WeakForms

The WeakForms syntax is used to create MFEM MFEMWeakFormBase-derived objects to set up MFEM EquationSystem operators that can be used by downstream solvers and preconditioners. If no WeakForms block has been added to an input file by the user, a default MFEMWeakFormBase-derived object will be added to the system, based on the NumericType (real or complex) used by the MFEMProblem, and whether the Executioner in use is transient or steady state.

Each weak form selects the kernels and boundary conditions that contribute to its equation system through its kernels and bcs parameters, which name blocks in the Kernels and BCs blocks respectively. If either parameter is omitted, all kernels or boundary conditions added in the input file are used, which is the behavior of the default weak form.

[WeakForms<<<{"href": "index.html"}>>>]
  [Darcy]
    type = MFEMWeakForm<<<{"description": "Builds a real-valued MFEM EquationSystem from the kernels and boundary conditions named by this weak form.", "href": "../../source/mfem/weakforms/MFEMWeakForm.html"}>>>
    kernels<<<{"description": "List of kernels to add to the weak form"}>>> = 'VelocityMass PressureGrad VelocityDiv'
    bcs<<<{"description": "List of boundary conditions to add to the weak form"}>>> = 'flux_boundaries'
  []
[]
(test/tests/mfem/weakforms/steady_weakform.i)

Selecting between multiple weak forms

More than one weak form may be added, in which case the equation system built by each is registered under the name of the block that created it. Objects that consume an equation system - the ProblemComposers that build problem operators, and MFEM linear solvers and preconditioners - then select one by name using their weak_form parameter. That parameter may be omitted only when the problem has a single weak form; if it is omitted while several are present, the object cannot infer which system was intended and an error is raised.

commentnote

On a solver, weak_form selects only the equation system that solver configures itself against, such as the system MFEMGeometricMultigridSolver builds its hierarchy from. It does not bind the solver to a particular problem operator: a problem still has a single driver solver, which is used by every problem operator regardless of which equation system that operator solves. In a problem with several weak forms, a solver must be provided a valid weak form name, which it shall use to configure itself if necessary.