A Multiscale Hybrid-Mixed Method for the Elastodynamic Model with Rough Coefficients

Antonio Tadeu Gomes¹; Diego Paredes²; Weslley Pereira¹; Roberto Souto¹; Frederic Valentin¹

¹ Laboratorio Nacional de Computacao Cientifica; ² Pontificia Universidad Catolica de Valparaiso

doi:10.20906/CPS/CILAMCE2017-0399

Resumo

We present a family of multiscale finite element methods for the linear elastodynamic model with highly heterogeneous coefficients, named Multiscale Hybrid-Mixed (MHM) methods. The MHM method consists of a strategy that naturally incorporates multiple scales in the numerical solutions while providing solutions with high-order precision for the primal and dual variables. It is a consequence of a hybridization procedure, which characterizes the unknowns as a direct sum of a coarse solution and the solutions to local problems with boundary conditions driven by the Lagrange multipliers. The completely independent local problems are embedded in the upscaling procedure, and computational approximations may be naturally obtained in a parallel computational environment. Numerical results verify the optimal convergence of the method, and its capacity to accurately incorporate heterogeneity and high-contrast coefficients in the numerical solution.

Palavras-chave: multiscale; finite element; elasticity; wave