hbeLabs.com

Note: This begins [with DS] January 1, 2017.
Note: This resumes with NS January 30, 2019 (continues)
Note: This starts with DA February 4, 2019 (continues)
Note: This starts with NA February 26, 2019


100-digit eigenvalues - the regular pentagon

Unit-edged Regular Pentagon, both Dirichlet and Neumann boundary conditions
Bob Jones
Winter 2017

This work is a numerical refinement of the initial GSVD sweep results.

The numbers on this page are the values of $\lambda$ to solutions of the Helmholtz problem $$ (\Delta+\lambda)\Psi(\mathbf{r}) = 0 \qquad\mathbf{r}\in\Omega , \qquad \mbox{D: }\Psi(\mathbf{r})=0\quad \mbox{or}\quad\mbox{N: } \frac{\partial\Psi}{\partial n}(\mathbf{r})=0 \qquad \mathbf{r}\in\partial\,\Omega $$ inside $\Omega$, the unit-edged regular pentagon, subject to either Dirichlet D or Neumann N boundary conditions on the pentagon's boundary $\partial\,\Omega$, where $n$ is the outward-pointing unit normal vector.


DA eigenvalues
$\#(787,736) = 10642 =\mbox{tally}$

$\mathrm{d}(\lambda)=N_w(\lambda)-\#(\lambda)$

cumsum($\mathrm{d}(\lambda))$