Help with finite element program I developed for Diff Eqns

In summary, the conversation discusses the development of a finite element program in Java for solving partial differential equations. The program is facing a problem with a generalized eigenvalue problem generated in wave propagation through a rectangular waveguide in TE mode. The program is producing correct results without specifying Dirichlet boundary conditions, but the field plots are different when the boundary conditions are applied. The program uses nodal based rectangular elements and a mesh generated in a flash program called Mmesh. More information, such as plots, will be needed to help solve the problem.
  • #1
mdn
49
0
I developed finite element program (MFEM) in java for BVP &IVP to compute partial differential equation.
I am facing one problem and description is as follows
my problem is on generalized eigenvalue problem generated in wave propagation through rectangular wave guide in TE mode. (Differential equation is scalar Helmholtz equation).

I am getting correct answer but without specifying Dirichlet boundary condition! (Tangential component of electric field should be zero on boundary element).
and if i applied boundary condition, getting same answer but field plot is different .
one thing i used nodal based rectangular element and mesh generated in my own flash program Mmesh.

please help me to solve above problem.
 
Engineering news on Phys.org
  • #2
mdn said:
I developed finite element program (MFEM) in java for BVP &IVP to compute partial differential equation.
I am facing one problem and description is as follows
my problem is on generalized eigenvalue problem generated in wave propagation through rectangular wave guide in TE mode. (Differential equation is scalar Helmholtz equation).

I am getting correct answer but without specifying Dirichlet boundary condition! (Tangential component of electric field should be zero on boundary element).
and if i applied boundary condition, getting same answer but field plot is different .
one thing i used nodal based rectangular element and mesh generated in my own flash program Mmesh.

please help me to solve above problem.

Welcome to the PF.

We probably will need a lot more information to be of help on this question. Can you post some plots that show the output from your program?
 
  • #3
Dear Berkeman,
I have attached field plots from my program for TE10(without bc),TE20 (without bc),TE11(without bc) and TM11 (with bc).
Thanks in advance.
 

Attachments

  • te10wbc.jpg
    te10wbc.jpg
    25.5 KB · Views: 396
  • te20wbc.jpg
    te20wbc.jpg
    25.9 KB · Views: 383
  • te11wbc.jpg
    te11wbc.jpg
    26.9 KB · Views: 399
  • tm11bc.jpg
    tm11bc.jpg
    27.5 KB · Views: 384

Related to Help with finite element program I developed for Diff Eqns

1. What is a finite element program for differential equations?

A finite element program for differential equations is a computer program that uses the finite element method to solve differential equations. The finite element method is a numerical technique for finding approximate solutions to differential equations by dividing the problem domain into smaller, simpler parts. These smaller parts are called finite elements, and the program uses mathematical equations and algorithms to solve for the unknown variables at each element, ultimately providing a solution for the entire problem.

2. How does a finite element program work?

A finite element program works by first dividing the problem domain into smaller finite elements, usually using a mesh. Then, the program uses mathematical equations and algorithms to calculate the values of the unknown variables at each element. These values are then combined to provide a solution for the entire problem. The program also usually includes features for visualization and analysis of the results.

3. What types of differential equations can be solved using a finite element program?

A finite element program can solve a wide range of differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and boundary value problems (BVPs). It can also handle different types of equations, such as elliptic, parabolic, and hyperbolic equations.

4. What are the advantages of using a finite element program for differential equations?

There are several advantages to using a finite element program for differential equations. First, it allows for the solution of complex problems that may not have analytical solutions. It also provides a more accurate solution compared to traditional numerical methods. Additionally, the program can handle a wide range of problem types and can easily be adapted for different equations and problem domains.

5. What are some tips for using a finite element program for differential equations?

One important tip for using a finite element program is to carefully choose the mesh size. A smaller mesh can provide a more accurate solution, but it may also increase the computation time significantly. It is also important to validate the results by comparing them to known solutions or using convergence analysis. Additionally, it is helpful to have a good understanding of the underlying mathematical principles and algorithms used in the program to effectively troubleshoot any issues that may arise.

Similar threads

How to apply divergence free (∇.v=0) in nodal finite element method?
    • Electrical Engineering
Replies
3
Views
848
B Incorporating boundary conditions in the Finite Element Method (FEM)
    • Differential Equations
Replies
4
Views
839
I Finding the weak form of an eq. with DG elements (finite elements)
    • Differential Equations
Replies
6
Views
2K
Abuse of the Finite Element Method
    • Mechanical Engineering
Replies
9
Views
2K
Engineering Current density calculation in anisotropic ferromagnetic film
    • Engineering and Comp Sci Homework Help
Replies
7
Views
829
PhD in Applied Mathematics - Finite Element Analysis
    • STEM Academic Advising
Replies
2
Views
2K
Finite element solving of Laplace's equation doesn't converge
    • Advanced Physics Homework Help
Replies
4
Views
1K
Matlab report help please (Finite Difference Method)
    • Engineering and Comp Sci Homework Help
Replies
5
Views
1K
Nonuniform finite element method
    • Calculus
Replies
8
Views
2K
Need A Finite Element Magnetics Code That Handles Dynamic Modeling
    • Electrical Engineering
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top