integratedSurfaceFieldSquared

integratedSurfaceFieldSquared

Works with VSimBase, VSimEM, VSimPD, and VSimMD licenses.

Integrates the magnitude squared of a field over a grid boundary, or part of a boundary, and stores the result in a history. Units recorded by this history are dependent on the units used for the field for which the history is taken. That is, when you point this history at an electric field, for example, rather than a magnetic field or another arbitrary user-defined field, the units will be registered in the same units as the selected field squared times meters squared.

One common use for integratedSurfaceFieldSquared is to compute the power dissipated due to heating the boundary of a device. In the example that follows, the magnitude of the magnetic field (H) is squared and integrated over the surface of the gridBoundary. Since Vorpal technically uses the magnetic induction (B) the coefficient parameter is used to convert the B field to the H field. When the surface integral of the H field squared is multiplied by the resistance at the surface of the conductor, the result is the total power loss due to surface resistance. Therefore, provided that you have an estimate of the resistance in the conductor, you can use this code block to compute the total power loss due to ohmic heating at the boundary.

integratedSurfaceFieldSquared Parameters

alpha (real, default value = 1.0)

Defines the offset distance from the boundary where the field will be measured. Interpolation on the boundary is effected by values in the boundary itself so a more accurate value for the field is achieved by computing the field slightly off the surface. The normal distance from the surface where the field is measured is given by alpha times the cell hypotenuse.

coefficient (real, optional, default = 1.0)

Coefficient by which the surface integral can be multiplied.

field (string, required)

Name of the field whose magnitude is computed at each surface point.

gridBoundary (string, required)

Name of the gridBoundary object over which the integral is performed.

lowerBounds (integer vector)

Lower bounds of the region for which the magnitude squared calculation is to be integrated.

upperBounds (integer vector)

Upper bounds of the region for which the magnitude squared calculation is to be integrated.

integratedSurfaceFieldSquared History Example

<History integralOfMagFieldSquared>
  kind = integratedSurfaceFieldSquared
  alpha = 1.0
  coefficient = $1/(MU0*MU0)$ # Converts B to H
  gridBoundary = cylindricalCav
  field = multiField.magField
</History>