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Algorithms for many hypergraph problems, including partitioning, utilize multilevel frameworks to achieve a good trade-off between the performance and the quality of results. In this paper we introduce two novel aggregative coarsening…

Data Structures and Algorithms · Computer Science 2022-06-16 Ruslan Shaydulin , Ilya Safro

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…

Numerical Analysis · Mathematics 2012-05-22 Lijian Jiang , Dylan Copeland , J. David Moulton

This article investigates the numerical solution of the Diffusive Wave equation posed on domains containing a large number of polygonal perforations, motivated by urban flood modeling. Such geometries induce strong multiscale effects driven…

Numerical Analysis · Mathematics 2026-03-10 Miranda Boutilier , Konstantin Brenner , Victorita Dolean

The Multiscale Finite Element Method (MsFEM) is developed in the vein of Crouzeix-Raviart element for solving viscous incompressible flows in genuine heterogeneous media. Such flows are relevant in many branches of engineering, often at…

Numerical Analysis · Mathematics 2014-04-11 Bagus Putra Muljadi , Jacek Narski , Alexei Lozinski , Pierre Degond

In this work we propose upscaling method for nonlinear Forchheimer flow in highly heterogeneous porous media. The generalized Forchheimer law is considered for incompressible and slightly-compressible single-phase flows. We use recently…

Numerical Analysis · Mathematics 2015-06-15 Eugenio Aulisa , Lidia Bloshanskaya , Yalchin Efendiev , Akif Ibragimov

Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…

Numerical Analysis · Mathematics 2015-01-16 Eric T. Chung , Yalchin Efendiev , Guanglian Li , Maria Vasilyeva

We consider anisotropic heat flow with extreme anisotropy, as arises in magnetized plasmas for fusion applications. Such problems pose significant challenges in both obtaining an accurate approximation as well in the construction of an…

Numerical Analysis · Mathematics 2024-12-12 Maria Vasilyeva , Golo A. Wimmer , Ben S. Southworth

In this paper, we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields. Mathematical model contains a coupled system of…

Numerical Analysis · Mathematics 2019-08-07 Aleksei Tyrylgin , Maria Vasilyeva , Denis Spiridonov , Eric T. Chung

Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…

Fluid Dynamics · Physics 2025-08-04 Bindi M. Nagda , Aaron Barrett , Boyce E. Griffith , Aaron L. Fogelson , Jian Du

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…

Numerical Analysis · Mathematics 2022-09-13 Maria Vasilyeva , Alexey Sadovski , D. Palaniappan

We present a multi-block finite-difference solver for massively parallel Direct Numerical Simulations (DNS) of incompressible flows. The algorithm combines the versatility of a multi-block solver with the method of eigenfunctions…

Computational Physics · Physics 2022-09-14 Pedro Costa

With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation.…

Fluid Dynamics · Physics 2022-05-24 Hao-Ran Liu , Chong Shen Ng , Kai Leong Chong , Detlef Lohse , Roberto Verzicco

The fluid antenna system (FAS) has emerged as a disruptive technology, offering unprecedented degrees of freedom (DoF) for wireless communication systems. However, optimizing fluid antenna (FA) positions entails significant computational…

Information Theory · Computer Science 2025-05-13 Tianyi Liao , Wei Guo , Hengtao He , Shenghui Song , Jun Zhang , Khaled B. Letaief

A number of different multiscale methods have been developed as a robust alternative to upscaling and as a means for accelerated reservoir simulation of high-resolution geomodels. In their basic setup, multiscale methods use a restriction…

Numerical Analysis · Mathematics 2020-01-07 Øystein Strengehagen Klemetsdal , Olav Møyner , Knut-Andreas Lie

This research investigates the application of Multigrid Neural Operator (MgNO), a neural operator architecture inspired by multigrid methods, in the simulation for multiphase flow within porous media. The architecture is adjusted to manage…

Computational Engineering, Finance, and Science · Computer Science 2024-07-04 Xinliang Liu , Xia Yang , Chen-Song Zhang , Lian Zhang , Li Zhao

Sequential implicit (SI) formulations are gaining increasing interest due to their ability to decouple reservoir simulation problems into distinct flow and transport subproblems, allowing for the use of specialized solvers tailored to each.…

Numerical Analysis · Mathematics 2025-04-29 Omar Chaabi , Mohammed Al-Kobaisi

In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…

Numerical Analysis · Mathematics 2020-04-22 Maria Vasilyeva , Wing T. Leung , Eric T. Chung , Yalchin Efendiev , Mary Wheeler

Efficient simulation of Darcy flow in highly heterogeneous porous media requires iterative solvers that remain robust under large permeability contrasts and mixed boundary conditions. Spectral coarse spaces in two-level overlapping Schwarz…

Numerical Analysis · Mathematics 2026-03-30 Yucheng Liu , Tak Shing Au Yeung , Eric T. Chung , Simon See

To acquire the ability to numerically study the rheology of particulate two-phase flows that lack scale separation, we present a general method to average or coarse-grain the equations of motion of a mixture of a continuous fluid of…

Fluid Dynamics · Physics 2026-01-22 Thomas Pähtz , Yulan Chen , Rui Zhu , Katharina Tholen , Zhiguo He

Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…

Machine Learning · Computer Science 2021-12-22 Ali Aghdaei , Zhiqiang Zhao , Zhuo Feng