Fixed-Time Solvers

function solve!(
    Target::FEVector,       # contains initial guess and final solution after solve
    PDE::PDEDescription;
    kwargs)

Solves a given PDE (provided as a PDEDescription) and writes the solution into the FEVector Target (which knows the discrete ansatz spaces).

Keyword arguments:

• anderson_iterations: use Anderson acceleration with this many previous iterates (to hopefully speed up/enable convergence of fixpoint iterations). Default: 0

• subiterations: an array of equation subsets (each an array) that should be solved together in each fixpoint iteration. Default: ''auto''

• showiterationdetails: show details (residuals etc.) of each iteration. Default: true

• anderson_unknowns: an array of unknown numbers that should be included in the Anderson acceleration. Default: [1]

• reltol: reltol for linear solver (if iterative). Default: 1.0e-12

• show_statistics: show some statistics like assembly times. Default: false

• anderson_metric: String that encodes the desired convergence metric for the Anderson acceleration (possible values: ''l2'' or ''L2'' or ''H1''). Default: ''l2''

• skipupdate: matrix update (for the j-th sub-iteration) will be performed each skipupdate[j] iteration; -1 means only in the first iteration. Default: [1]

• linsolver: any AbstractFactorization from LinearSolve.jl (default = UMFPACKFactorization). Default: LinearSolve.UMFPACKFactorization(true, true)

• damping: damp the new iteration with this part of the old iteration (0 = undamped), also a function is allowed with the interface (olditerate, newiterate, fixed_dofs) that returns the new damping value. Default: 0

• time: time at which time-dependent data functions are evaluated or initial time for TimeControlSolver. Default: 0

• parallel_storage: assemble storaged operators in parallel for loop. Default: false

• showsolverconfig: show the complete solver configuration before starting to solve. Default: false

• anderson_damping: Damping factor in Anderson acceleration (1 = undamped). Default: 1

• abstol: abstol for linear solver (if iterative). Default: 1.0e-12

• checknonlinearresidual: check the nonlinear residual in last nonlinear iteration (causes one more reassembly of nonlinear terms). Default: ''auto''

• fixed_penalty: penalty that is used for the values of fixed degrees of freedom (e.g. by Dirichlet boundary data or global constraints). Default: 1.0e60

• target_residual: stop fixpoint iterations if the absolute (nonlinear) residual is smaller than this number. Default: 1.0e-12

• maxiterations: maximal number of nonlinear iterations (TimeControlSolver runs that many in each time step). Default: ''auto''

Depending on the subiterations and detected/configured nonlinearities the whole system is either solved directly in one step or via a fixed-point iteration.