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Mesh and Simulation

The way a structure is discretized strongly influences the accuracy of the results. The computed results converge towards the "continuous world” results when the mesh size gets smaller and smaller until the discrete lengths vanish or, being more exact, become differentials. So, generally speaking the structure and the fields are simulated best with a very fine mesh.

Mesh and Simulation Time

As far as the results are concerned, the finer the mesh, the better. However, a very fine mesh has a large number of mesh cells and with this a large number of unknowns to be solved. Every increase of unknowns extends the need of memory and simulation time.

For the increase of simulation time, there are two different mechanisms. One is quite obvious: the more unknowns that are present, the more operations must be computed. The other mechanism is caused by the properties of the solver. The frequency domain and the eigenvalue solver converge slower with smaller mesh step sizes than with greater ones. Also, for smaller mesh step sizes, the time domain solver needs smaller time steps to remain stable.

Artificial Dispersion

Another effect of the discrete simulation is that an additional dispersion due to the mesh can be observed. This dispersion gets worse as the differences between two neighboring mesh step sizes become larger. The smallest dispersion will occur in an equidistant mesh.

To avoid these effects, the mesh generator may be forced to insert additional mesh lines that decrease the differences of mesh lengths.

Mesh and Spatial Signal Sampling Rate

Sampling Rate: An important value for the spatial sampling rate is the number of mesh lines per wavelength. This value is connected to the wavelength of the highest frequency of the simulation. It defines the minimum number of mesh lines in each coordinate direction that are used for a distance equal to this wavelength. In a way, it sets the spatial sampling rate for the signals or fields inside of the structure, see Mesh Properties (Surface), Mesh Properties (Hexahedral) and Mesh Properties (Tetrahedral).

Very often a good compromise between calculation time and the achievable accuracy is the default value of 10 lines per wavelength for hexahedral or 4 lines per wavelength for tetrahedral meshing. For surface meshing 6 lines per wavelength is the default value.

However, the wavelength inside of a structure depends on its material. Therefore it is possible to let the mesh generator adjusts the mesh according to the influence of the material on the wavelength.


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