Related papers: Learning macroscopic parameters in nonlinear multi…
Large-scale or high-resolution geologic models usually comprise a huge number of grid blocks, which can be computationally demanding and time-consuming to solve with numerical simulators. Therefore, it is advantageous to upscale geologic…
Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic…
Coarse-scale surrogate models in the context of numerical homogenization of linear elliptic problems with arbitrary rough diffusion coefficients rely on the efficient solution of fine-scale sub-problems on local subdomains whose solutions…
This work presents the application of the non-local multicontinuum method (NLMC) for the Darcy-Forchheimer model in fractured media. The mathematical model describes a nonlinear flow in fractured porous media with a high inertial effect and…
Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…
A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…
This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the…
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…
In this paper, we develop and analyze a rigorous multiscale upscaling method for dual continuum model, which serves as a powerful tool in subsurface formation applications. Our proposed method is capable of identifying different continua…
Multiscale problems can usually be approximated through numerical homogenization by an equation with some effective parameters that can capture the macroscopic behavior of the original system on the coarse grid to speed up the simulation.…
In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we…
In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…
Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in…
In this paper, we propose a multicontinuum homogenization approach for nonlinear problems involving dynamically evolving multiscale media. The main idea of the proposed approach is that one of the fine-scale variables defines continua. It…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…