Related papers: Constraint Energy Minimizing Generalized Multiscal…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
We develop a partially explicit time discretization based on the framework of constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for the problem of linear poroelasticity with high contrast. Firstly,…
This work presents an Iterative Constraint Energy Minimizing Generalized Multiscale Finite Element Method (ICEM-GMsFEM) for solving the contact problem with high contrast coefficients. The model problem can be characterized by a variational…
This paper applies topology optimisation to the design of structures with periodic microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all…
This paper proposes a methodology to estimate stress in the subsurface by a hybrid method combining finite element modeling and neural networks. This methodology exploits the idea of obtaining a multi-frequency solution in the numerical…
In this paper, we propose a multiscale method for the Darcy-Forchheimer model in highly heterogeneous porous media. The problem is solved in the framework of generalized multiscale finite element methods (GMsFEM) combined with a multipoint…
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop…
Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…
Finite element model updating of a structure made of linear elastic materials is based on the solution of a minimization problem. The goal is to find some unknown parameters of the finite element model (elastic moduli, mass densities,…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
In this work, we propose a local multiscale model reduction approach for the time-domain scalar wave equation in a heterogenous media. A fine mesh is used to capture the heterogeneities of the coefficient field, and the equation is solved…
We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…
Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite…
In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) framework. The main idea of GMsFEM is to approximate the solution…
In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…
In this paper, we develop a local multiscale model reduction strategy for the elastic wave equation in strongly heterogeneous media, which is achieved by solving the problem in a coarse mesh with multiscale basis functions. We use the…
A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…