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pro vyhledávání: '"Park, Jun Sur Richard"'
We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynam
Externí odkaz:
http://arxiv.org/abs/2403.05848
Autor:
Park, Jun Sur Richard, Zhu, Xueyu
Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively expensive, especi
Externí odkaz:
http://arxiv.org/abs/2307.01027
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 techniques wi
Externí odkaz:
http://arxiv.org/abs/2205.11294
Autor:
Park, Jun Sur Richard, Zhu, Xueyu
Multiscale elliptic equations with scale separation are often approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). The traditional homogenization techniques typically rely on the periodic
Externí odkaz:
http://arxiv.org/abs/2202.09712
Autor:
Park, Jun Sur Richard, Zhu, Xueyu
Publikováno v:
In Journal of Computational Physics 1 April 2024 502
Publikováno v:
Journal of Computational and Applied Mathematics, 397:113648, 2021
In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pres
Externí odkaz:
http://arxiv.org/abs/2010.09181
Autor:
Park, Jun Sur Richard, Hoang, Viet Ha
We study homogenization of a locally periodic two-scale dual-continuum system where each continuum interacts with the other. Equations for each continuum are written separately with interaction terms (exchange terms) added. The homogenization limit d
Externí odkaz:
http://arxiv.org/abs/1910.07098
Publikováno v:
Journal of Computational and Applied Mathematics Volume 374, 15 August 2020, 112782
We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle, model reduction is employed. In \cite{rh2}, homogenization was nicely
Externí odkaz:
http://arxiv.org/abs/1909.04722
Autor:
Park, Jun Sur Richard, Hoang, Viet Ha
Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum technique, whe
Externí odkaz:
http://arxiv.org/abs/1906.04635
Publikováno v:
In Journal of Computational Physics 15 March 2023 477