nonsymmetric dynamics

Epetra_CrsMatrix TMatrix(...);
Epetra_CrsMatrix KnMatrix(...);
// Fill Matrices Here
// Build Maxwell Preconditioner
ML_Epetra::MultiLevelPreconditioner(CurlCurlMatrix, TMatrix, KnMatrix);
7.5 Solver #2: RefMaxwell
The RefMaxwell solver is accessed through the ML Epetra::RefMaxwellPreconditioner
class, which can be found in the directory ml/src/RefMaxwell. This preconditioner handles
the range and null space of the curl operator with a dedicated MultiLevelPreconditioner
object for each and has demonstrated excellent parallel scalability in practice. The solver
algorithm is detailed in [3]
7.5.1 Operators that the user must supply
The user must provide four matrices:
1. the first-order edge element matrix K (e) .
2. the discrete gradient matrix T .
3. the inverse of the (lumped) nodal mass matrix M 0 .
4. the edge mass matrix M 1 .
The matrices K (e) and T are identical to the matrices used in Maxwell (described in
Section 7.4). The matrix M 0 is used for the algebraic gauging of the edge space and should
include appropriate factors for the permeability (µ). The matrix M 1 is used only for the
edge space, meaning that it does not include the conductivity (σ).
7.5.2 Coarse nullspaces
RefMaxwell will automatically calculate the nullspace for the coarse edge problem from the
discrete gradient matrix T and nodal coordinates. For periodic problems, however, this
calculation will not be correct (since the nodes on the periodic boundary are really in two
places at the same time). In this case, the user can specify nullspace options (using the
standard syntax) as part of refmaxwell: 11list.
7.5.3 Smoother options
Unlike the Maxwell solver, it is not particularly advantageous to use the so-called Hiptmair
hybrid smoother with RefMaxwell. A more traditional smoother, such as Chebyshev (in
parallel) or Gauss-Seidel (in serial) should be used.
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