An efficient multi-time step FEM–SFEM iterative coupling procedure for elastic–acoustic interaction problems

An iterative coupling methodology between the Finite Element Method (FEM) and the Spectral Finite Element Method (SFEM) for the modeling of coupled elastic-acoustic problems in the time domain is presented here. Since the iterative coupling procedure allows the use of a nonconforming mesh at the interface between the subdomains, the difference in the element sizes concerning the FEM and SFEM is handled in a straightforward and efficient manner, thereby retaining all the advantages of the SFEM. By means of the HHT time integration method, controllable numerical damping can be introduced in one of the subdomains, increasing the robustness of the method and improving the accuracy of the results; besides, independent time-step sizes can be considered within each subdomain, resulting in a more efficient algorithm. In this work, a modification in the subcycling procedure is proposed, ensuring not only an efficient and accurate methodology but also avoiding the computation of a relaxation parameter. Numerical simulations are presented in order to illustrate the accuracy and potential of the proposed methodology.CAPES, UFJF, UFSJ, FAPEMIG and CNP

Fuzzy arithmetic based on dimension-adaptive sparse grids: A case study of a large-scale finite element model under uncertain parameters

Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh's extension principle, one can obtain a fuzzy-valued extension of any real-valued objective function. An efficient and accurate approach to computing expensive multivariate functions of fuzzy numbers is given by fuzzy arithmetic based on sparse grids. In many cases, not all uncertain input parameters carry equal weight, or the objective model exhibits separable structure. These characteristics can be exploited by dimension-adaptive algorithms. As a result, the treatment of even higher-dimensional problems becomes possible. This is demonstrated in this paper by a case study involving two large-scale finite element models in vibration engineering that are subjected to fuzzy-valued input data.14556157

Multigrid Methods for Mortar Finite Elements

The framework of mortar methods [3,4] provides a powerful tool to analyze the coupling of different discretizations across subregion boundaries. We present an alternative Lagrange multiplier space without loosing the optimality of the a priori bounds [10]. By means of the biorthogonality between the nodal basis functions of our new Lagrange multiplier space and the finite element trace space, we derive a symmetric positive definite mortar formulation on the unconstrained product space. This new variational problem is the starting point for the application of our multigrid method. Level independent convergence rates for the W—cycle can be established, provided that the number of smoothing steps is large enough

Multigrid methods for mortar finite elements

Multigrid methods for mortar finite elements / R. Krause ; B. Wohlmuth. - In: Multigrid methods VI / Erik Dick ... (ed.). - Berlin u.a. : Springer, 2000. - S. 136-142 (Lecture notes in computational science and engineering ; 14

Mortar Element Coupling Between Global Scalar and Local Vector Potentials to Solve Eddy Current Problems

The formulation of the magnetic field has been introduced in many papers for the approximation of the magnetic quantities modeled by the eddy current equations. This decomposition allows to use a scalar function in the main part of the computational domain, reducing the use of vector quantities in the conducting parts. We propose here to approximate these two quantities on different and non-matching grids so as to be able for instance to tackle a problem where the conducting part can move in the global domain. The connection between the two grids is managed with the mortar element tools. The numerical analysis will be presented resulting in error bounds of the solution

A smoother based on nonoverlapping domain decomposition methods for H(div) problems: A numerical study

The purpose of this paper is to introduce a V-cycle multigrid method for vector field problems discretized by the lowest order Raviart-Thomas hexahedral element. Our method is connected with a smoother based on a nonoverlapping domain decomposition method. We present numerical experiments to show the effectiveness of our method