7.3     Stability factor

Fundamentals of FDTD method clearly define the limitations regarding the numerical stability of the algorithm. According to them the maximum time step Dt is limited by the size of the smallest cell in the FDTD grid. This defines the stability factor:

where:

 is effective cell size,

Dx,Dy,Dz stand for the smallest cell size in respective directions,

c is a speed of light in vacuum,

Dt is FDTD time step.

For the purpose of assuring numerical stability of the FDTD algorithm the Courant criterion must be obeyed:

• For 2D problems:      

• For 3D problems:      

In QuickWave, time step Dt always obeys the Courant criterion.

The user is provided with the advanced option of setting the stability factor multiplier. This is available in Export Options. The multiplier allows decreasing the time step Dt. It is recommended to increase the stability factor multiplier value if any unexpected algorithm instabilities appear during electromagnetic simulation. It is not recommended to decrease it below it default value.