Solving System PDEs with Comsol - Help Needed

It is also important to note that the system of PDEs provided is defined in a two-dimensional domain and involves the variables u, v, h, and k. In summary, the conversation is about solving a system of PDEs using Comsol and the advice is to first learn how to use the software before attempting to find the solution.
  • #1
ManuelF
8
0
Hello!
I have to solve a system of PDEs with Comsol and do not know where to start ...
This is the system:
[tex]&u_{,x}+v_{,y}=k y+h x\ \ \ &in\ \mathcal{A}[/tex]
[tex]v_{,x}-u_{,y}=k x-h y\ \ \ &in\ \mathcal{A}[/tex]
[tex]u n_x+v n_y=0\ \ \ &on\ \partial\mathcal{A}[/tex]

[tex]\mathcal{A}\ in\ \mathbb{R}^2[/tex],[tex]\boldsymbol{v}=(u,v)[/tex], [tex]h,k\ \in\mathds{R}[/tex] and [tex]\boldsymbol{v}=(nx,ny)[/tex] is the normal vector.
Someone can help me?
My e-mail address is <email address removed>, please contact me!
Can you send me the solution made with Comsol?
Thank you all!

(Sorry for the bad english)
 
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  • #2
Unfortunately, it is not possible to send you the solution made with Comsol as it is a complex process which requires a thorough understanding of the PDEs and the different parameters involved. It is best that you learn how to solve the PDEs using the Comsol software before attempting to find the solution yourself. There are many tutorials available online which can help you understand the basics of the software and how to use it to solve the system of PDEs.
 
  • #3


Hello, solving a system of PDEs with Comsol can be a complex task, but I am happy to help you get started. First, you will need to create a model in Comsol by selecting the "PDEs and Multiphysics" option and then selecting "2D" for the spatial dimension. Next, you will need to define your geometry and boundary conditions. In this case, your domain is \mathcal{A} and your boundary condition is u n_x+v n_y=0 on \partial\mathcal{A}. Once your model is set up, you can use the "PDEs" interface to define your equations, which in this case are &u_{,x}+v_{,y}=k y+h x and v_{,x}-u_{,y}=k x-h y. You will also need to define the coefficients k, h, and the vector \boldsymbol{v}=(nx,ny). After solving your model, you can export the results as a solution file and send it to me. I am unable to provide you with a solution made with Comsol, but I can guide you through the process. If you have any further questions, please feel free to contact me at <email address removed> and I will do my best to assist you. Best of luck with your project!
 

1. What is Comsol and how is it used to solve system PDEs?

Comsol is a commercial software package that utilizes the finite element method to solve partial differential equations (PDEs) and other complex mathematical problems. It is commonly used in scientific and engineering applications to simulate and analyze physical phenomena. Comsol allows for the creation of customized models and provides a user-friendly interface for solving system PDEs.

2. Can Comsol solve all types of system PDEs?

Comsol is a versatile software that can handle a wide range of PDEs, including stationary and time-dependent problems, linear and nonlinear equations, and multiphysics problems. However, the complexity and size of the problem may affect the efficiency of the solution, so it is important to carefully consider the capabilities and limitations of the software before use.

3. What are the steps involved in solving system PDEs with Comsol?

The general steps for solving system PDEs with Comsol include setting up the geometry and boundary conditions, selecting the appropriate PDEs and physics, meshing the model, and solving the equations. It is important to carefully define the parameters, material properties, and numerical settings to obtain accurate and reliable results.

4. How accurate are the results obtained from Comsol?

The accuracy of the results obtained from Comsol depends on various factors, such as the complexity of the problem, the quality of the mesh, and the numerical settings used. Comsol provides various tools and techniques to improve the accuracy of the results, such as adaptive mesh refinement and error estimation. It is also important to validate the results against experimental data or analytical solutions whenever possible.

5. Is it necessary to have prior experience with PDEs to use Comsol?

While having prior knowledge of PDEs can be helpful in understanding the underlying physics and setting up the model, it is not a requirement to use Comsol. The software provides tutorials, documentation, and technical support to assist users in solving system PDEs without prior experience. However, a basic understanding of mathematical concepts and physics principles is recommended for using Comsol effectively.

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