3 papers
math.NA2025
A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy
Ben S. Ashby, Abdalaziz Hamdan, Tristan Pryer
We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is…
math.NA2025
A nodally bound-preserving finite element method for hyperbolic convection-reaction problems
Ben S. Ashby, Abdalaziz Hamdan, Tristan Pryer
In this article, we present a numerical approach to ensure the preservation of physical bounds on the solutions to linear and nonlinear hyperbolic convection-reaction problems at t…
math.NA2024
asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond
Joshua Hope-Collins, Abdalaziz Hamdan, Werner Bauer +2
Modern high performance computers are massively parallel; for many PDE applications spatial parallelism saturates long before the computer's capability is reached. Parallel-in-time…