In the famous book of A. Taflove "Computational Electrodynamics" magnetic field time updates are about n+3/2 and n+1/2 timesteps. The same time updates in Numerical Electromagnetics - the FDTD Method - U. Inan, R. Marshall (Cambridge, 2011) appeared between n+1/2 and n-1/2 timesteps. I know that there is no difference between them, as there is only one timestep between two different times, but I think that I am missing something. Any help will be appreciated.
Hi Dimitris, when we say that time updates of magnetic field at (n+1/2), we mean that the magnetic field values at (n-1/2) and electric field values at n are used to calculate the magnetic field value at time (n+1/2) [the electric and magnetic fields are interleaved in space also, but I am only specifying the time indices for the sake of understanding]. So, when you say, "magnetic field time updates are about n+3/2 and n+1/2 timesteps", it probably means you are trying to get the magnetic field values at (n+3/2) in terms of the magnetic field values at (n+1/2) and electric field values at (n+1). So they seem to be consistent, only with the difference that in one case by present time step we mean (n+3/2) and in the other case the present time-step refers to (n+1/2). I had a look at chapter 3 and 4 of Taflove once again, the update is the same as that of Inan and Marshall. Can you please specify the particular portion of Taflove's book? I might get a clear picture.
Thanks for your reply
In Taflove's book I refer to the PML chapter, especially to the UPML section, whereas in the Marshall's book I refer to chapter 9, pp 218 and forward.
I aggree with your opinion that's is relevant only to the diffrerence, not the timesteps itself
Ok, I saw the portion. Actually here they are trying to evaluate the field at t=(n+3/2). So, your present instant is (n+3/2). You can always make the substitution n=(m-1). So, yes, both of the notations are essentially same.
Thanks, I'm glad that my first thought is right, because with so many indices, there's always a chance that something is missing. Basically, the notation is the same because first you have to calculate magnetic and the electric field
Me too. It's more intuitive for me also because you only have to "move" inside a n±1/2 time space.
Если вы численно решаете уравнение с шагом по времени 1, то у вас будет правильным только один знак после запятой. Если временный шаг разбить на два, каждый с шагном 1/2, то у вас будут верными два знака после запятой. Если же будет экстраполлировать на пол шага вперед, т. Е. С итоговым шагом 3/2, то уже получите три или четыре верных знака после запятой.
One more, additional question
Magnetic field some times is calculated for half-integer timesteps and other for integer timesteps. Is there a difference between two notations? It's about what to calculate first, magnetic or electric field. It's the same I think but maybe there is a difference in the results. Thank you
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