2026 Abstracts

Title: Bridging domain decomposition and scientific machine learning for PDEs

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Solving large-scale PDEs at the frontier of modern applications increasingly requires combining the rigour and scalability of classical numerical methods with the flexibility of machine learning. In this talk I will discuss how ideas from domain decomposition - locality, coarse-space correction, and parallel scalability - can inform and improve neural network–based approaches to PDEs, and conversely how SciML techniques can enrich classical solvers. I will illustrate these connections through a few representative problems, ranging from wave propagation to multiscale models, and outline open questions and opportunities for the broader community working on numerical approximation of PDEs.

Title: Data assimialtion: from climite science to neuroscience

Title: Scalable Wave Solvers in Large-Scale Scientific Computing: From Convergence to Energy Efficiency

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Wave simulations are central to many areas of scientific computing, but their large-scale numerical solution remains challenging. Increasing model fidelity and grid resolution lead to stiff,strongly coupled, and often severely ill-conditioned systems, for which standard solvers may stagnate. These bottlenecks increasingly affect not only runtime and iteration count, but also energy-to-solution on modern architectures. At the same time, AI-based solvers are reshaping the field by offering new routes to acceleration. However, these methods also introduce their own costs and unresolved questions of robustness. This talk examines scalable wave solvers through the combined lens of convergence, accuracy, and energy efficiency. We focus on multilevel methods and advanced preconditioning strategies as mechanisms for improving convergence, and as paradigms in providing both practical tools for deployment and useful benchmarks for emerging approaches. The talk concludes by asserting that future solver development should move beyond standard metrics and should adopt a systems approach that connects algorithmic design to hardware execution and energy use.

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Title: Dealing with singularities in numerical methods

Title:  Modeling and Multiharmonic Simulation of Contrast-Enhanced Ultrasound

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Nonlinear acoustic effects physically underpin various medical and industrial applications of ultrasound.  Harmonic generation, in particular, plays a key role in contrast-enhanced ultrasound, for both imaging and therapeutic applications. We will discuss models for the interaction of ultrasound waves with contrast agents, in which the acoustic field is governed by a nonlinear Westervelt-type wave equation coupled to a Rayleigh-Plesset-type ODE that describes the dynamics of microbubble contrast agents. This coupling gives rise to nontrivial analytical and computational questions, including the existence of time-periodic solutions and the handling of nonlinearity and differing time scales. Direct time-domain simulation is prohibitively expensive for capturing nonlinear effects, which motivates a frequency-domain discretization based on a multiharmonic Ansatz applied to the wave–bubble system.  We will present a priori error estimates that characterize the approximation error in terms of the number of retained harmonics and a contribution arising from the fixed-point iteration. Additionally, numerical experiments will illustrate how the number of retained harmonics and the presence of microbubbles influence ultrasound propagation. The talk is based on joint work with Teresa Rauscher (University of Graz, Austria).

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Title: Adaptive methods for nonlinear, doubly-degenerate diffusion equations

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Degenerate parabolic equations appear as mathematical models for many situations of practical relevance. Among these we mention porous media flows, or reactive transport, biofilms, but also phase change or tumour growth. In such equations, the nonlinear diffusion coefficient may vanish or blow up for certain values of the unknown, leading to a change in the character of the equation from parabolic into hyperbolic, or elliptic. The regions in which the equation has one or another type are not known a priori, and are separated by so-called free boundaries. Usually, the solution lacks regularity, which makes the mathematical and numerical analysis for such equations a challenging task.
Motivated by the low regularity of the solution, we consider an Euler implicit time-stepping, leading to a sequence of nonlinear, time-discrete problems. These are reformulated in terms of a new unknown, which allows working with nonlinearities that are Lipschitz continuous, though maybe not strictly monotone. For the resulting equations, a splitting strategy is applied, which leads to a formulation that is more suitable for dealing with the degeneracies. Based on this splitting, different iterative linearisation strategies are considered.
After presenting some convergence results, we focus on a scheme that combines ideas related to Banach contraction arguments and to the Newton scheme (the so-called M-scheme). This scheme converges under mild restrictions for the time step, but for any spatial discretisation and mesh. We further present an adaptive strategy for selecting the optimal parameters, relying on a posteriori estimations. This strategy accelerates the convergence of the M-scheme while preserving its robust convergence w.r.t. to the spatial discretisation. Moreover, the adaptive M-scheme consistently out-competes the Newton scheme, showing quadratic convergence behavior.
Finally, if time allows we discuss an iterative scheme using the same splitting strategy, but designed at the level of the fully continuous problem. For this, an adaptive space-time discretisation is presented.
This work is done jointly with Ayesha Javed (Hasselt) and Koondanibha Mitra (Eindhoven) 

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Title: Efficient numerical solution of PIDEs for electricity derivatives under jump dynamics

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Title: Large Eddy Simulation of  Turbulence Through Integrated Filtering, Modeling and Discretization

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Title: The Art of Geometric Paper Folding

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