On a parallel implementation of the mortar element method
A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations
We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the rapid and reliable evaluation prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are (i) (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space spanned...
On a Parallel Implementation of the Mortar Element Method
We discuss a parallel implementation of the domain decomposition method based on the macro-hybrid formulation of a second order elliptic equation and on an approximation by the mortar element method. The discretization leads to an algebraic saddle- point problem. An iterative method with a block- diagonal preconditioner is used for solving the saddle- point problem. A parallel implementation of the method is emphasized. Finally the results of numerical experiments are presented.
A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations
We present in this article two components: these components can in fact serve various goals independently, though we consider them here as an ensemble. The first component is a technique for the prediction of linear functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential features are () (provably) rapidly convergent global reduced–basis approximations — Galerkin projection onto a space spanned by solutions...
convergence of the Greedy algorithm for the parametrized reduced basis method
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...
A priori convergence of the greedy algorithm for the parametrized reduced basis method
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...
convergence of the Greedy algorithm for the parametrized reduced basis method
The convergence and efficiency of the reduced basis method used for the approximation of the solutions to a class of problems written as a parametrized PDE depends heavily on the choice of the elements that constitute the “reduced basis”. The purpose of this paper is to analyze the convergence for one of the approaches used for the selection of these elements, the greedy algorithm. Under natural hypothesis on the set of all solutions to the problem obtained when the parameter varies, we prove that...
Page 1