Built-In Global Variables
The following variables represent time (t), frequency (freq), eigenvalue (lambda), phase angle (phase), and the number of degrees of freedom (numberofdofs).
The Time Variable
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For time-dependent problems, use the time variable (t) with the unit seconds (s).
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It can be part of any expression in the point, edge, boundary, and domain settings, as well as during analysis.
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It is always scalar, even when the solution contains more than one output time.
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The value of t for results evaluation corresponds to the selection made in the Time list in the Data sections for the visualization and data evaluation nodes in the Results branch in the Model Builder. See the Results Analysis and Plots section.
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When computing derivatives with respect to time, you must use the mesh time symbol TIME instead of t, or use one of the frame-specific time derivative operators, frame.dt(expr), that automatically add convective terms derived from the mesh motion. For example, the time derivative of a temperature field T computed with respect to fixed points in the mesh is d(T,TIME) or equivalently mesh.dt(T). The corresponding time derivative for a fixed point in the spatial frame is spatial.dt(T).
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The TIME symbol is not a variable in the usual sense. It cannot be evaluated, but it is equal to the time t in the sense that d(t,TIME) is equal to 1.
The Frequency Variable
The frequency variable (freq) is the global frequency for models in the frequency domain (time-harmonic models and frequency response analysis, for example).
The Eigenvalue Variable
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When specifying an eigenvalue problem, use the eigenvalue variable (lambda) like any other variable.
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The eigenvalue solver extracts the Jacobian, the damping matrix, and the mass matrix through Taylor expansion of the problem with respect to the eigenvalue variable around a specified eigenvalue linearization point (which is zero by default).
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Other solvers treat the eigenvalue variable as a constant with value zero, unless it is set by an eigenvalue solution used as initial solution.
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After solving an eigenvalue problem, the eigenvalue name is available as a scalar variable for use in expressions.
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To choose between different eigenvalues, select one from the Eigenvalue list in the Data sections for the visualization and data evaluation nodes in the Results section of the Model Builder. The value of the eigenvalue variable corresponds to the selection made in the Eigenvalue list. See the Results Analysis and Plots section.
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For many physics interfaces, the default is to use an eigenfrequency study and compute and display the eigenfrequencies rather than the eigenvalues.
The Phase Angle Variable
The phase angle variable (phase) is the phase angle (in radians), primarily for postprocessing of models in the frequency domain, and you can specify its value in the Settings window for a dataset, using the Solution at angle (phase) field. The default value is 0.
By default, the COMSOL Multiphysics software plots the real part of complex-valued data. You can use the imag function to plot the imaginary part and the abs function to plot the absolute value (modulus) of complex-valued data.
The Number Of Degrees Of Freedom Variable
The variable numberofdofs returns the total number of degrees of freedom (DOFs), which is the number of DOFs solved for plus any internal DOFs that the solver might add. The number of DOFs solved for plus the number of internal DOFs are reported in the Messages window when you compute the solution. COMSOL Multiphysics sometimes uses internal DOFs for storing information during solution that would be expensive or impossible to recompute afterward. Internal DOFs have no equations and therefore do not make the system matrices larger.
These variables are built-in variables with reserved variable names. If you use a parameter called t, for example, COMSOL Multiphysics uses it for a stationary study, but the time-dependent solver overrides it with the value of t from the solver. Any variable or parameter using one of these names can be overridden during solution or postprocessing. Avoid using these reserved variable names for user-defined parameters and variables, unless you are aware of how they are handled in COMSOL Multiphysics.