Workshop — Taming the PDEs: Tailored Methods, Multiscale Approaches, and Real-World Application

Partial differential equations (PDEs) are central to modeling complex phenomena across the physical, biological, and engineering sciences. Many of these models involve tightly coupled processes spanning multiple spatial and temporal scales, leading to significant analytical and computational challenges. This workshop addresses these challenges by presenting modern strategies that combine mathematical rigor with computational efficiency. Key topics include adaptive discretizations, domain decomposition, multiscale and multilevel formulations, and problem-adapted approximation spaces. Special attention is given to scalable hierarchical solvers and emerging machine learning techniques that complement or accelerate traditional numerical methods. The overarching goal is to bridge the gap between theoretical advances and real-world applications—showcasing methods that enable robust, efficient simulations in fields such as quantum mechanics, fluid dynamics, optics, and materials science. By fostering cross-disciplinary dialogue, the workshop seeks to advance the development of next-generation PDE tools that are both practically effective and mathematically sound.

Topics: This workshop is aimed at the participants in the Trimester Program "Computational multifidelity, multilevel, and multiscale methods". It is not possible to apply only for this workshop.