High-Frequency - Time-domain

The Full Wave Solver takes into account all terms of Maxwell's equations. Due to this the wavelength can be smaller than the analyzed part dimensions and even very high frequencies are allowed. In the time domain results are the electric and magnetic field for every time step.

Features

• Plot: Magnetic Fluxdensity, Magnetic Fieldstrength, Electric Fieldstrength, Current Density, Eddy Current Losses Density, Vectorpotential, Nodal Force - virtual, Nodal Moment - virtual, Forcedensity - virtual, Lorentz Force, Poynting Vector. 
• Table: Total Force - virtual, Total Moment - virtual, Total Lorentz Force, Electrode Voltage, Electrode Current, Voltage on Circuits, Current on Circuits, Power on Circuits, Eddy Current Losses.
• 4D Fields:  Force - virtual NodeID Table, Forcedensity - virtual XYZ Table, Lorentz Force NodeID Table.
• Coupled Thermal: Temperature.
• Coupled Structural: Structural Deformation.

Examples

Wind Turbine Tower Lightning Strikes	Waveguide Combiner

Theory and Basics

Formulations

The basis equations:
(1)        rot h = j + δ_t d
(2)        rot e = -δ_t b
(3)        div b = 0

Constitutive relations:
(4)        b = µ h
(5)        d = ε e
(6)        j = σ e

The following a-v-formulation is used for 3D

Magnetic vectorpotential a, 
electric scalar potential v:             
(7)        b = rot a
(8)      e = -δ_t a – grad v

Magnetodynamic  weak  a-v-formulation with full wave extension:
(9)            (µ^-1 rot a, rot a’ )_Ω
                + (σ δ_t a, a’ ) _Ωc
                + (σ grad v, a’ ) _Ωc 
                + (σ δ_t a, grad v’ ) _Ωc
                    + (σ grad v, v’ ) _Ωc

                + (ε δ²_t a, a’ ) _Ω 
                + (ε δ_t grad v, a’ ) _Ω 
                + (ε δ²_t a, grad v’ ) _Ω 
                + (ε δ_t grad v, grad v’ ) _Ω 

                      = 0

+Silver-Müller radiaton condition at infinity (outgoing waves)

The equation can be solved in the time or frequency domain.