Presentation for Numerical Field Theory
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This document describes a program to numerically solve Poisson's equation for the electrostatic potential of a T-shaped structure. The program uses the method of moments with basis functions to expand Poisson's equation. Point matching is used to approximate matrix integration. The structure is divided into subsections and the charge distribution is calculated for each subsection and summed. The potential function is then calculated using the total charge. The results are demonstrated in MatLab. Theoretical proofs are shown by varying the angle of the horizontal plate and tracking the capacitance to validate the results.
![Poisson’s Equation and Method of
Moment
• Poisson’s Equation is applied on the electrostatic
potential.
• Using method of moments, the Poisson’s equation is
expanded in a series of functions in the domain of
Laplace operators.
• The expanded function is known as basis function.
• [Lmn][ αn] = [gm]](https://image.slidesharecdn.com/fea584f5-3343-44c5-ac76-7a9cb69b0827-150430054320-conversion-gate01/85/Presentation-for-Numerical-Field-Theory-3-320.jpg)
Presentation for Numerical Field Theory
- 1. Numerical Solution of Poisson’s Equation for T-Shaped Structure Presented By: Indraneel Pole 1063525 Jonas Heberer 922405 X Y Z
- 2. Introduction • The objective of the project is to develop a program which will be used to solve Poisson’s equation for T- shaped structure. • The structure is composed by small squares. • Programming language used to create the program is C++ • Software used to demonstrate the results is MatLab.
- 3. Poisson’s Equation and Method of Moment • Poisson’s Equation is applied on the electrostatic potential. • Using method of moments, the Poisson’s equation is expanded in a series of functions in the domain of Laplace operators. • The expanded function is known as basis function. • [Lmn][ αn] = [gm]
- 4. Point Matching and Subsectional Bases • While point matching is used to approximate the integration of L – matrix at discrete points in the region of interest. • The plates are divided into small square subsections and charge distribution is found on each subsection, later on summed up to calculate total charge distribution.
- 5. An Example of Square Plate 2b 2a Y X S
- 6. L – Matrix is calculated For m != n For m = n
- 8. L-Matrix calculation for T-structure • The total L matrix will be of 2NX2N dimension, where N is number of subsections on one plate •The distance coupling for T-structure can be calculated as
- 9. Charge Distribution and Total Charge • Total charge can be calculated as charge distribution over the area.
- 10. Potential Function • Potential Function can be calculated using the formula Where Q is charge, and R is distance between the point on plate and the plane perpendicular to the structure.
- 11. Potential Function • The line of constant potential on a predefined plane can be visualized using MatLab function.
- 13. Theoretical Proofs • To theoretically prove our results, we will change the inclination of the horizontal plate and track the change in capacitance until the it takes the shape of parallel plate. • The capacitance of the structure decreases as the angle with the vertical axis decreases. • The trade off between angle to capacitance is shown on next slide • Parallel pate capacitance for d = 0.025 and N = 49; C = 370pF from the program, and 340pF by Calculation.
- 14. Theoretical Proofs 0 20 40 60 80 100 120 0 20 40 60 80 100 Series1 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Series1 Capacitance Vs Angle of inclination N = 25 N = 121
- 15. Questions
- 16. Thank You
Editor's Notes
- #4: Method of moments is mathematical technique to reduce functional equations to matrix equations.