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Implement magnetostatic micromagnetics solver option #99

@prkkumar

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@prkkumar

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:

  1. 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.

  2. From phi, H_dipolar can be calculated using H_dipolar = -grad(phi).

  3. Compute H_eff = H_dipolar + H_bias + H_exchange + H_anisotropy + ...

  4. Solve LLG equation.

For first order accurate scheme, we could use H_dipolar computed from phi 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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