Related papers: Space-Time Nonlinear Upscaling Framework Using Non…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
In this paper we propose simple multiscale basis functions with constraint energy minimization to solve elliptic problems with high contrast medium. Our methodology is based on the recently developed non-local multicontinuum method (NLMC).…
We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for…
Recently, several approaches for multiscale simulations for problems with high contrast and no scale separation are introduced. Among them is the nonlocal multicontinua (NLMC) method, which introduces multiple macroscopic variables in each…
We consider image denoising using a nonlinear diffusion process, where we solve unsteady partial differential equations with nonlinear coefficients. The noised image is given as an initial condition, and nonlinear coefficients are used to…
We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…
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…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
The typical temporal resolution used in modern simulations significantly exceeds characteristic time scales at which the system is driven. This is especially so when systems are simulated over time-scales that are much longer than the…
In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation operator to define a fine detail space and local orthogonal…
We present an adaptive space-time mesh refinement approach based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments…
Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible due to the strong coupling…
Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of the deformation, its…
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…