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Reduction multigrids have recently shown good performance in hyperbolic problems without the need for Gauss-Seidel smoothers. When applied to the hyperbolic limit of the Boltzmann Transport Equation (BTE), these methods result in very close to $\math
Externí odkaz:
http://arxiv.org/abs/2408.08262
Autor:
Silva, Vinicius L S, Regnier, Geraldine, Salinas, Pablo, Heaney, Claire E, Jackson, Matthew D, Pain, Christopher C
Reactive transport in porous media plays a pivotal role in subsurface reservoir processes, influencing fluid properties and geochemical characteristics. However, coupling fluid flow and transport with geochemical reactions is computationally intensiv
Externí odkaz:
http://arxiv.org/abs/2405.14548
Recently, there has been a huge effort focused on developing highly efficient open source libraries to perform Artificial Intelligence (AI) related computations on different computer architectures (for example, CPUs, GPUs and new AI processors). This
Externí odkaz:
http://arxiv.org/abs/2402.17913
Autor:
Chen, Boyang, Heaney, Claire E., Gomes, Jefferson L. M. A., Matar, Omar K., Pain, Christopher C.
This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network whose weigh
Externí odkaz:
http://arxiv.org/abs/2401.06755
In this paper we solve the Boltzmann transport equation using AI libraries. The reason why this is attractive is because it enables one to use the highly optimised software within AI libraries, enabling one to run on different computer architectures
Externí odkaz:
http://arxiv.org/abs/2301.09991
This paper presents a new approach which uses the tools within Artificial Intelligence (AI) software libraries as an alternative way of solving partial differential equations (PDEs) that have been discretised using standard numerical methods. In part
Externí odkaz:
http://arxiv.org/abs/2301.09939
Previously we developed an adaptive method in angle, based on solving in Haar wavelet space with a matrix-free multigrid for Boltzmann transport problems. This method scalably mapped to the underlying P$^0$ space during every matrix-free matrix-vecto
Externí odkaz:
http://arxiv.org/abs/2301.06579
We develop a reduction multigrid based on approximate ideal restriction (AIR) for use with asymmetric linear systems. We use fixed-order GMRES polynomials to approximate $A_\textrm{ff}^{-1}$ and we use these polynomials to build grid transfer operato
Externí odkaz:
http://arxiv.org/abs/2301.05521
Autor:
Cheng, Sibo, Chen, Jianhua, Anastasiou, Charitos, Angeli, Panagiota, Matar, Omar K., Guo, Yi-Ke, Pain, Christopher C., Arcucci, Rossella
Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which co
Externí odkaz:
http://arxiv.org/abs/2204.03497
Publikováno v:
In Journal of Computational Science December 2024 83
