Standard Benchmark Problem for Computational Solution of Poisson Equation

In summary, the speaker has written a poisson solver for FEM methods and has tested it on simple problems, such as a parallel plate capacitor and potential inside and outside a hollow sphere of charge. They have also compared their results to a published paper by their advisor for a parallel plate capacitor with rough surfaces. However, they have not yet tested their solver on a real-life problem and are seeking a "gold standard" problem with complex requirements but not contentious solutions. They are also looking for data to use for error calculations and verification. The speaker mentions that their solver is 3D and asks about the possibility of using a calculable capacitor for their project. They suggest searching on Google Scholar for data on calculable capacitors.
  • #1
badwaik.jayesh
4
0
Hi,

I am working on FEM methods as a part of my senior year project and I have written a poisson solver for the same purpose. The solver works pretty well on the simple problems that I have designed as of now and seems to give correct answer (i.e. the data matches the theoretical prediction)
1. Parallel Plate Capacitor
2. Potential inside and outside a hollow sphere of charge
3. Parallel Plate Capacitor with rough surfaces (In this case, I have obtained a good co-relation between the calculations in my advisors pulblished paper and my paper.)

However, I have not yet designed any real life problem as of now. So before I design it, I would like to ask if there is any such gold standard for such a thing (a standard problem which is complex enough to demand good convergence requirements from the solver but not so complex as the solution to be contentious) and is there a place where I can get data so that I can verify my own results by running actual error calculations and such stuff rather than just checking the shapes of the graphs.

P.S. My solver is a 3D solver so I would like to have a 3D problem for the same.
 
Last edited:
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  • #2
What about a calculable capacitor?
They are often used in precision metrology and are extremely well characterized.
You should be able to find data for one if you do a search using Google Scholar.
 

1. What is the Poisson equation?

The Poisson equation is a mathematical equation that describes the relationship between the distribution of electric charge in a region and the resulting electric potential. It is commonly used in physics and engineering to model phenomena such as electrostatics, heat transfer, and diffusion.

2. What is a standard benchmark problem for computational solution of Poisson equation?

A standard benchmark problem for computational solution of Poisson equation is a well-defined problem that is commonly used in the field of computational physics or engineering to test the accuracy and efficiency of different numerical methods for solving the Poisson equation. It typically involves a known electric charge distribution and boundary conditions, and the goal is to find the corresponding electric potential distribution.

3. Why is it important to have a standard benchmark problem for computational solution of Poisson equation?

Having a standard benchmark problem allows researchers to compare and evaluate different numerical methods for solving the Poisson equation in a consistent and objective manner. It also provides a way to validate new methods and algorithms, and to identify areas for improvement in existing methods.

4. What are some common methods used to solve the Poisson equation computationally?

Some common methods for solving the Poisson equation computationally include finite difference methods, finite element methods, and boundary element methods. Each of these methods has its own advantages and limitations, and the choice of method often depends on the specific problem being solved.

5. Are there any real-world applications of the Poisson equation and its computational solutions?

Yes, there are many real-world applications of the Poisson equation and its solutions. Some examples include modeling electric fields in electronic devices, predicting temperature distributions in heat transfer problems, and simulating fluid flow in porous media. The Poisson equation is also used in image processing and computer vision for edge detection and image restoration.

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