10. Electrostatic Solver

The Electrostatic solver required for CMUTS is applied in the same way that the electromechanical solver for piezoelectric materials is done in OnScale. It is controlled through the piez command.

1. Be sure to use piez wndo to cover all the electrodes and areas with strong electric fields
2. Electrodes are defined in the same way as Piezoelectric models
3. Must be completely in the Large Deformation region
4. Solver recalculates matrix at every timestep and is therefore costly. It is advisable to make this region as small as is possible
5. Use the esta command to invoke the electrostatic solver
6. Must be used with the Iterative Solver option slvr cgds

As with piezoelectric models, a damping resistor can be applied to the electrodes to help with ring down times, especially for in air models. The resistor value should be based on an approximate value of the capacitance of the device, in order to provide the real part of the reactance.

```/* Create damping resistor to help ring down faster.
symb cval = 70.e-9 /* C = Er*Eo*(A/d)
symb rval = 1. / \$twopi / \$freqint / \$cval /* value of resistor
circ
defn damp
elem rest sers \$rval
end
/* Set electrostatic window, electrodes and solver
piez
/* Electrostatic window
wndo \$i1 \$i3 \$j2 \$j4
/* Top electrode
defn ctop
node \$i1 \$i3 \$j4 \$j4
/* Bottom electrode - creating 'hoop' electrode (8 elements = 800um = isolated island)
defn cbot
node \$i1+8 \$i2-1 \$j2 \$j2
/* Apply voltage boundary conditions
bc cbot grnd
bc ctop volt func
/* Connect damping resistor to top electrode - not necessary but can help ring down.
/* Solver options - must use these for electrostatic analysis
esta
end```