For more information about this meeting, contact Becky Halpenny.
|Title:||"Nonlocal Exterior Calculus on Riemannian Manifolds"|
|Seminar:||Ph.D. Thesis Defense|
|Speaker:||Thinh Le, Adviser: Qiang Du, Penn State|
|Exterior calculus and diﬀerential forms are basic mathematical concepts that have been around for centuries. Extensions of these concepts have also been made over the years such as the discrete exterior calculus and the ﬁnite element exterior calculus. In this work, motivated by the recent studies of nonlocal vector calculus we develop a nonlocal exterior calculus framework on Riemannian manifolds which mimics many properties of the standard (local/smooth) exterior calculus. However the key diﬀerence is that nonlocal interactions (functions, operators, ﬁelds,...) are not required to be smooth. Also any point/particle can interact directly with any other point/particle in the studied domain (at least in principle). Just as in the standard context, we introduce all necessary elements of exterior calculus such as forms, vector ﬁelds, exterior derivatives, etc. We point out the relationships between these elements with the known ones in (local) exterior calculus, discrete exterior calculus, etc. We also introduce nonlocal Hodge Theory and its connections with existing works.|
Room Reservation Information
|Date:||07 / 06 / 2012|
|Time:||10:00am - 02:00pm|