Summary of Built-In Variables With Reserved Names

These language elements are built-in or user-defined. In addition there are operators that cannot be user-defined, and expressions, which are always user-defined.

Built-in variables have reserved names, names that cannot be redefined by the user. It is not recommended to use a reserved variable name for a user-defined variable, parameter, or function. For some of the most common reserved variable names, such as pi, i, and j, the text where you enter the name turns orange and you get a tooltip message if you select the text string. Reserved function names are reserved only for function names, which means that such names can be used for variable and parameter names, and vice versa. The following tables list most built-in elements and hence those reserved names.

There are three different types of constants: built-in mathematical and numerical constants, built-in physical constants, and parameters. Parameters are user-defined constants that can vary over parameter sweeps. Constants are scalar valued. The following table lists the built-in physical constants. Constants and parameters can have units.

Name	Description
g_const	Acceleration of gravity
N_A_const	Avogadro constant
k_B_const	Boltzmann constant
Z0_const	Characteristic impedance of vacuum (impedance of free space)
me_const	Electron mass
e_const	Elementary charge
F_const	Faraday constant
alpha_const	Fine-structure constant
G_const	Gravitational constant
V_m_const	Molar volume of ideal gas (at 273.15 K and 1 atm)
mn_const	Neutron mass
mu0_const	Permeability of vacuum (magnetic constant)
epsilon0_const	Permittivity of vacuum (electric constant)
h_const	Planck’s constant
hbar_const	Planck’s constant over 2 pi
mp_const	Proton mass
c_const	Speed of light in vacuum
sigma_const	Stefan-Boltzmann constant
R_const	Universal gas constant
b_const	Wien displacement law constant

Name	Description
abs	Absolute value
acos	Inverse cosine (in radians)
acosh	Inverse hyperbolic cosine
acot	Inverse cotangent (in radians)
acoth	Inverse hyperbolic cotangent
acsc	Inverse cosecant (in radians)
acsch	Inverse hyperbolic cosecant
arg	Phase angle (in radians)
asec	Inverse secant (in radians)
asech	Inverse hyperbolic secant
asin	Inverse sine (in radians)
asinh	Inverse hyperbolic sine
atan	Inverse tangent (in radians)
atan2	Four-quadrant inverse tangent (in radians)
atanh	Inverse hyperbolic tangent
besselj	Bessel function of the first kind
bessely	Bessel function of the second kind
besseli	Modified Bessel function of the first kind
besselk	Modified Bessel function of the second kind
ceil	Nearest following integer
conj	Complex conjugate
cos	Cosine
cosh	Hyperbolic cosine
cot	Cotangent
coth	Hyperbolic cotangent
csc	Cosecant
csch	Hyperbolic cosecant
erf	Error function
exp	Exponential
floor	Nearest previous integer
gamma	Gamma function
imag	Imaginary part
log	Natural logarithm
log10	Base-10 logarithm
log2	Base-2 logarithm
max	Maximum of two arguments
min	Minimum of two arguments
mod	Modulo operator
psi	Psi function and its derivatives
range	Create a range of numbers
real	Real part
round	Round to closest integer
sec	Secant
sech	Hyperbolic secant
sign	Signum function
sin	Sine
sinh	Hyperbolic sine
sqrt	Square root
tan	Tangent
tanh	Hyperbolic tangent

Name	Description	Type
t	Time.	Scalar
freq	Frequency.	Scalar
lambda	Eigenvalues.	Scalar
phase	Phase angle.	Scalar
numberofdofs	Number of degrees of freedom.	Scalar
x, y, z, r, X, Y, Z, R	Position.	Field
s, s1, s2	Edge/surface parameters.	Field
n, nx, ny, nz, nr	Edge/surface normals.	Field
tx, ty, tz, tr	Edge tangents.	Field
t1x, t1y, t1z, t2x, t2y, t2z	Surface tangents.	Field
un, unx, uny, unz	Edge/surface upward normals.	Field
dn, dnx, dny, dnz	Edge/surface downward normals.	Field
eps, i, j, pi, inf, Inf, nan, NaN	Numerical constants.	Scalar
h	Local mesh element size (length of the longest element edge).	Field
dom	The domain number, boundary number, edge number, or point number.	Field
meshtype	Mesh type index for the mesh element; this is the number of edges in the element.	Field
meshelement	Mesh element number.	Field
meshvol	Volume of the (linearized) mesh element.	Field
dvol	Volume scale factor variable; this is the determinant of the Jacobian matrix for the mapping from local (element) coordinates to global coordinates.	Field
qual	A mesh quality measure between 0 (poor quality) and 1 (perfect quality). The absolute value of the mesh element quality is based on the ratios of the inscribed and circumscribed circles’ or spheres’ radii for the simplex corresponding to each corner of the element. A negative value means a contradiction to the numbering convention for mesh element vertices and the element is then referred to as an inverted element.	Field
reldetjac	Determinant of the Jacobian matrix for the mapping from the straight mesh element to the possibly curved element used when solving.	Field
reldetjacmin	The minimum value of the reldetjac variable in each element.	Field
linearizedelem	One inside elements that have been linearized; zero otherwise.	Field
niterCMP	Iteration number for nonlinear iterations.	Scalar
gmg_level	Geometric multigrid level.	Scalar
timestep	Current time step.	Scalar
particleindex	A unique positive integer to define each particle or ray. This variable is only defined when using the Geometrical Optics interface, Ray Acoustics interface, or one of the particle tracing physics interfaces.	Scalar
particlestatus	An integer that corresponds to the status of a particle or ray, which indicates whether the particle or ray is active or has been subjected to certain types of boundary conditions. This variable is only defined when using the Geometrical Optics interface, Ray Acoustics interface, or one of the particle tracing physics interfaces. By default it cannot be used during postprocessing.	Scalar

Default name	Description	Type
x, y, z	Spatial coordinates (Cartesian)	Field
r, z	Spatial coordinates (cylindrical)	Field
u, T, and so on	Dependent variables (solution)	Field