Examples of uses for the Poisson Eqn in 1d

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In summary, the conversation is about the final section of the speaker's dissertation on using the finite element method to solve the 1D version of the Poisson equation. They are struggling to find real-world examples to use and are seeking suggestions or resources from others. One suggestion is to use Poisson's equation in electricity and magnetism or gravitational potential energy fields.
  • #1
Carla1985
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Hi all,

I have almost finished my dissertation on using the finite element method to solve the 1D version of the Poisson equation. For the last section I would like to run through a couple of examples but am struggling to find some. Obviously I can make up any equations that satisfy the equation, this is what most of the exercises in the books are, but ideally I would like to use some that have real world value. Could anyone either suggest some examples or point me in the direction of some please.

Thanks
Carla
 
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  • #2
Well, I don't know if you can shoe-horn such a problem into one dimension, but you use Poisson's equation to find the potential due to source charges in electricity and magnetism, and you can also use the exact same math to find the gravitational potential energy field due to an arrangement of masses. So it's of great importance!
 

What is the Poisson Equation in 1D?

The Poisson Equation in 1D is a mathematical expression that describes the relationship between a function and its second derivative. It is often used in physics and engineering to model phenomena such as heat transfer, fluid flow, and electric fields.

What are some common uses for the Poisson Equation in 1D?

The Poisson Equation in 1D has a wide range of applications, including predicting the behavior of electric fields in electronic devices, modeling the flow of fluids through pipes and channels, and understanding the distribution of heat in materials.

How is the Poisson Equation in 1D solved?

The Poisson Equation in 1D can be solved using various numerical methods, such as finite difference methods or finite element methods. These involve discretizing the equation and solving it for a set of discrete points, which can then be used to approximate the solution for the entire domain.

What are some examples of real-world problems that can be solved using the Poisson Equation in 1D?

The Poisson Equation in 1D can be applied to a wide range of problems, such as calculating the distribution of electric potential in a circuit, predicting the temperature distribution in a heated plate, or simulating the flow of air around an airplane wing.

What are the limitations of using the Poisson Equation in 1D?

The Poisson Equation in 1D is a simplified model and may not accurately capture all aspects of a complex real-world problem. It also assumes certain boundary conditions and may not be suitable for problems with changing or dynamic boundaries. Additionally, the accuracy of the solution depends on the numerical method used and the resolution of the discretized points.

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