Magnetostatic

A constant time step is usually applied for most finite difference applications. However, for magnetostatic or quasi-magnetostatic configurations, the displacement current becomes small or negligible allowing the permittivity values of associated materials to be increased without significantly impacting model electromagnetic behavior. Increasing the permittivity values enables an increase in the value of the time step. An increased time increment value can significantly reduce the number of time steps required to complete a temporal description. Magnetostatic time steps are often employed for lightning analysis investigations.

Specification of magnetostatic time steps also requires the specification of constant time steps discussed in Section 5.2.1. The constant time step specification defines the initial time step and the computational time window. The magnetostatic time steps are specified in addition to the constant time step information. The magnetostatic time steps information specifies the manner in which the permittivity is to increase.

Magnetostatic time steps are realized by specifying a series of time and associated permittivity increase factors. The factors are all referenced with respect to the initial permittivity values assigned to each individual material. The time step increase factor is equal to the square root of the associated permittivity increase factor. For example, if the following magnetostatic information was provided:

where tn is the time for the permittivity to have increased by a factor of fn over its initial value ε. Therefore, at time tn the permittivity would be specified to have increased to:

and the associated time step value will have increased to:

The method of increase is exponential, minimal at first and then exponentially increasing to achieve the specified value.

The first increase value, f0 at time t0, should always be assigned the value of 1.0. Therefore, the value t0 specifies the time to begin the increase from 1.0 to the value f1 at time t1. If the first increase factor is not "1.0" an error message will be issued in EMA3D® and the program terminated.

By specifying the pairs of parameters discussed above, the time step can be increased in nearly any manner desired. However, if the increase is too rapid, the accuracy of the numerical solution may be impacted. The rate of increase is dependent upon the particular problem. Some experimentation may be required.

Although many pairs of magnetostatic parameters can be specified, usually only two are required. The first pair to specify the beginning of the permittivity increase and the final pair to specify the final permittivity increase factor.