4 Electrostatic application: calculating and analyzing fields In this chapter, we will use the mesh file we created to find a field solution. To get started, run EStat from the FPController . Click the 1 tool and choose the Mesh file CoaxialCylinders.MOU . The program determines the defined regions in the mesh and displays the dialog of Fig. 15 . The values shown are appropriate to the solution parameters discussed in the previous chapter. Fill in the fields and click OK , accepting the output file name CoaxialCylinders.EIN ( E Stat IN put). To understand the action of the dialog, choose File/Edit script (EIN) and load the file in the editor. Here is the content: * File:
CoaxialCylinders.EIN Mesh = CoaxialCylinders Geometry = Rect DUnit = 1.0000E+02 ResTarget = 5.0000E-08 MaxCycle = 5000 * Region 1: DIELECTRIC Epsi(1) = 1.0000E+00 * Region 2: INNERELECTRODE Potential(2) = 1.0000E+02 * Region 3: OUTERBOUNDARY Potential(3) = 0.0000E+00 EndFile You’ll recognize many of the entries. The ResTarget and MaxCycle parameters that control the solution accuracy are described in the EStat manual. The default values are fine for this calculation. Exit the editor and click the 2 tool. After you choose CoaxialCylinders.EIN , EStat generates and solves the finite-element equations in less than a second.
Larger meshes will take longer, but generally the run times of practical solutions are less than a minute. The program creates the files CoaxialCylinders.ELS (a diagnostic listing file that you can inspect with an editor) and CoaxialCylinders.EOU (a record of the mesh coordinates and potential values at the nodes). To see the results, press the 3 tool and choose CoaxialCylinders.EOU . You can generate interesting plots in the Analysis menu (Fig. 16 ). For this discussion, let’s concentrate on hard numbers. First, let’s check the absolute accuracy of the solution with a single point calculation. At radius r = 10 . 0 cm, the formulas listed in the previous article give the values:
E r ( r ) = 910 . 23923 (V / m) , φ ( r ) = 36 . 90703 (V) . (2) Numerical interpolations in EStat involve the collection of potential values from surround- ing nodes. On symmetry boundaries, there are only half the available nodes, so the accuracy is not optimal. We should use an internal point for a good comparison. On a 45 o line, the 21