Assuming that \(\Delta x = 1\) metre, if you wanted to allocate a rectangle with its x dimension equal to 3 metres and its lower x coordinate at 1 then the x range would be. The space coordinates range from the left edge of the first cell to the right edge of the last one. Only one row of cells in the x direction is depicted. 3 illustrates the coordinate system of gprMax. The stability condition is known as the CFL condition after the initials of Courant, Freidrichs and Lewy and is given by,Ī right-handed Cartesian coordinate system is used with the origin of space coordinates in the lower left corner at (0,0,0). FDTD is a conditionally stable numerical process. The price you have to pay for obtaining a solution directly in the time domain using the FDTD method is that the values of \(\Delta x\), \(\Delta y\), \(\Delta z\) and \(\Delta t\) can not be assigned independently. Hence by specifying the number of iterations you can instruct the FDTD solver to simulate the fields for a given time window. In each iteration the electromagnetic fields advance (propagate) in the FDTD grid and each iteration corresponds to an elapsed simulated time of one \(\Delta t\). The numerical solution is obtained directly in the time domain in an iterative fashion.
These equations are discretized in both space and time and applied in each FDTD cell.
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