Hi, I have written a code for solving the second-order Helmholtz-Maxwell electromagnetic equation using finite-difference time-domain (FDTD) method. There is not much material available online for this second-order differential equation, except for its discretized forms. All the algorithms I've found online or offline are based on Yee's leap frog method.
I have been following the book "Computational electrodynamics" by Taflov and a PDF by Prof. John S, which is available online. When I use Yee's grid and implement the Total-Field Scattered-Field (TFSF) method, it works fine. However, when I try to implement TFSF on the code for the second-order Maxwell differential equation code then, it doesn't work at all. I'm following the same method to suppress the leftward traveling wave as mentioned in above books, albeit with slight modification.
If someone has prior experience with this and can help me, it would be of greatly appreciated.
You're trying to use the TFSF on the Helmholtz equation and not the Maxwell ones, is that right?
Can you describe what happens?
Sorry for a late reply.
Yes, back then I was trying to implement the TFSF on Maxwell-Helmholtz equation rather than on Maxwell ones. TFSF works very well on Maxwell first order update equations i.e. I get one wave travelling towards the scatterer.
However, when I tried to implement the TFSF on second order update equation then it didn't work. Source was stubbornly generating two pulses which travel in opposite directions.
Sounds to me like the sign of the source term in the scattered field region is wrong. Have you tried flipping it?
I'm using the waves u(ct-x) and u(ct+x) travelling towards right hand side and left hand side respectively. Ideally only u(ct-x) come out of the source at TFSF. I didn't flip the signs.
I've attached the write up and will appreciate if you can have a look at it whenever you find time. TFSF section is at the end of the document.
Hello. Isn't the M-H equation the same as the Wave equation? That equation is discussed in Taflove 2nd Ed., Section 2.5. When you implement the Wave Equation and the FDTD equations, without separation into TF-SF, do you get identical results? What additional info about the Wave equation are you looking for? Why do you want to extract the SF (I assume SF=Field without Scatterer-Field With Scatterer)?
Hello Dmitry,
Yes you are right, the M-H equation is same as that of wave equation. Taflov (3rd Ed.) discusses that equation in 2nd chapter. Problem is that book does not discuss TFSF and how to implement it on wave equation.
The problem I was working on required on SF and therefore I was trying to figure out how to implement TFSF in wave equation.
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