Institut für Allgemeine Elektrotechnik, Uni Rostock - Universität ...

Limitations of the Leap-Frog Scheme
2. Modelling of small geometrical details:
Functions of the grid: i) sampling the wave in space and time
ii) map the material distribution to discrete space
Difficulty if ratio of wavelength to geometrical detail is large:
over-sampling
of the wave in space and time
Example : Plane wave of 30 MHz (wavelength ≈ 10 m) incident
on perfect conductor with surface details in
mm-range
Δ x = Δ y = Δz ≈ Δt
≈ ⋅
−12
For 1mm we get 2 10 s from CFL
−8
For a period of 3,3 10 s we would need more
T
≈
than 17,000 time steps per period!
This leads to an enormous computational effort why subgrids or
a
conformal approach are used then.
⋅
Prof. Dr. Ursula van Rienen, Universität Rostock, Fakultät für Informatik und Elektrotechnik (IEF), Institut für Allgemeine Elektrotechnik (IAE)
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