Ahh, finally, an example with the appropriate symmetry... Learned how to create some interesting 3D meshes. This example is essentially the same as the previous, but with a different global mesh. I also changed the numerical method to something symplectic, and of higher order: Störmer-Verlet timestepping. The energy that is preserved here (or, only close to being preserved, actually—symplectic integrators do not exactly preserve energy, but do a lot better than more generic methods) is the field energy, 1/2(E, D) + 1/2 (B, H). Or, the energy that would be (close to) preserved, if it weren't for this oscillation being a driven one, caused by currents in the wire, rather than natural oscillations given by some initial, non-equilibrium configuration (as in the vibrating drum post). It's time for a different example, perhaps the analogue of a cavity resonator.
Monday, December 10, 2012
A non-cubical example!
Ahh, finally, an example with the appropriate symmetry... Learned how to create some interesting 3D meshes. This example is essentially the same as the previous, but with a different global mesh. I also changed the numerical method to something symplectic, and of higher order: Störmer-Verlet timestepping. The energy that is preserved here (or, only close to being preserved, actually—symplectic integrators do not exactly preserve energy, but do a lot better than more generic methods) is the field energy, 1/2(E, D) + 1/2 (B, H). Or, the energy that would be (close to) preserved, if it weren't for this oscillation being a driven one, caused by currents in the wire, rather than natural oscillations given by some initial, non-equilibrium configuration (as in the vibrating drum post). It's time for a different example, perhaps the analogue of a cavity resonator.
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