&CELL: FIELD-MAP: FILES: contents

ELECTRIC-FIELD

Some finite element programs output maps of the electric field, most do not.

One reason is that the electric field is discontinuous across element boundaries. As a result, a node will typically have as many different electric field values associated with it, as there are elements of which the node is part. Potentials in contrast are unique.

Another reason is that the shape function method enables one to compute the electric field from the potential without need to take numerical derivatives. One does need the Jacobian of the coordinate transformation, but this is anyhow needed to compute the local isoparametric coordinates.

In other words, there is no significant gain in CPU time, and a major saving in memory, if one computes the electric field as needed, using the potentials.

The first finite element interfaces developed for Garfield were for programs that did output the electric field maps - and Garfield still allocates memory to store the electric field maps. All interfaces developed later arrange for the electric field to be computed from the potential map and it is expected that the stored electric field map will disappear in the foreseeable future.

See also the COMPUTE-ELECTRIC-FIELD and INTERPOLATE-ELECTRIC-FIELD options.

D-FIELD

MATERIAL

MESH

MODEL

BACKGROUND

POTENTIAL

The potential, even though not used for the simulations of physics processes, plays nevertheless a key role when the field calculations are performed using the finite element method: the primary quantity computed by these programs is the potential, and the electric field is computed (by Garfield, in many cases) from the potential.

WEIGHTING-FIELD

Weighting fields form the basis of signal calculations. Induced currents are proportional to the charge Q of the moving particle as well as its velocity v. The current not only depends on the magnitude of the velocity but also on the direction of motion: a charged particle moving parallel with the plates of a capacitor doesn't induce (net) current in the capacitor plates while a charged particle moving perpendicular to the plates will induce a current.

Since the current is a scalar and the velocity a vector, an intuitively plausible ansatz for the current reads:

I = factor Q Ew.v

where Ew is a vectorial quantity called "weighting field". The formula can be derived using Green reciprocity and the factor turns out to be equal to -1. Such a calculation also shows that the weighting field Ew is obtained by setting the potential of all conductors to 0, except for the conductor (or set of conductors) that is read out. The potential of these conductors is to be set to 1.

Weighting fields resemble ordinary electric fields, and finite element programs do not distinguish them from electric fields. There are differences, though. For instance, as can be seen from the above formula, the unit of the weighting field is 1/cm, not V/cm.

Garfield stores only one mesh at the time and uses this mesh both for the ordinary field and for the weighting field. Care needs to be taken therefore that no mesh refinements occur between solving for the 2 types of field.

Finite element programs such as ANSYS output the weighting potential instead of the weighting field - Garfield computes the gradient internally.

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Formatted on 21/01/18 at 16:55.