14 papers
Variational Principles for the Helmholtz equation: application to Finite Element and Neural Network approximations
G. Makrakis, C. Makridakis, D. Mitsoudis +2
In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been…
Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification
Aaron Pim, Tristan Pryer
We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define…
A finite element method preserving the eigenvalue range of symmetric tensor fields
Abdolreza Amiri, Gabriel R. Barrenechea, Tristan Pryer
This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion eq…
A posteriori analysis for nonlinear convection-diffusion systems
Andreas Dedner, Jan Giesselmann, Kiwoong Kwon +1
This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we…
A nodally bound-preserving composite discontinuous Galerkin method on polytopic meshes
Abdolreza Amiri, Gabriel R. Barrenechea, Emmanuil H. Georgoulis +1
We introduce a nodally bound-preserving Galerkin method for second-order elliptic problems on general polygonal/polyhedral, henceforth collectively termed as \emph{polytopic}, mesh…
Surrogate Modelling of Proton Dose with Monte Carlo Dropout Uncertainty Quantification
Aaron Pim, Tristan Pryer
Accurate proton dose calculation using Monte Carlo (MC) is computationally demanding in workflows like robust optimisation, adaptive replanning, and probabilistic inference, which…