Examples

Example Input file

This example simulates a rectangular VO₂ device, supplied with a direct voltage through a series resistor. The input file is written in xml form. Below is an example of the input file.

<?xml version="1.0"?>
<input>
 <external>
  <temperature unit='K'>300.1</temperature>
  <voltage unit='V'>5.6</voltage>
  <resistor unit='Ohm'>2.5e5</resistor>
  <capacitor unit='nF'>0.0</capacitor>
  <heatdiss unit='W/m^2K'>3e6</heatdiss>
  <Lx unit='nm' mesh='100'>100.0</Lx>
  <Ly unit='nm' mesh='40'>40.0</Ly>
  <Lz unit='nm'>20.0</Lz>
 </external>
 <time>
  <endtime unit='ns'>2e3</endtime>
  <savemethod>auto</savemethod>
  <saveperiod>20</saveperiod>
 </time>
 <initialization>
  <temperature unit='K'>300.0</temperature>
  <SOP>1.119</SOP>
  <EOP>-1.293</EOP>
  <Tcvariance method='nucleus1'>
   <Tcshift unit='K'>-5.0</Tcshift>
   <radius unit='nm'>3.0</radius>
  </Tcvariance>
 </initialization>
 <solverparameters>
  <Newtonabsolutetolerance>1e-5</Newtonabsolutetolerance>
  <Newtonrelativetolerance>1e-3</Newtonrelativetolerance>
  <Newtonmaxiteration>15</Newtonmaxiteration>
  <timesteptolerance>1e-2</timesteptolerance>
  <directsolver>pastix</directsolver>
  <loglevel>INFO</loglevel>
 </solverparameters>
</input>

Almost all the parameters are self-explanatory. The units are fixed and serve only to remind the user of the corresponding parameter’s unit. The external section defines external parameters:

Name	Explanation
temperature	Ambient temperature
voltage	Direct voltage applied
resistor	Resistance of the series resistor
capacitor	The capacitance representing the parasitic capacitance or the external capacitor parallelly connected with the series resistor
heatdiss	Heat transfer coefficient from the device to the environment
Lx	Width of the device
Ly	Length of the device, along the electric field
Lz	Thickness of the device

The time section defines the parameters related to the time:

Name	Explanation
endtime	Simulation end time; beginning time is zero
savemethod	Method of saving time-dependent solutions, used with saveperiod parameter. auto means to save every saveperiod-step solution; fixed means to save every saveperiod-nanosecond solution
saveperiod	See savemethod

The initialization section defines parameters for initialization:

Name	Explanation
temperature	Initial temperature of the device
SOP	Initial value for the structural order parameter
EOP	Initial value for the electronic order parameter
Tcvariance	method: how to set up a nucleus of the high-temperature phase. nucleus1 means to set up a semicircle with a radius of radius and a transition temperature shift of Tcshift, located at the midpoint of the \(y = 0\) edge

The solverparameters section defines the parameters for both the Newton’s iteration solver (for nonlinear differential equations) and the linear solver (for solving linear equations in each iteration of the Newton’s method):

Name	Explanation
Newtonabsolutetolerance	Absolute tolerance for the Newton iteration
Newtonrelativetolerance	Relative tolerance for the Newton iteration. Meeting either the absolute tolerance or the relative tolerance is considered converged
Newtonmaxiteration	Limit of the iteration times for the Newton’s method
timesteptolerance	Relative tolerance for the adaptive time stepping error
directsolver	Which direct solver to use for solving the linear problem
loglevel	Log level; see FEniCS manual