Cactus Code Thorn Maxwell
Author(s)    : Erik Schnetter 
               David Radice ,
Maintainer(s): Erik Schnetter 
Licence      : LGPL
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1. Purpose

Solve the Maxwell equations



2. Formulation (see )

Electric potential: phi
Magnetic potential: A
Lorenz gauge:       div A = - dt phi

Electric field: E = - grad phi - dt A
Electric flux:  D = *E + P (polarization)
Magnetic flux:  B = curl A
Magnetic field: H = *B - M (magnetization)

Homogeneous electric equation: curl E + dt B = 0
Homogeneous magnetic equation: div B = 0

Inhomogeneous electric equation: div D = rho
Inhomogeneous magnetic equation: curl H - dt E = J

Charge density:  rho
Current density: J

Charge conservation: dt rho + div J = 0



State vector:        phi
                     A
                     D
                     B
Auxiliaries:         E = *D
                     H = *B
Equations of motion: dt phi = - div A
                     dt A   = - grad phi - E
                     dt D   = curl H - J
                     dt B   = - curl E
Constraints:         B = curl A
                     div D = rho
                     div B = 0



3. Discretization

phi: not present
A:   not present
D:   faces of primal grid
B:   faces of primal grid
E:   edges of primal grid (calculated via lossy Hodge dual)
H:   edges of primal grid (calculated via lossy Hodge dual)
rho: cells of primal grid
J:   faces of primal grid
div D: cells of primal grid
div B: cells of primal grid