Cactus Code Thorn Maxwell Author(s) : Erik Schnetter schnetter@gmail.com David Radice dradice@astro.princeton.edu, Maintainer(s): Erik Schnetter schnetter@gmail.com Licence : LGPL
- Purpose
Solve the Maxwell equations
- Formulation (see https://en.wikipedia.org/wiki/Maxwell%27s_equations)
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
- 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