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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > BIMSA numerical analysis seminar Towards Finite Element Tensor Calculus
Towards Finite Element Tensor Calculus
Organizer
Shuo Yang
Speaker
Kaibo Hu
Time
Monday, August 26, 2024 2:00 PM - 3:00 PM
Venue
A3-1-301
Online
Zoom 537 192 5549 (BIMSA)
Abstract
Finite Element Exterior Calculus (FEEC) provides a cohomology framework for structure-preserving discretisation of a large class of PDEs. In FEEC, de Rham complexes for problems involving differential forms have been extensively discussed. A canonical construction of finite elements exists, which has a discrete topological interpretation and can be generalized to other discrete structures, e.g., graph cohomology.

There has been significant interest in extending FEEC to tensor-valued problems with applications in continuum mechanics, differential geometry and general relativity etc. In this talk, we first review the de Rham sequences and their canonical discretisation with Whitney forms. Then we provide an overview of some efforts towards Finite Element Tensor Calculus. On the continuous level, we characterise algebraic and differential structures of tensors using the Bernstein-Gelfand-Gelfand (BGG) machinery. On the discrete level, we discuss analogies of the Whitney forms. A special case is Christiansen’s finite element interpretation of Regge calculus, a discrete geometric scheme for metric and curvature. We present a correspondence between algebra (BGG sequences), continuum mechanics (microstructure), Riemann-Cartan geometry (curvature and torsion) and discretization (de Rham’s currents).
Beijing Institute of Mathematical Sciences and Applications
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