12.1 Define Solution Staggers (Optional)

The procedure allows the use of a multistagger solution strategy in which the full system of coupled equations defined in the problem domain is partitioned into smaller subsystems of equations. Each subsystem is then solved separately assuming that the unknown variables of the other subsystems are temporarily frozen. The equation subsystems are referred to as "staggers," and the approach amounts to a partial decoupling of the full system of coupled equations. Each stagger is assigned its own time-stepping parameters, nonlinear iteration procedure, linear equation solver and/or eigen solver. In each stagger, the active variables are solved while all the other variables belonging to the other staggers are held fixed. In turn, after update of the solution variables of the current stagger, they are held fixed when solving for the variables of the subsequent staggers. The staggers are solved sequentially and repeatedly in a predetermined sequence until they all have converged to a self consistent set of solution variables. The iterative procedure is handled by the Stagger_control command. The procedure is equivalent to solving the coupled system (see e.g. [1-5]). Solution staggers may also be used to selectively solve for the equations defined in various parts of the mesh. Element groups belonging to the same region cannot be assigned to the same solution stagger.

12.1.1 Define Staggers

DEFINE_STAGGER

DEFINE_STAGGER name = "<string>", etc...

Set up solution staggers to use for solving the equations defined in the problem.

Note	Variable Name	Type	Default	Description
	Name	string	[none]	Stagger name
				Name must be enclosed in quotation marks.
(1)	Element_group(s)	string	[none]	Element groups belonging to the stagger.
				Name(s) must be enclosed in quotation marks
	Variable	list	[all]	Active variable selection for the stagger:
	all			All degrees of freedom Solid displacement Solid displacement and rotation Fluid velocity Fluid velocity and pressure Temperature Potential Electric potential Pressure Scalar transport Level set Stream function Coupled porous continuum (hyperbolic) Coupled continuum (parabolic) Coupled thermo-solid continuum ALE mesh motion
	solid_displacement solid_displacement_and_rotation fluid_velocity fluid_velocity_and_pressure temperature potential electric_potential pressure scalar_transport level_set stream_fct solid_displacement_and_fluid_velocity solid_displacement_and_fluid_pressure solid_displacement_and_temperature mesh_motion

(cont’d)

(cont’d)

Note	Variable Name	Type	Default	Description
	Activation_time	real	[0.0]	Time at which stagger becomes active
	Deactivation_time	real	[0.0]	Time at which stagger becomes inactive (only active if deactivation_time > activation_time)
	External_loads	string	[on]	External loads option
	on / off
	Nodal_loads	string	[on]	Nodal loads option
	on / off
	Surface_loads	string	[on]	Surface loads option
	on / off
	Heat_loads	string	[on]	Heat loads option
	on / off
	Multi_flow_initialize	string	[off]	Multi-flow initialization (viz., p2 = p1)
	on / off
(2)	Time_integration	command	[none]	Time integration parameters used in the stagger
	Nonlinear_iterations	command	[none]	Nonlinear iterations used in the stagger
	Linear_solver	command	[none]	Linear solver used in the stagger
	Eigen_solver	command	[none]	Eigen solver used in the stagger

EXAMPLE

Define_stagger / # define a solution stagger

name = "stagger1" / # set name

element_group(s) = / # include element groups 1 and 2
"Group1" , "Group2" /

time_integration / # time integration parameters, etc...

equation_type = ... , etc...

Notes/

(1) List all element group names or numbers belonging to the solution stagger. Element groups belonging to the same region cannot be assigned to the same solution stagger.

(2) The requested analysis parameters may be entered directly without use of the main commands keywords.

12.1.2 Staggers Control

STAGGER_CONTROL

STAGGER_CONTROL name = "<string>", etc...

The staggers are solved sequentially and repeatedly in a predetermined sequence until they all have converged to a self consistent set of solution variables. The iterative procedure is handled by the stagger_control command. When solution staggers are used to selectively solve for the equations defined in various parts of the mesh, then an interface between the various physical solution domains will be defined.

Note Variable Name Type Default Description

Name string [none] Stagger name

Name must be enclosed in quotation

marks

Balance_of_mass string [off] Balance of mass option

on / off

Coupling string [on] Coupling option

on / off

Interface string [on] Interface option

on / off

Solver_name string [*] Solver name

CG_Mf / CG_EBE

Max_number_of_iterations integer [0] Maximum number of iterations

Min_number_of_iterations integer [0] Minimum number of iterations

Convergence_check list [on] Convergence check

on / off

Convergence_tol_sol real [1.E-3] Convergence tolerance for solution

0.0

Convergence_tol_mass real [0.0] Convergence tolerance for mass (in %)

0.0

EXAMPLE

Stagger_control /

max_number_of_iterations = 5 /

convergence_check = on

References / Bibliography

1. Farhat, Charbal, K.C. Park and Yves DuBois-Pelerin, "An Unconditionally Stable Staggered Algorithm for Transient Finite Element Analysis of Coupled Thermoelastic Problems," Comp. Meth. Appl. Mech. Eng., 85, (1991), 349-365.

2. Felippa, C.A. and K.C. Park, "Staggered transient analysis procedures for coupled mechanics problems: formulation," Comp. Meth. Appl. Mech. Eng., 24, (1980), 61-111.

3. Park, K.C.,"Partitioned transient analysis procedures for coupled field problems: stability analysis", J.Appl. Mech., 47, (1980), 370-376.

4. Park, K.C. and C.A. Felippa,"Partitioned transient analysis procedures for coupled field problems: accuracy analysis", J. Appl. Mech., 47, (1980), 919-926.

5. Prevost, J. H., "Partitioned Solution Procedure for Simultaneous Integration of Coupled-Field Problems," Comm. Num. Meth. Eng., 13, No. 4, (1997), pp. 239-247.

Notes . .