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Related papers: Multiscale Methods for Model Order Reduction of No…

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Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…

Numerical Analysis · Mathematics 2021-10-22 Felipe Rocha , Simone Deparis , Pablo Antolin , Annalisa Buffa

This work presents an efficient numerical method based on spectral expansions for simulation of heat and moisture diffusive transfers through multilayered porous materials. Traditionally, by using the finite-difference approach, the problem…

Computational Engineering, Finance, and Science · Computer Science 2020-02-20 Suelen Gasparin , Denys Dutykh , Nathan Mendes

Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…

Numerical Analysis · Mathematics 2026-04-16 Arnob Barua , Christopher E. Kees , Dmitri Kuzmin

Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…

Numerical Analysis · Mathematics 2018-06-28 Marco Favino , Alessio Quaglino , Sonia Pozzi , Rolf Krause , Igor Pivkin

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…

Numerical Analysis · Mathematics 2023-02-08 Tina Mai , Siu Wun Cheung , Jun Sur Richard Park

Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…

Fluid Dynamics · Physics 2025-11-04 Rik Verbiest , Julian Koellermeier

The time discrete scheme of characteristics type is especially effective for convection-dominated diffusion problems. The scheme has been used in various engineering areas with different approximations in spatial direction. The lowest-order…

Numerical Analysis · Mathematics 2022-04-28 W. Sun

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…

Statistics Theory · Mathematics 2009-11-11 G. A. Pavliotis , A. M. Stuart

Asymptotic multiple scale homogenisation allows to determine the effective behaviour of a porous medium by starting from the pore-scale description, when there is a large separation between the pore-scale and the macroscopic scale. When the…

Classical Physics · Physics 2019-03-06 Pascale Royer

This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…

Numerical Analysis · Computer Science 2019-07-30 Boris Kramer , Karen Willcox

The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…

Numerical Analysis · Mathematics 2022-02-11 Vladimír Lukeš , Eduard Rohan

In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable…

Numerical Analysis · Mathematics 2020-08-04 Nicola Giuliani , Martin W. Hess , Antonio DeSimone , Gianluigi Rozza

Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the…

Numerical Analysis · Mathematics 2016-09-12 Eric T. Chung , Shubin Fu , Yanfang Yang

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

Machine Learning · Computer Science 2021-04-30 Sourav Dutta , Peter Rivera-Casillas , Matthew W. Farthing

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…

Numerical Analysis · Mathematics 2024-07-25 Konstantinos Vlachas , Konstantinos Tatsis , Konstantinos Agathos , Adam R. Brink , Eleni Chatzi

We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…

Numerical Analysis · Mathematics 2025-10-30 Abbas Kabalan , Fabien Casenave , Felipe Bordeu , Virginie Ehrlacher , Alexandre Ern

In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…

This paper deals with fast simulations of the haemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical…

Numerical Analysis · Mathematics 2018-01-19 Claudia M. Colciago , Simone Deparis

To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand,…

Optimization and Control · Mathematics 2021-07-20 Christian Himpe , Sara Grundel , Peter Benner

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