add iterative solving to the amrex time integrator

[jackieyao0114]

We used iteration to realize semi-implicit solving of the LLG equation in Artemis (Link to the paper), which enables a larger time step dt compared to the explicit solver, such as RungeKutta.

In MagneX, TimeIntegratorOption = 3 enables us to solve for M in an iterative way exactly the same as Artemis, and TimeIntegratorOption = 2 chooses a predictor-corrector algorithm, which realized a similar semi-implicit numerical strategy.

However, when TimeIntegratorOption = 4, the explicit solvers are selected, namely

 integration.type can take on the following string or int values: (without the quotation marks)
"ForwardEuler" or "0" = Native Forward Euler Integrator
"RungeKutta" or "1"   = Native Explicit Runge Kutta
"SUNDIALS" or "2"     = SUNDIALS ARKODE Integrator

Even though some of these explicit are higher order accurate, e.g. RK4, their explicit nature makes the dt requirement more stringent.

What would be a more advanced strategy is to combine the iteration and higher-order time integrator. To do so, we need to find a way to add iteration on top of the AMReX time integrators.