# Fascinating theoretical challenge: Simulating EM eigenmodes in a tetrahedron **URL:** \ **Category:** General Discussion\ **Created:** [August 30, 2025, 9:51am UTC](https://community.freefem.org/t/fascinating-theoretical-challenge-simulating-em-eigenmodes-in-a-tetrahedron/4049 "2025-08-30T09:51:25Z")\ **Posts on this page:** 1\ **Showing post:** 10
**Author:** ![fb77](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/fb77/32/3796_2.png) [@fb77](https://community.freefem.org/u/fb77)\ **Post date:** [September 5, 2025, 10:42am UTC](https://community.freefem.org/t/fascinating-theoretical-challenge-simulating-em-eigenmodes-in-a-tetrahedron/4049/10 "2025-09-05T10:42:59Z")
Dear Frodo, I have written a version with Laplacian and boundary condition E\times n =0 ![laplace-ev](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/d/d478cc676352810e0965e3fd2ada9f8ea4102b2f.png) [EMtet.edp](https://community.freefem.org/uploads/short-url/AobXDpCZsR0nsGFhn5FxXqcv0sg.edp) (7.8 KB) I get for the 10 first eigenvalues 78.88776433 79.02651853 79.02651853 153.9973688 163.2695866 163.7718604 163.7718604 174.020952 175.1561748 197.8465549 It seems that there is a first eigenvalue with triple multiplicity, then an eigenvalue 154 (your fundamental mode ?), then again an eigenvalue with triple multiplicity. You have to run the code EMtet.edp to plot (built-in with medit, but also possible with paraview with file E.pvd). I use SLEPc as eigenvalue solver. About the method: I use a Lagrange multiplier formulation (to avoid large coefficients in the matrix if we use penalty), using that ![curlcurl](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/f/f85d0fe737b21214c7bb2f6d966b9c7c8bfe14aa.png) ![laplace-varf](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/a/a561d24ebfe57e5a4f157b8cdf45dc60aa384a88.png) I fix the value E=0, p=0, phi=0 on all 6 edges. --- _[View the full topic](https://community.freefem.org/t/fascinating-theoretical-challenge-simulating-em-eigenmodes-in-a-tetrahedron/4049)._