The mass matrix is formed by integrating
the outer product of two sets of basis functions. A mass
matrix can appear in the discretization of an unsteady
partial differential equation (PDE) using a finite element
method (FEM). The accuracy, stability, and performance of
a numerical method is tied to the handling of the mass
matrix. In classical FEM, a common technique is to "lump"
a mass matrix, summing the off-diagonals to the diagonal,
resulting in a diagonal matrix. The simplification results
in a trade-off between increased performance of the method
and reduced accuracy. In this seminar, Dr. Brazell will
discuss his work with mass matrices across four different
topics. The first is lumping techniques for high-order
streamline-upwind-Petrov-Galerkin (SUPG) methods. The
second is psuedo-transient continuation as a globalization
technique for the Newton-Rhapson method for solving
problems using a Discontinuous Galerkin (DG) method. The
third is an explicit DG method with applications in
overset meshing and adaptive mesh refinement. Lastly,
connections between high-order PADE schemes and a
high-order B-spline FEM formulation. Some applications of
these methods will include aerodynamics and wind energy.
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