Dr. Kathryn Trapp, 25 September, 2006
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Discrete Div-Curl Systems
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Abstract:
Div-curl systems are an important type of partial differential equation
that arise in fluid dynamics and electro- and magnetostatics. On
arbitrary domains (an airplane, say, as opposed to a sphere) it is rare
to have an analytic solution. Instead one uses a numerical method to
get an approximate solution. This talk will describe a broad class of
methods for solving these systems on triangular meshes. These
discretization methods rely on a discrete vector calculus structure
(think Stokes' Theorem on triangles) to preserve the underlying
physical properties in the equations and to prevent the occurrence of
spurious solutions. This talk should be accessible to students who have
taken multivariable calculus and linear algebra.
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Biographical sketch: Kathryn Trapp received her PhD in mathematics from
Carnegie Mellon University with a focus in numerical methods for
solving partial differential equations. She is currently Assistant
Professor of Mathematics at University of Richmond and consults at
Sandia National Laboratories.
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