Least-Squares Methods for Computational Electromagnetics

Eigenmodes of a Fichera Corner

Below are some results for the electrostatic eigenvalue problem

with boundary conditions

in the Fichera corner [-1,1]³ \ [-1,0]³.

Table1: Benchmark results from M. Dauge's site.

relible digits conjectured eigenvalue 1 3.31380523357e+00 1 3.2???e+00 9.106385702998711e-02 2 5.88634994607e+00 3 5.88??e+00 2.886076542374565e-02 3 5.88634994619e+00 3 5.88??e+00 2.886076542256893e-02 4 1.06945143272e+01 4 1.0694e+01 8.743350060814515e-03 5 1.06945143276e+01 4 1.0694e+01 8.743350060160473e-03 6 1.07005804029e+01 2 1.07??e+01 8.733439796514905e-03 7 1.23345495948e+01 3 1.232?e+01 6.572845272636814e-03 8 1.23345495949e+01 3 1.232?e+01 6.572845272530238e-03

Table2: Results on hexahedral mesh with 31841 vertices, 89088 faces and 28672 elements.

1 3.287499015589240e+00 2.630621798076005e-02 3.041826005903042e-01 2.414714575262600e-03 2 5.903261677666660e+00 1.691173159666004e-02 1.693978777500615e-01 4.866872455426552e-04 3 5.903301089741780e+00 1.695114355177996e-02 1.693967468028539e-01 4.878181892869204e-04 4 1.075672540567040e+01 6.221107847039953e-02 9.296509507185623e-02 5.407874212496055e-04 5 1.075675199032270e+01 6.223766272269948e-02 9.296486531432992e-02 5.410171752785742e-04 6 1.080382492695220e+01 1.032445240522009e-01 9.255981161868973e-02 8.930631178046267e-04 7 1.245522774951550e+01 1.206781547154989e-01 8.028757242426975e-02 7.855135700157723e-04 8 1.245669014178740e+01 1.221405468873993e-01 8.027814681248151e-02 7.949391811467310e-04 9 1.346559488811500e+01   7.426333617704627e-02   10 1.353063898365770e+01   7.390633961986566e-02

Table3: Results on tetrahedral mesh with 28489 vertices, 323072 faces and 159744 elements.

1 3.234319711779175e+00 7.948552179082524e-02 3.091840291354214e-01 7.416143120379803e-03 2 5.882672524227550e+00 3.677421842450457e-03 1.699907645515776e-01 1.061995559734075e-04 3 5.883705328962450e+00 2.644617227550050e-03 1.699609249765645e-01 7.635998442367953e-05 4 1.067894347106443e+01 1.557085613556985e-02 9.364222244546860e-02 1.363399523627712e-04 5 1.068323659414085e+01 1.127773345915095e-02 9.360459175344328e-02 9.870926383478973e-05 6 1.069449926493125e+01 6.081137968749317e-03 9.350601418797970e-02 5.313945148534283e-05 7 1.236526854633587e+01 3.071895153586901e-02 8.087167668479989e-02 2.014093094856312e-04 8 1.237226331699513e+01 3.771372209513046e-02 8.082595515295510e-02 2.471308406731404e-04 9 1.342793827676227e+01   7.447159641257443e-02   10 1.347486653120520e+01   7.421223784919816e-02