Solving Poisson's Equation in Finite Difference Method with Matlab

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Discussion Overview

The discussion revolves around solving Poisson's equation using the finite difference method in MATLAB, specifically focusing on a one-dimensional case. Participants explore the formulation of the equation, its representation in different coordinate systems, and the implications of the doping concentration function N(x).

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the Poisson equation in finite difference form, specifying the function N(x) as a combination of Gaussian terms.
  • Another participant questions the correctness of the equation's representation and seeks clarification on the coordinate system used and the placement of N(x).
  • A participant confirms that the problem is in Cartesian coordinates and specifies that N(x) is indeed in the numerator, describing it as a Gaussian doping concentration.
  • Another participant raises a question about the validity of integrating the equation and applying boundary conditions, suggesting that N(x) is a function of x only.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the formulation of the equation and its implications, with some questions remaining about the integration process and the nature of N(x).

Contextual Notes

There are unresolved questions regarding the integration of the equation and the application of boundary conditions, as well as the specific definitions and assumptions related to the coordinate system and the function N(x).

indrani
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I have a problem solving poisson equation in finite difference method using matlab.

the equation is (δ^2 φ)/(δx^2 )=(-ρ/ϵ N(x))

where N(x)= a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)
 
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Is this written correctly?
\frac{\partial}{\partial x} \left( \frac{\partial \psi}{\partial x} \right)=\frac{- \rho}{\varepsilon} N\left( x \right)
Is this equation in cartesian coordinates, or spherical or cylindrical coordinates? Is N(x) in the numerator?
 
it is in cartesian coordinate.I have to solve in 1Dimention. N(x) is in numerator and it is the doping concentration which is a Gaussian in nature
 
Is this true (i.e., 1-D Poisson equation); with N(x) being a function of x only?
-d \left( \frac{\partial \psi}{\partial x} \right)= d E_x (x) =\frac{+ \rho}{\varepsilon} N\left( x \right) dx
Then can't you integrate both sides and put in boundary conditions?
 

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