67 citations · 324 across the 36 of their papers we have counts for
8 papers · 1 filter
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…
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…
A Unified Framework from Boltzmann Transport to Proton Treatment Planning
Andreas E. Kyprianou, Aaron Pim, Tristan Pryer
This work develops a rigorous mathematical formulation of proton transport by integrating both deterministic and stochastic perspectives. The deterministic framework is based on th…
Deep Uzawa for Kinetic Transport with Lagrange-Enforced Boundaries
Charalambos Makridakis, Aaron Pim, Tristan Pryer +1
We propose a neural network framework for solving stationary linear transport equations with inflow boundary conditions. The method represents the solution using a neural network a…
PINN-DG: Residual neural network methods trained with Finite Elements
Georgios Grekas, Charalambos G. Makridakis, Tristan Pryer
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integ…
A nodally bound-preserving finite element method for time-dependent convection-diffusion equations
Abdolreza Amiri, Gabriel R. Barrenechea, Tristan Pryer
This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respe…