Selecting the Study Type
To carry out different kinds of simulations for a given set of parameters in a physics interface, you can select, add, and change the Study Types at almost every stage of modeling.
Studies and Solvers in the COMSOL Multiphysics Reference Manual
Comparing the Time Dependent and Frequency Domain Studies
When variations in time are present there are two main approaches to represent the time dependence. The most straightforward is to solve the problem by calculating the changes in the solution for each time step; that is, solving using the Time Dependent study (available with the Electromagnetic Waves, Transient and Electromagnetic Waves, Time Explicit interfaces). However, this approach can be time consuming if small time steps are necessary for the desired accuracy. It is necessary when the inputs are transients like turn-on and turn-off sequences.
However, if the Frequency Domain or Wavelength Domain studies, available with the Electromagnetic Waves, Frequency Domain and the Electromagnetic Waves, Beam Envelopes interfaces, are used, this allows you to efficiently simplify and assume that all variations in time occur as sinusoidal signals. Then the problem is time harmonic and in the frequency domain. Thus you can formulate it as a stationary problem with complex-valued solutions. The complex value represents both the amplitude and the phase of the field, while the frequency is specified as a scalar model input, usually provided by the solver. This approach is useful because, combined with Fourier analysis, it applies to all periodic signals with the exception of nonlinear problems. Examples of typical frequency or wavelength domain simulations are wave-propagation problems.
For nonlinear problems you can apply a Frequency Domain or Wavelength Domain study after a linearization of the problem, which assumes that the distortion of the sinusoidal signal is small. You can also couple waves at different frequencies, for example in applications like second harmonic generation, by coupling several physics interfaces, defined for the different frequencies, using weak expression coupling terms.
Use a Time Dependent study when the nonlinear influence is strong, or if you are interested in the harmonic distortion of a sine signal. It can also be more efficient to use a time dependent study if you have a periodic input with many harmonics, like a square-shaped signal.
comparing the electromagnetic waves, frequency domain and the electromagnetic waves, beam envelopes interfaces
Both the Electromagnetic Waves, Frequency Domain and the Electromagnetic Waves, Beam Envelopes interfaces solve the time-harmonic Maxwell’s equations. For the Frequency Domain interface, the dependent variable is the total electric field. Since the electric field has a spatial variation on the scale of a wavelength, the maximum mesh element size must be a fraction of a wavelength. If this mesh requirement is fulfilled, the Frequency Domain interface is very flexible for solving both propagation and scattering problems.
For many optical applications the propagation length is much longer than the wavelength. For instance, a typical optical wavelength is 1 μm, but the propagation length can easily be on the millimeter to centimeter scale. To apply the Frequency Domain interface to this kind of problems, requires a large amount of available memory. However, many problems are such that the electric field can be factored into a slowly varying amplitude factor and a rapidly varying phase factor. The Electromagnetic Waves, Beam Envelopes interface is based on this assumption. Thus, this physics interface assumes a prescribed rapidly varying phase factor and solves for the slowly varying amplitude factor. Thereby it can be used for solving problems extending over domains that are a large number of wavelengths long, without requiring the use of large amounts of memory.
comparing the electromagnetic waves, frequency domain and the electromagnetic waves, Boundary Elements interfaces
Both the Electromagnetic Waves, Frequency Domain and the Electromagnetic Waves, Boundary Elements interfaces solve the time-harmonic Maxwell’s equations. For the Frequency Domain interface, the dependent variable is the electric field in the domains. However, for the Electromagnetic Waves, Boundary Elements interface the dependent variable is the electric field on the boundaries. This physics interface solves for the dependent variable using the Boundary Element Method (BEM).
Typically, much fewer degrees of freedom (unknown variables) will be solved for when using the Boundary Elements interface. However, when solving the problem using BEM, the matrices are no longer sparse. So, even though the degrees of freedom will be much less when using the Boundary Elements interface, the problem may still require a large amount of memory during the solving process.
The Boundary Element Method is based on the knowledge of the Green’s function for the vector Helmholtz equation. Since we only know the Green’s function, if the domain material is homogeneous, the Electromagnetic Waves, Boundary Elements interface can only be used for problems where the materials are homogeneous or piece-wise homogeneous.
Some applications where it could be advantageous to use the Electromagnetic Waves, Boundary Elements interface are:
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Applications where there is a structure transmitting waves very far from the structure receiving the waves.
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Scattering problems with several scattering elements, potentially located far apart.
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Applications where a wave or beam is propagating through several simple elements, located far apart.
When discussing above about elements located far apart, it is meant that the elements are located many wavelengths apart. If the Electromagnetic Waves, Frequency Domain interface would be used for solving such problems, there will be a large number of degrees of freedom in the domain mesh. On the other hand, for the Electromagnetic Waves, Boundary Elements interface, only the size and complexity of the boundaries, not the separation between the elements, determine the number of degrees of freedom required to represent the problem.