Minisymposium

We extended the capabilities of the numerical simulation framework Trixi.jl to be able to simulate adaptively coupled multiphysics systems. Coupling is performed through the boundary values of the systems where the coupling functions can be freely defined, depending on the physical nature of the interface. This allows us to couple any pair of systems, like Navier-Stokes equations with magnetohydrodynamic equations. This is particularly useful for hierarchical systems found in e.g. Astrophysics where we can have a complex model for a small part of the domain and a simplified model on a larger part. This can greatly reduce the computational cost and decrease the computational time. To account for dynamic changes in the physics that need to be solved at any given point in space, we support adaptively coupled domains. The criteria for changing the domain boundaries can be freely defined and tailored to the problem. One application is the propagation of magnetic fields in space where we solve the magnetohydrodynamic equations only for the part of the domain with a significant magnetic field.

The GPU4GEO project aims at developing new High-Performance Computing (HPC) tools for modelling geodynamics and ice sheet dynamics written in the Julia language. This initiative is a response to the practical demands of HPC, particularly the need for optimal performance in supercomputing environments that rely on GPU accelerators. We will present our flagship applications JustRelax.jl (geodynamics) and FastIce.jl (ice flow). These applications offer a high-level API for massively parallel thermo-mechanical Stokes solvers based on the highly-scalable pseudo-transient iterative method. We will further discuss the developed software upon which these applications are built: (i) portability to multi-GPU systems (ParallelStencil.jl and ImplicitGlobalGrid.jl); (ii) solver-agnostic material physics computations (GeoParams.j); and (iii) particles-in-cell advection (JustPIC.jl).We tackle the increasing demand for merging data-driven workflows with physics-based modelling, utilising Julia’s native support for differentiable programming. Leveraging automatic differentiation (AD), we efficiently compute model sensitivities, offering a unified framework for both inverse modelling and physics-informed machine learning. We will demonstrate Julia’s powerful AD application via Enzyme.jl for computing adjoint sensitivities in our solvers, and present benchmarks showcasing multi-GPU performance and scalability.

Solving sparse linear systems on GPU-accelerated systems efficiently is a highly specialized and demanding task. The implementation of efficient solvers incorporates not only deep insights into the problem but also an extensive understanding of the underlying hardware and the respective platform-specific languages. This interdisciplinary orchestration poses significant challenges in scientific software development.

This talk presents recent developments on Ginkgo.jl, a Julia wrapper package of the modern C++-based sparse linear algebra library Ginkgo. We demonstrate its performance through a series of benchmarks and showcase an example where we solve the sparse linear system assembled from the finite element toolbox package, Ferrite.jl, using a preconditioned iterative solver. We highlight its interoperability with existing packages in the Julia package ecosystem.

Modern data-driven discovery algorithms and workflows require the tight interpretation of Simulation, Data Analysis, and AI. This means that all too often modern workflows fail to mesh well with HPC environments which are optimized for isolated applications over integrated workflows; and high utilization over fast feedback.

An example of this is real-time data analysis for experiment steering: time at large scientific instruments (such as particle accelerators, electron microscopes, or telescopes) is a scarce resource. Yet modern instruments often produce data at a rate that outpaces local computing resources. Therefore, scientists are turning to live data processing at HPC centers in order to gain the necessary insight to effectively steer their experiments.

In this talk, we demonstrate how Julia’s unique language features make it a natural language for developing tightly integrated Simulation + Analysis + AI workflows. We will also show an example of a workflow that flexibly grows its pool of compute nodes on an HPC system, thereby overcoming the constraints of the resource scheduler.