Analytic

An Analytic function () is defined by a symbolic expression. Analytic functions have the ability to bind arguments during function calls. In other words, they do not require the actual argument names in an expression when writing the function. For example, you can define a function f(x) = x2 with the input argument x and the expression x^2 and the call it as f(T), where T is the temperature in a heat transfer model. The default Function name is an1.

The Analytic, Interpolation, and Piecewise functions can also be added to Materials. See Using Functions in Materials.

• See Function Names and calling Functions for information about allowed function names. • See Units for information about the Unit section. • See Plot Parameters for information about Plot Parameters (plot range) settings.

Definition

In the Expression field, enter the mathematical expression that defines the function, such as sin(x)*cos(y)+g_const or a+b*cos(c). Enter Arguments to the analytic function as comma-separated entries (x, y and a, b, c for the functions above). In addition to the arguments that are defined, analytic functions also recognize global parameters and physical constants.

From the Derivatives list, Automatic is selected by default and computes the derivatives symbolically. COMSOL uses the derivatives of a function if a variable that depends on the solution is used in a function argument. Select Manual to specify the function derivatives with respect to its arguments in a table. If Manual is selected, enter the derivatives with respect to the function’s arguments. For undefined derivatives, COMSOL uses 0 as the value of the derivative. In the second example above, enter a, b, and c in the top three rows of the Argument column, and 1, cos(c), and -b*sin(c)in the associated text fields in the Partial derivative column.

Periodic Extension

Select the Make periodic check box to make the function periodic and extend its definition within an interval to the whole real axis. Then define the interval by entering values in the Lower limit (default is 0) and Upper limit (default is 1) fields.

Advanced

Select the May produce complex output for real arguments check box if the defined function works similarly to sqrt; that is, if it sometimes returns complex values for a real-valued input.

• If you have the AC/DC Module, see A Geoelectrical Forward Problem: Application Library path ACDC_Module/Other_Industrial_Applications/geoelectrics. • If you have the RF Module, see Second Harmonic Generation of a Gaussian Beam: Application Library path RF_Module/Tutorials/second_harmonic_generation.