All Outputs (3)

Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights (2022)
Journal Article
Brevis, I., Muga, I., & van der Zee, K. G. (2022). Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights. Computer Methods in Applied Mechanics and Engineering, 402, Article 115716. https://doi.org/10.1016/j.cma.2022.115716

There is tremendous potential in using neural networks to optimize numerical methods. In this paper, we introduce and analyse a framework for the neural optimization of discrete weak formulations, suitable for finite element methods. The main idea of... Read More about Neural Control of Discrete Weak Formulations: Galerkin, Least Squares & Minimal-Residual Methods with Quasi-Optimal Weights.

Linearization of the Travel Time Functional in Porous Media Flows (2022)
Journal Article
Rourke, C. J., Houston, P., Rourke, C., & van der Zee, K. G. (2022). Linearization of the Travel Time Functional in Porous Media Flows. SIAM Journal on Scientific Computing, 44(3), B531-B557. https://doi.org/10.1137/21M1451105

The travel time functional measures the time taken for a particle trajectory to travel from a given initial position to the boundary of the domain. Such evaluation is paramount in the postclosure safety assessment of deep geological storage facilitie... Read More about Linearization of the Travel Time Functional in Porous Media Flows.

Projection in negative norms and the regularization of rough linear functionals (2022)
Journal Article
Millar, F., Muga, I., Rojas, S., & Van der Zee, K. G. (2022). Projection in negative norms and the regularization of rough linear functionals. Numerische Mathematik, 150(4), 1087-1121. https://doi.org/10.1007/s00211-022-01278-z

In order to construct regularizations of continuous linear functionals acting on Sobolev spaces such as W01,q(Ω), where 1 < q< ∞ and Ωis a Lipschitz domain, we propose a projection method in negative Sobolev spacesW-1,p(Ω) , pbeing the conjugate expo... Read More about Projection in negative norms and the regularization of rough linear functionals.