Are there some Matlab codes of FEM for discretizing the three-dimensional Helmholtz equation with first order Sommerfeld boundary conditions? Certainly, the FEniCS package (or other C++ -based codes) for Helmholtz equations have been available online. However, I am not very be good at the these codes? In addition, if I want to write myself the Matlab codes of FEM for Helmholtz equations, what needs to be considered ? Especially, how to deal with the boundary nodes, when I evaluate the entries of stiff matrices. If who are interested into this topic, please send email ([email protected]) to me. Recently, I have a interesting ideas about a physics simulations problem, in which the 3D Helmholtz (even Maxwell ) equations are need to discretized by FEM, or weak FEM, Hybrid Discontinuous Galerkin method.
Hello, Xian-Ming Gu! Please, take a look at these papers:
1) http://www.sciencedirect.com/science/article/pii/S0898122111008868
2) http://www.sciencedirect.com/science/article/pii/0045782595009876
3) http://www.sciencedirect.com/science/article/pii/S004578259800334X
4) http://epubs.siam.org/doi/abs/10.1137/090761057
Best regards and good luck with your research!!!!
@Lauro de Paula Thank you for your answer. Hey, in fact, I had read some papers about this problems, also I can understand the mathematical description of the finite element methods for Helmholtz equations, However, I am not very familiar with writing the corresponding codes for the FEM. It is always a big problem for me. I often feel that we should begin with numerical discretizations (FEM, FVM, FDM) of the specified real problems, then we can consider to develop some NLA techniques to solve the resulted systems of linear equations. This is a complete procedure of my research, but t in most cases I only can master one of these two steps. It make me very depressed. Best wish with your future research.
Dear Xian-Ming,
I have written some FEM codes for Helmholtz and Poisson equations in 3-D using GMSH tetrahedral meshing. I did not test them very extensively, though managed to match analytical solution for some simple problem. Unfortunately, I only implemented Dirichlet BC. (a cube, potential at boundaries equal to zeros, eq. Lap(phi)=(-rho(x,y))/(eps(x,y). Where phi - electric scalar potential, rho - charge density, and eps - is the dielectric permittivity.
Please, let me know what thoughts do you have in mind, and we might think about some collaboration.
@Anton Menshov, Thank you very much for your attentions. Recently, I am busy in preparing some presentations, so I will contact with you for details of this problems later.
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