The Auxiliary-Space Maxwell (AMS) node () is an attribute that handles parameters for linear system solvers/preconditioners that use the auxiliary-space Maxwell solver (AMS). Right-click an Iterative, Krylov Preconditioner, or Coarse Solver node to add an Auxiliary-Space Maxwell (AMS) node.

The AMS solver uses the auxiliary-space Maxwell solver preconditioner from the Lawrence Livermore National Laboratory linear solver/preconditioner library hypre, a software library of high performance preconditioners and solvers (Ref. 6). AMS provides edge finite element discretization of variational curl-curl problem stemming from stationary or time-dependent Maxwell’s equations. The version of AMS available in COMSOL Multiphysics is designed for the lowest-order edge elements. For higher-order discretizations, use it together with the geometric multigrid (GMG) solver with the option Lower element order first and a sufficient number of levels so that AMS can work efficiently as a coarse solver. For details, see Ref. 7.

The Settings window contains the following section:

Enter the Number of iterations of the AMS solver. The default is 2.

In the Variables field, add the applicable dependent variables that use vector elements (such as magnetic scalar potential) and that you want to include in the AMS solver. Use the Delete () and Add () buttons to configure the list of variables.

From the Cycle type list, select one of the available AMS cycle types 1–14 (the default is cycle type 1, a multiplicative solver that should work well in most cases; see Ref. 7 for details). These cycle types are various combinations of smoothing and applications of algebraic multigrid on decomposed problems.

From the Magnetostatics list, select Automatic (the default), On, or Off. The automatic case determines magnetostatics by comparing the maximum row sum of absolute values for the projected matrix TTAT and A. Here T is the discrete gradient matrix; see documentation for SOR Vector. Magnetostatics is deduced if the projected matrix is negligible compared to A. If magnetostatics is deduced or chosen, AMS skips the subspace corrections associated with the projected matrix TTAT.

From the Divergence cleaning list, select Automatic (the default), On, or Off. The automatic case is the same as for the determination of magnetostatics. In the magnetostatic case, AMS should skip corrections associated with TTAT and use divergence cleaning of the right-hand side. You can also manually specify the magnetostatics and divergence cleaning settings. This can be useful if divergence cleaning has already been made or if you suspect that the automatic detection fails.