Numerical Analysis and Scientific Computing

Faculty involved

Peter Alfeld, Elena Cherkaev, Yekaterina Epshteyn, Aaron Fogelson, Fernando Guevara Vasquez, Christel Hohenegger, Akil Narayan, Braxton Osting, Jingyi Zhu.

Our group focuses on analysis and implementation of

With applications to:

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A numerical simulation of 2D Saint-Venant system of Shallow Water equations. (from “Well-Balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System”, S. Bryson, Y. Epshteyn, A. Kurganov and G. Petrova)

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Cloaking with active sources for the Laplace equation in 2D. (from “Active exterior cloaking for the 2D Laplace and Helmholtz Equations”, F. Guevara Vasquez, G. W. Milton, D. Onofrei)

Homer surface

Let $\lambda_1(M,g)$ denote the first nontrivial Laplace-Beltrami eigenvalue of a closed Riemannian surface. The first conformal eigenvalue is defined by the eigenvalue optimization problem of maximizing $\lambda_1(M,g)$ as $g$ varies within a conformal class $[g_0]$ of fixed volume, $\text{vol}(M,g) = 1$. Plotted here is the conformal factor which attains the first conformal eigenvalue for a “Homer Simpson surface”. (from “Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces”, C.-Y. Kao, R. Lai, and B. Osting)

Webmaster: Fernando Guevara Vasquez. (Created by Yekaterina Epshteyn and FGV)