# Full Wave - Time

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

Outputs of the solution are:
• 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.

## Theory and Basics

### Formulations

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

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

#### a-v-Formulation

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

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

Magnetodynamic  weak  a-v-formulation with full wave extension:
(9)            (µ-1 rot a, rot a’ )Ω
+ (σ δt aa’ ) Ωc
+ (σ grad v, a’ ) Ωc
+ (σ δt a, grad v’ ) Ωc

+ (σ grad v, v’ ) Ωc

+ (ε δ2t aa’ ) Ω
+ (ε δt grad v, a’ ) Ω
+ (ε δ2t a, grad v’ ) Ω