67 citations · 324 across the 36 of their papers we have counts for
41 papers
Residual Minimisation for Transport-Based Optimal Control
Tristan Pryer, Nikolaos Rekatsinas
We consider an optimal control problem governed by a stationary linear transport equation in two or three spatial dimensions, motivated by photon transport in radiotherapy treatmen…
Batched Wavefront Sweeps for Linear Transport Uncertainty Quantification
Tristan Pryer
We develop a graph-compatible batched wavefront formulation for upwind discontinuous Galerkin discretisations of linear transport. For sweepable discretisations, the cell equations…
Polytopic symmetric interior-penalty approximation of elliptic SPDEs driven by spatial white noise
Tristan Pryer
We analyse symmetric interior-penalty discontinuous Galerkin approximations of elliptic stochastic partial differential equations driven by spatial Gaussian white noise on quasi-un…
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…
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…
Optimal control of a kinetic equation
Aaron Pim, Tristan Pryer, Alex Trenam
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-pos…
A Deep Uzawa-Lagrange Multiplier Approach for Boundary Conditions in PINNs and Deep Ritz Methods
Charalambos G. Makridakis, Aaron Pim, Tristan Pryer
We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics…
Deep Uzawa for PDE constrained optimisation
Charalambos G. Makridakis, Aaron Pim, Tristan Pryer
In this work, we present a numerical solver for optimal control problems constrained by linear and semi-linear second-order elliptic PDEs. The approach is based on recasting the pr…
A nodally bound-preserving discontinuous Galerkin method for the drift-diffusion equation
Gabriel R. Barrenechea, Tristan Pryer, Alex Trenam
In this work, we introduce and analyse discontinuous Galerkin (dG) methods for the drift-diffusion model. We explore two dG formulations: a classical interior penalty approach and…
A nodally bound-preserving finite element method for reaction-convection-diffusion equations
Abdolreza Amiri, Gabriel R. Barrenechea, Tristan Pryer
This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete so…
A Nodally Bound-Preserving Finite Element Method
Gabriel Barrenechea, Emmanuil Georgoulis, Tristan Pryer +1
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator…
Conservative Galerkin methods for dispersive Hamiltonian problems
James Jackaman, Tristan Pryer
An energy conservative discontinuous Galerkin scheme for a generalised third order KdV type equation is designed. Based on the conservation principle, we propose techniques that al…
Quasinorms in semilinear elliptic problems
James Jackaman, Tristan Pryer
In this note we examine the a priori and a posteriori analysis of discontinuous Galerkin finite element discretisations of semilinear elliptic PDEs with polynomial nonlinearity. We…
A finite element method for the Monge-Ampère equation with transport boundary conditions
Ellya Kawecki, Omar Lakkis, Tristan Pryer
We address the numerical solution via Galerkin type methods of the Monge-Ampère equation with transport boundary conditions arising in optimal mass transport, geometric optics and…
Recovered finite element methods on polygonal and polyhedral meshes
Zhaonan Dong, Emmanuil H. Georgoulis, Tristan Pryer
Recovered finite element methods (R-FEM) have been recently introduced for meshes consisting of simplicial and/or box-type meshes. Here, utilising the flexibility of R-FEM framewor…
Recovered Finite Element Methods
Emmanuil H. Georgoulis, Tristan Pryer
We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces. This new family, termed…