ABSTRACT. Simulating and Optimising Thermochemical Energy Storage Reactors with Firedrake Torben Prill, Thomas Jahnke

Thermochemical energy storage (TCES), where thermal energy is stored in a reversible chemical reaction in a porous powder bed, is a promising technology for large-scale and long-term heat storage. It has been under long-standing investigation for prospective applications, such as the capture of excess heat from industrial processes or storing energy in concentrated solar power plants to offset their unpredictable energy generation.

As heat transport from a heat source to the reactive material is a limiting factor in current reactor designs, fin structures are incorporated to enhance heat transfer. The geometry of these heat transfer structures has a major influence on the performance characteristics of the reactor, such as capacity and power delivery.

In this talk we show how we are using Firedrake for the simulation and optimization of TCES reactors. First, we give a short introduction into problem setting and the reactor model, which is implemented with a finite volume discretization with an immersed interface. Then we show, how to use firedrake.adjoint for sensitivity analysis and topology optimization. Finally, we show how the optimization can be sped up by using firedrakes pyTorch interface to construct a fast surrogate model, which is then used for optimization.

ABSTRACT. Heat conduction in magnetic confinement fusion can reach anisotropy ratios of 10^9−10^10, and in complex problems the direction of anisotropy may not be aligned with (or is impossible to align with) the spatial mesh. Such problems pose major challenges for both discretization accuracy and efficient implicit linear solvers. In this talk, we outline novel continuous and discontinuous discretizations of the underlying anisotropic diffusion operator and their implementation in Firedrake, using stabilization techniques developed for hyperbolic problems. Our approach reformulates the problem in a first-order directional-gradient form, introducing a directional heat flux along magnetic field lines as an auxiliary variable. We demonstrate that our novel discretizations significantly improve accuracy over standard methods in realistic tokamak configurations. Finally, we discuss possible strategies for efficient solvers, along with their testing in Firedrake including the external algebraic multigrid library pyAMG.

ABSTRACT. Within the last year we developed a scale-resolved toolbox for electrochemistry and batteries based on Firedrake with robust and scalable low-order approaches. At its core, this toolbox encompasses a p=0 Discontinuous Galerkin (DG0) formulation, due to inherent jumps in the domain, and an adaptive time stepping strategy with a naïve feedback-controller to handle violent transients. Although this already offers appealing engineering opportunities as designing performant batteries, there are several challenges that prohibit to tap further potentials. These challenges will be the main subject of our talk and include going towards higher order polynomials, adjoint-assisted model parametrization and coupling of electrochemistry with fluid dynamics.

ABSTRACT. It has been demonstrated that a superconductor with a suitable ferromagnetic coating can render itself and its enclosed region invisible to external magnetic fields. This is known as "magnetic cloaking". However, most existing results heavily depend on the assumption that the superconductor has a circular cross-section, such as a disk or a sphere. In this talk, we present the application of PDE-constrained optimization techniques to achieve geometry-free magnetic cloaking. We explore two strategies: (1) optimizing the spatially varying ferromagnetic permeability on a fixed-shape coating, and (2) empolying shape optimization to find the optimal coating geometry while the materials remain isotropic. Our implementation uses Firedrake and its shape optimization toolbox Fireshape.

ABSTRACT. We present finite element schemes for multicomponent (i.e. consisting of multiple chemical species) electrolyte flows. The model is based on the coupled Navier--Stokes and Onsager--Stefan--Maxwell equations, which capture momentum transport, cross-diffusion and electromigration in thermodynamically non-ideal electrolytes. The implementation uses a mélange of advanced Firedrake features: R spaces, EquationBCs, Irksome, ngsPETSc...

ABSTRACT. The Geoscientific ADjoint Optimisation PlaTform (G-ADOPT - https://gadopt.org) is a next-generation computational framework for simulating geoscientific flows. Developed and maintained by researchers at the Research School of Earth Sciences, Australian National University, in collaboration with international partners, G-ADOPT delivers accurate, efficient, flexible, and extensible open-source software for both forward and inverse, data-driven geoscientific simulations (Davies et al. 2022; Ghelichkhan et al. 2024; Scott et al. 2025). Its design emphasises scalability, transparency, and reproducibility, making it well suited to modern high-performance computing environments.

Current applications span geodynamics (including mantle convection and its diverse surface expressions), glacial isostatic adjustment and sea-level change, and groundwater modelling. These problems typically demand large-scale HPC, with simulations routinely executed on more than 1000 cores.

In this talk I will provide an overview of G-ADOPT, its applications, and its integration with Firedrake. I will also highlight ongoing development efforts and outline opportunities for collaboration on core Firedrake functionality to support the next generation of geoscientific models.