BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kaibo Hu DTSTART:20260325T080000Z DTEND:20260325T090000Z DTSTAMP:20260422T122025Z UID:MathMAC/55 DESCRIPTION:Title: Modelling Generalized Continua with Homological Algebra\nby Kaibo Hu as part of Modelling of materials - theory\, model reduction and efficient numerical methods (UNCE MathMAC)\n\n\nAbstract\nStructure-preserving disc retization within the frameworks of Finite Element Exterior Calculus (FEEC ) and Finite Element Tensor Calculus (FETC) motivates the investigation of the differential structures underlying physical models\, namely\, the spa ces in which variables reside and the differential operators that connect them. These structures are encoded in differential complexes and their ass ociated cohomology. In computational electromagnetism\, discretizing the e ntire differential complex avoids spurious solutions and yields many desir able properties.\n\nRecent efforts to extend this perspective to continuum mechanics have also led to progress in modelling. In elasticity\, strain and stress tensors fit naturally into the elasticity (Calabi\, Kröner) co mplex\, which can be viewed as a special case of the Bernstein–Gelfand –Gelfand (BGG) construction. The intermediate steps in the BGG construct ion turn out to correspond to continuum microstructures\, such as the Coss erat model. From this viewpoint\, the BGG construction can be interpreted as a cohomology-preserving elimination of microstructural degrees of freed om.\n\nIn this talk\, we explore mechanical models\, such as classical ela sticity\, the Cosserat model\, various plate models (dimension reduction)\ , continuum defects\, and mixed-dimensional models\, through the lens of d ifferential complexes\, the BGG machinery\, and the Čech complex.\n LOCATION:https://researchseminars.org/talk/MathMAC/55/ END:VEVENT END:VCALENDAR