Geometric Mechanics Formulations for Continuum Mechanics (25w5441)

The Banff International Research Station will host the “Geometric mechanics formulations for continuum mechanics” workshop in Banff from March 16 - 21, 2025.

Complex multiphysics models are at the heart of many important fields of science with strong societal impact: climate, aerospace, materials science, biomedicine, porous media, combustions and plasma dynamics. In all cases addressing current and future challenges requires robust, reliable and efficient computer simulations. A powerful approach to developing simulations codes capable of this is the use of discrete geometric mechanics models, which consist of three pillars: a continuous geometric mechanics formulation, a structure-preserving discretization that preserves the key elements of the continuous formulation, and an efficient implementation of these numerics. This process is well understood for certain types of models such as electrodynamics and velocity-based formulations of fluids (often used in low-Mach applications), which at their heart are based on scalar-valued differential forms and their exterior calculus. However, for other types of models such as momentum-based formulations of fluids, or fluids with internal microstructure; a different type of object must be considered: (vector) bundle-valued differential forms. In this case the three pillars of discrete geometric mechanics models are still poorly understood. This workshop will bring together a diverse, interdisciplinary and international group of experts in these three areas, with the aim of kickstarting a global research effort to address development of discrete geometric mechanics models for (vector) bundle-valued differential forms.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta’s Advanced Education and Technology.