In this paper,a multiscale problem arising in material science is considered.The problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in ...In this paper,a multiscale problem arising in material science is considered.The problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in the body of the text.The homogenized limit is then computed by using a perturbation approach.This computation requires repeatedly solving a corrector-like equation for various configurations of the material.For this purpose,the reduced basis approach is employed and adapted to the specific context.The authors perform numerical tests that demonstrate the efficiency of the approach.展开更多
We introduce and analyze a multiscale finite element type method (MsFEM) in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We il...We introduce and analyze a multiscale finite element type method (MsFEM) in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We illustrate numerically the efficiency of the approach and compare it with several variants of MsFEM.展开更多
In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed that aim at coupling an atomistic model （discrete mechan...In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed that aim at coupling an atomistic model （discrete mechanics） with a macroscopic model （continuum mechanics）. We provide here a theoretical basis for such a coupling in a one-dimensional setting, in the case of convex energy.展开更多
基金Project supported by EOARD(European Office of Aerospace Research and Development) (No.FA865510-C-4002)
文摘In this paper,a multiscale problem arising in material science is considered.The problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in the body of the text.The homogenized limit is then computed by using a perturbation approach.This computation requires repeatedly solving a corrector-like equation for various configurations of the material.For this purpose,the reduced basis approach is employed and adapted to the specific context.The authors perform numerical tests that demonstrate the efficiency of the approach.
基金supported by ONR under Grant (No. N00014-12-1-0383)EOARD under Grant (No. FA8655-10-C-4002)
文摘We introduce and analyze a multiscale finite element type method (MsFEM) in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We illustrate numerically the efficiency of the approach and compare it with several variants of MsFEM.
文摘In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed that aim at coupling an atomistic model （discrete mechanics） with a macroscopic model （continuum mechanics）. We provide here a theoretical basis for such a coupling in a one-dimensional setting, in the case of convex energy.
