4 papers
Locally Subspace-Informed Neural Operators for Efficient Multiscale PDE Solving
Alexander Rudikov, Vladimir Fanaskov, Sergei Stepanov +4
Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use th…
Dynamic nonlinear multicontinuum homogenization of systems with intrinsically evolving microstructure
Mohammed Al-Kobaisi, Dmitry Ammosov, Yalchin Efendiev +2
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…
Multicontinuum splitting schemes for multiscale wave problems
Mohsen Alshahrani, Buzheng Shan
In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The p…
Multicontinuum splitting scheme for multiscale flow problems
Yalchin Efendiev, Wing Tat Leung, Buzheng Shan +1
In this paper, we propose multicontinuum splitting schemes for multiscale problems, focusing on a parabolic equation with a high-contrast coefficient. Using the framework of multic…