. ILIASH, Y. KUZNETSOV, Y. VASSILEVSKI, AND B. WOHLMUTH, Analysis and parallel implementation of adaptive mortar finite element methods, East-West J. of Numer. Math., 6 (1998), pp. 223--248.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....valuable in optimal design studies, where the relative position of parts of the model is not xed a priori. The mortar methods also allow for local re nement of nite element models in only certain subregions of the computational domain, and they are also well suited for parallel computing; cf. [29]. We have used geometrically nonconforming mortar nite elements. Three FETI algorithms with di erent preconditioners for the dual problem have been considered: the Dirichlet preconditioner of Farhat and Roux [25] the block diagonal preconditioner of Lacour [34] and the new preconditioner of ....

R. H. W. Hoppe, Y. Iliash, Y. Kuznetsov, Y. Vassilevski, and B.I. Wohlmuth. Analysis and parallel implementation of adaptive mortar nite element methods. East-West J. Numer. Math., 6(4):223-248, 1998.

....subdomains. Here, the weak continuity is realized by a L 2 orthogonality between the jump on the interface and an adequate discrete space. In the last couple of years, a lot of work has been done on the construction of efficient iterative solvers for the arising algebraic linear system [1, 2, 3, 11, 12, 13, 19, 21, 22, 23, 27, 28, 33]. Taking the matching condition at the interface as starting point, there are two different approaches to obtain the discrete mortar solution. Either the weak continuity condition is imposed on the global discrete space or it is satisfied by means of Lagrange multipliers. The first technique ....

R. H. W. HOPPE, Y. ILIASH, Y. KUZNETSOV, Y. VASSILEVSKI, AND B. WOHLMUTH, Analysis and parallel implementation of adaptive mortar finite element methods, East-West J. of Numer. Math., 6 (1998), pp. 223--248.

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R. Hoppe, Yu. Iliash, Yu. Kuznetsov, Yu. Vassilevski, and B. Wohlmuth. Analysis and parallel implementation of adaptive mortar element methods. East West J. Num. An., 6(3):223--248, 1998.

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R. Hoppe, Y. Iliash, Y. Kuznetsov, Y. Vassilevski, and B. Wohlmuth. Analysis and parallel implementation of adaptive mortar finite element methods. East--West J. of Numer. Math., 6:223--248, 1998.

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R.H.W. Hoppe, Y. Iliash, Y. Kuznetsov, Y. Vassilevski, and B.I. Wohlmuth. Analysis and parallel implementation of adaptive mortar nite element methods. East-West J. Numer. Math., 6:223-248, 1998.

....subdomains. Here, the weak continuity is realized by a L 2 orthogonality between the jump on the interface and an adequate discrete space. In the last couple of years, a lot of work has been done on the construction of efficient iterative solvers for the arising algebraic linear system [1, 2, 3, 11, 12, 13, 19, 21, 22, 23, 27, 28, 33]. Taking the matching condition at the interface as starting point, there are two different approaches to obtain the discrete mortar solution. Either the weak continuity condition is imposed on the global discrete space or it is satisfied by means of Lagrange multipliers. The first technique ....

R. H. W. HOPPE, Y. ILIASH, Y. KUZNETSOV, Y. VASSILEVSKI, AND B. WOHLMUTH, Analysis and parallel implementation of adaptive mortar finite element methods, East-West J. of Numer. Math., 6 (1998), pp. 223--248.

....replace the pointwise continuity at the interfaces. The arising variational problems are either positive definite nonconforming problems or saddle point problems. Efficient iterative solvers for the discrete nonconforming as well as the discrete saddle point problem are well established, see [1, 2, 3, 10, 11, 12, 15, 16, 17, 18, 19, 22, 23, 28]. Working with the nonconforming variational problem has the drawback that the corresponding nodal basis functions have in general a non local support. Thus it might be advantageous to work with the unconstraint product space for the numerical realization of the mortar method. Even if the starting ....

....is that the solution of the modified Schur complement system in each smoothing step might be too expensive. In [31] a generalization of this type of smoother is investigated. A different approach for the construction of an efficient iterative solver for the saddle point problem is given in [2, 17, 18, 22, 23]. The saddle point problem is solved by a multilevel preconditioned Lanczos iteration. The preconditioner is a block diagonal matrix involving a good preconditioner for the exact Schur complement. Mathemetisches Institut, Universitat Augsburg, D 86135 Augsburg, Germany. E mail: ....

R.H.W. Hoppe, Y. Iliash, Y. Kuznetsov, Y. Vassilevski, and B.I. Wohlmuth, Analysis and parallel implementation of adaptive mortar finite element methods. East-West J. of Numer. Math., 6 (1998), pp.223-248.

....iterative solvers for linear equation systems arising from mortar finite element discretization are very often based on the saddle point formulation or work with the product space X h instead of the nonconforming mortar space. Different types of efficient iterative solvers are developed in [1, 2, 3, 11, 15, 16, 19, 20, 18, 25]. However, most of these techniques require that each iterate satisfies the constraints exactly. In most studies of multigrid methods, these constraints have to be satisfied even in each smoothing step [11, 12, 18, 25] If we replace e V h by V h the constraints are much easier to satisfy, since ....

R.H.W. Hoppe, Y. Iliash, Y. Kuznetsov, Y. Vassilevski, and B.I. Wohlmuth, Analysis and parallel implementation of adaptive mortar finite element methods. East-West J. of Numer. Math., 6 (1998), pp.223-248.

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