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/* Discretizing Planar Structures */
EM.Picasso generates two types of mesh for a planar structure: a pure triangular and a hybrid triangular-rectangular. In both case, EM.Picasso attempts to create a highly regular mesh, in which most of the cells have almost equal areas. The hybrid mesh type tries to produce as many rectangular cells as possible especially in the case of objects with rectangular or linear boundaries. In connection or junction areas between adjacent objects or close to highly curved boundaries, the use of triangular cells is clearly inevitable. EM.Picasso's default mesh type is hybrid. The uniformity or regularity of mesh is an important factor in warranting a stable MoM numerical solution.
The mesh density gives a measure of the number of cells per effective wavelength that are placed in various regions of your planar structure. The higher the mesh density, the more cells are created on the geometrical objects. Keep in mind that only the finite-sized objects of your structure are discretized. The free-space wavelength is defined as <math>\lambda_0 = \tfrac{2\pi f}{c}</math>, where f is the center frequency of your project and c is the speed of light in the free space. The effective wavelength is defined as <math>\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, where e<sub>eff</sub> is the effective permittivity. By default, [[EM.Picasso]] generates a hybrid mesh with a mesh density of 20 cells per effective wavelength. The effective permittivity is defined differently for different types of traces and embedded object sets. This is to make sure that enough cells are placed in areas that might feature higher field concentration. For PEC and conductive sheet traces, the effective permittivity is defined as the larger of the permittivity of the two substrate layers just above and below the metallic trace. For slot traces, the effective permittivity is defined as the mean (average) of the permittivity of the two substrate layers just above and below the metallic trace. For embedded object sets, the effective permittivity is defined as the largest of the permittivities of all the substrate layers and embedded dielectric sets.
The most important rule of object connections in EM.Picasso is that only objects belonging to the same trace can be connected to one another. For example, if two objects reside on the same Z-plane and geometrically have a common edge which you can clearly see in the project workspace, but organizationally they belong to two different metal traces, then the bridge basis functions will not be generated between them, and the simulation engine will see them disconnected. If two objects belong to the same trace and have a common overlap area, [[EM.Picasso]] first merges the two objects using the "Boolean Union" operation and converts them into a single object for the purpose of meshing. The mesh of "unioned" areas is usually made up of triangular cells.
