Minisymposium

Electrical Treeing is one of the main causes for the degradation of the insulating components of cables: partial discharges occur in a gas-filled defect in the polymer under strong electrical fields.This phenomenon can be modeled by a system of PDEs, describing the movement of charges in the defect and the evolution of the electrical field and potential in both the gas and the solid dielectric material. However, the geometry of the defect makes the problem very challenging: such ramified subdomain with very small diameter can hardly be discretized by a 3D mesh in realistic cases. To overcome this limitation we approximate the treeing as a one-dimensional graph, and derive a mixed-dimensional 3D-1D system of equations, reducing the problem complexity. The numerical solution is based on Mixed FEM for the electrostatic problem and Finite Volumes for the charges movement, and on a splitting to manage the multiphysics coupling with reactive phenomena. The method is implemented in the parallel C++ code Morgana.

Given their pervasive occurrence in science and engineering, obtaining solutions to Partial Differential Equations (PDEs) is of paramount importance across multiple domains. However, numerically solving PDEs often presents significant challenges, especially in multi-physics contexts or for problems requiring simultaneous high-resolution and large-scale analysis. In this talk, I will present instances of real-world problems in science and engineering where the synergy of advanced numerical methods, state-of-the-art software implementations, and high-performance hardware enable the high-fidelity modeling of complex physics at scale. Case studies include fracture and fragmentation of large-scale structures under impact loading, the complex dynamics of flexible fibers sedimenting in viscous flow, and the large-deformation mechanics of novel architected materials exposed to extreme environments. In each case, the resulting simulations provide unique physical insights that would be otherwise unattainable, thus enabling analyses of engineering significance.

The development of robust and efficient multi-physics block preconditioners is crucial for drastically improving the computational performance of large-scale, thermo-mechanically coupled ice-sheet models. The primary challenge in simulating ice sheets at scale is solving the linear system associated with a thin, high-aspect ratio mesh. This problem is exacerbated by the coupling of first-order Stokes, a nonlinear elliptic problem for ice velocity, with the enthalpy formulation, an advection dominated problem. In this presentation, we show the performance of various multi-physics preconditioning strategies to assess a viable strategy for simulating the large, coupled ice-sheet model on large GPU supercomputers such as Perlmutter and Frontier.

The use of virtual human twins, powered by supercomputer-based multi-physics simulations, enables efficient and safe exploration of complex biomedical phenomena. These digital replicas integrate high-fidelity physics-based models to capture the complex interactions governing human physiology, offering new possibilities for understanding diseases and personalizing treatments. In this talk, we present our framework for high-fidelity cardiac modeling, which integrates electrophysiology, mechanics, and blood flow dynamics across multiple scales. Using the high-performance finite element solver Alya, developed at the Barcelona Supercomputing Center jointly with ELEM Biotech, we demonstrate how these comprehensive models can be personalized with patient data to create virtual human populations. Our methodology enables a detailed investigation of cardiac function in both healthy and pathological conditions, providing a powerful platform for diverse clinical applications, from evaluating the cardiac safety of drugs to analyzing how specific diseases influence the heart’s electromechanical behavior.