4.1 A First Modeling Program
We are now in a position to actually write a complete modeling program. We will use it to learn some more electrostatics, and then we will look at its limitations and inaccuracies and plan how we might improve it.
The basic components of this first program are as follows:
- Data input — we have to be able to “tell” the program what structure and what boundary conditions we want to examine.
- Data input processing — the program must be able to take the input data information and convert it into the subrectangles (cells) as described by the data input.
- Calculation of all the Li,j coefficients.
- Adding the extra row and column to the Li,j matrix (and the extra column to the V vector) as described in Chapter 3 to ensure that charge neutrality is maintained.
- Solving the linear equation set.
- Postprocessing and presentation of results — do we want capacitance, voltage, or electric field at some specific points?
- Warnings of possible inaccuracies from the program.
- Automatic improvements of the accuracy of the calculations.
Components 1 and 2 are in general a very sophisticated technology. We want our modeling software to be able to interact with our computer-aided design (CAD) software and extract necessary modeling information from the drawings as accurately and automatically as possible. This is a very important component of electrostatic (or general electromagnetic, mechanical, etc.) modeling. On the other hand, it is not ...