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The GLOBAL VARIABLES section is used to define auxiliary or summary values which are intricately linked to the field variables.  

 

Each GLOBAL VARIABLE takes on a single value over the entire domain, as opposed to the nodal finite element field representing a VARIABLE.  

 

GLOBAL VARIABLES differ from simple DEFINITIONS in that DEFINITIONS are algebraically substituted in place of their references, while GLOBAL VARIABLES represent stored values which are assigned a row and column in the master coupling matrix and are solved simultaneously with the finite element equations.

 

The GLOBAL VARIABLES section must follow immediately after the VARIABLES section.

 

Rules for declaring GLOBAL VARIABLES are the same as for VARIABLES, and a GLOBAL VARIABLE may have a THRESHOLD, and may be declared to be COMPLEX, VECTOR or ARRAY, as with VARIABLES.

 

Each GLOBAL VARIABLE will be associated with an entry in the EQUATIONS section, with rules identical to those for VARIABLES.  

 

GLOBAL VARIABLES do not have boundary conditions.  They may be either steady-state or time-dependent, and may be defined in terms of integrals over the domain, or by point values of other functions.

 

Examples:

Samples | Applications | Control | Control_Steady.pde

Samples | Applications | Control | Control_Transient.pde

 

Note: In previous versions of FlexPDE, Global Variables were referred to as SCALAR VARIABLES.  This usage is still allowed for compatibility, but the newer terminology is preferred.