Association between Equations, Variables and Boundary Conditions

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Association between Equations, Variables and Boundary Conditions

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In problems with a single variable, there is no ambiguity about the assignment of boundary conditions to the equations.

In problems with more than one variable, FlexPDE requires that equations be explicitly associated with variables by tagging each equation with a variable name.  This process also allows optimal ordering of the equations in the coupling matrix.



U:   div(k*grad(u))+u*dx(u)= 0        { associates this equation with the variable U }



Boundary conditions are defined in the BOUNDARIES section, and are associated with equations by use of the variable name, which selects an equation through the association tag. VALUE(U)=0, for example, will cause the nodal equations for the equation tagged U: to be replaced by the equation u=0 along the selected boundary .


Natural boundary conditions must be written with a sign corresponding to the sign of the generating terms when they are moved to the left side of the equal sign. We suggest that all second-order terms should be written on the left of the equal sign, to avoid confusion regarding the sign of the applied natural boundary condition.