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Maxwell-LLG solver in ARTEMIS can be computationally expensive in simulations of devices which require evolution of M for a large time due to time-step limit imposed by the CFL condition. In many of these applications dynamics of H field is not important and magnetostatic approximation can be used to reduce Maxwell's equation to a poisson equation. We would then need to solve the Poisson's equation with open boundary conditions together with LLG equation.
This can be accomplished as follows:
Solve Poisson's equation with open boundary condition:
Laplacian(phi) = divergence(M), such that phi = 0 as x -> \infty
where -divergence(M) = rho_M is the magnetic charge density.
From phi, H_dipolar can be calculated using H_dipolar = -grad(phi).
Maxwell-LLG solver in ARTEMIS can be computationally expensive in simulations of devices which require evolution of
M
for a large time due to time-step limit imposed by the CFL condition. In many of these applications dynamics ofH
field is not important and magnetostatic approximation can be used to reduce Maxwell's equation to a poisson equation. We would then need to solve the Poisson's equation with open boundary conditions together with LLG equation.This can be accomplished as follows:
Solve Poisson's equation with open boundary condition:
Laplacian(phi) = divergence(M)
, such thatphi = 0 as x -> \infty
where
-divergence(M) = rho_M
is the magnetic charge density.From
phi
,H_dipolar
can be calculated usingH_dipolar = -grad(phi)
.Compute
H_eff = H_dipolar + H_bias + H_exchange + H_anisotropy + ...
Solve LLG equation.
For first order accurate scheme, we could use
H_dipolar
computed fromphi
at the previous time step.For second order scheme, we would need to iterate between Poisson and LLG to converge.
If we can use Poisson solver with open BC from WarpX, then most of existing infrastructure in ARTEMIS could be used to accomplish this.
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