# enorm#

EQ = enorm {Galerkin_wt} ENORM {Interpol_fnc} <float1> <float2>


## Description / Usage#

This card provides information for solving a “dependency” equation for the norm of the electric field. Definitions of the input parameters are defined below. Note that <float1> and <float2> define the constant multipliers in front of each type of term in the equation. The Galerkin weight and the interpolation function must be the same for the code to work properly.

 enorm Name of the equation to be solved. {Galerkin_wt} Two-character value that defines the type of weighting function for this equation, where: P0-Piecewise constant P1-Piecewise linear Q1-Linear Q2-Quadratic ENORM Name of the variable associated with this equation. {Interpol_fnc} Two-character value that defines the interpolation function used to represent the variable ENORM, where: P0-Piecewise constant P1-Piecewise linear Q1-Linear Q2-Quadratic Multiplier on advection term. Multiplier on source term.

Note: These multipliers are intended to provide a means of activating or deactivating terms of an equation, and hence should be set to zero or one. If a multiplier is zero, the section of code that evaluates the corresponding term will be skipped. See below for important information regarding this.

## Examples#

The following is a sample card that uses quadratic continuous interpolation for the enorm equation and turns on all the term multipliers (the usual usage):

EQ = enorm Q2 ENORM Q2 1.0 1.0


## Technical Discussion#

This equation allows the user to use the variable ENORM, the norm of the electric field, which is equal to $$\mid$$ $$\underline{E}$$ $$\mid$$, or $$\mid$$ $$\underline \Delta$$ V $$\mid$$, with V being the voltage potential. As such, the VOLTAGE equation must be present. We refer to this as a “dependent” equation or “auxiliary” equation because, although it’s value can technically be derived from the V variable directly, we would lose derivative information by doing so. This equation is introduced solely so one can access higher derivatives of V than its interpolation would normally allow. For example, V if were interpolated with a linear basis, then $$\underline \Delta$$ V would have a constant interpolant. If we wanted access to $$\underline \Delta$$ ($$\underline \Delta$$ V) , it would be zero! (In reality, we would use bilinear or trilinear basis functions, so this isn’t precisely true but it expresses the essential problem.) By introducing this primitive variable, we can retrieve useful values for $$\underline \Delta`_{enorm}$$.

The two term multipliers refer to the multiple on the assembled value of enorm (stored in the “advection” term–it has nothing to do with advection), and the multiple on the assembled value derived from the voltage equation (stored in the “source” term–again the name of the term is somewhat artificial).

No References.