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<td> [[Image:FDTD5E.png|thumb|left|300px320px|The Add New Material dialog.]]
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<td> [[Image:FDTD5F.png|thumb|left|600px720px|A new custom material entry in the Materials List.]] </td>
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== Calculating Scattering Parameters Using Prony's Method ==
[[EM.Picasso]] provides a special source type called '''[[Glossary of EMGlossary_of_EM.Cube's Excitation Sourcess_Materials,_Sources,_Devices_&_Other_Physical_Object_Types#Scattering Wave Port Scattering_Wave_Port | Scattering Wave Port]]''' that is specifically intended for computing the S-parameters of planar structures. This is done by analyzing the current distribution patterns on the port transmission lines. The discontinuity at the end of a port line (junction region) gives rise to a standing wave pattern in the line's current distribution. From the location of the current minima and maxima and their relative levels, one can determine the reflection coefficient at the discontinuity, <i>i.e.</i> the S<sub>11</sub> parameter. A more rigorous technique is Prony’s method, which is used for exponential approximation of functions. A complex function f(x) can be expanded as a sum of complex exponentials in the following form:
:<math> f(x) \approx \sum_{n=1}^N c_i e^{-j\gamma_i x} </math>
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<td> [[Image:PMOM49.png|thumb|left|480px|Defining gap sources on an array of rectangle strip objects.]] </td><td> [[Image:PMOM49_2nd.png|thumb|left|480px|Defining gap sources on an array of rectangle strip objects with a Chebyshev amplitude distribution.]] </td>
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<br />
<b> The Nonlinear Diode Device </b>
A diode is a rectifying device. The time-domain relationship between the voltage and current of a diode is given by the nonlinear equation:
# Click the '''Mesh Settings''' [[File:mesh_settings.png]] button of the Simulate Toolbar.
# The Mesh Settings dialog of the currently c=active [[EM.Cube]] module opens up.
# From the '''Host''' drop-down list, select a line object. Note that only line parallel to one of the three principal axes are listed.
# By default, the lumped source is placed at the midpoint of the host line object. You can modify the '''Offset''' parameter, which is measured from the start point of the line and is always positive.
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<td> [[Image:PO2.png|thumb|360px420px|Two ellipsoids of different compositions.]] </td></tr><tr><td> [[Image:PO3.png|thumb|360px420px|Trinagular surface mesh of the two ellipsoids.]] </td>
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=The following general rules apply to [[EM.Cube]]'s surface mesh generators: * The surface mesh generator merges all the objects that belong to the same group in the navigation Tree using the Boolean Union operation before meshing. The union operation is carried out temporarily and solely for the purpose of mesh generation. * As a result of the Boolean union operation, all the overlapping objects are transformed into a single consolidated object leading to a contiguous and consistent mesh in the transition and junction areas between connected objects. * In general, objects of the same CAD category can be "unioned". For example, surface objects can be merged together, and so can solid objects. However, a surface object and a solid in general do not merge. * In general, objects that belong to different groups on the navigation tree are not merged during mesh generation even if they have the same material composition and physically overlap.* Only [[EM.Libera]]'s surface mesh generator creates a special junction mesh between overlapping objects that have different material compositions. * All '''Polymesh''' objects as well as [[EM.Terrano]]'s terrain objects are considered already discretized and are not re-meshed once again by the surface mesh generator. == Controlling the Resolution & Quality of the Surface Mesh ===
You can control the average mesh cell size using the "Mesh Density" parameter. By default, the mesh density of [[EM.Illumina]] and [[EM.Libera]] is expressed in terms of the free-space wavelength. The default mesh density is 10 cells per wavelength. This usually creates slightly more than 100 regular triangular cells per squared wavelength. The default mesh density of [[EM.Picasso]] is expressed in terms of the effective wavelength, which takes into account the material properties of a planar structure's substrate layers. The default planar mesh density is 20 cells per effective wavelength. Alternatively, you can base the definition of the mesh density on "Cell Edge Length" expressed in project units. [[EM.Terrano]]'s mesh density is always expressed in cell edge length and its default value is 100 units. This large edge length is intended to create the fewest number of triangular facets on cubic objects with rectangular faces.
You can change the value of '''Mesh Density''' from the Mesh Settings dialog and generate a triangular mesh with a higher or lower resolution.
=== Refining the Surface Mesh Quality === Surface mesh generation in [[EM.Cube]] is a two-step process. First, a tessellated version of an object in your project workspace is created. Then, the tessellated object undergoes a surface re-meshing to generate regularized triangular cells. This process is fairly straightforward in the case of flat planar structures. For curved surfaces and curved [[Solid Objects|solid objects]], the quality of the initial tessellation of the object is very important and directly affects the quality of the final surface mesh. You can access some additional mesh [[parameters]] by clicking the {{key|Tessellation Options}} button of the Mesh Settings dialog. In the Tessellation Options dialog, you can change '''Curvature Angle Tolerance''' expressed in degrees, which as a default value of 15°. This parameter can affect the shape of the mesh especially in the case of solid CAD objects. It determines the apex angle of the triangular cells of the primary tessellation mesh which is generated initially before cell regularization. Lower values of the angle tolerance result in a less smooth and more pointed mesh of curved surface like a sphere.
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== General Rules of EM.Cube's Surface Mesh Generators ==
* The surface mesh generator merges all the objects that belong to the same group in the navigation Tree using the Boolean Union operation before meshing. The union operation is carried out temporarily and solely for the purpose of mesh generation.
* As a result of the Boolean union operation, all the overlapping objects are transformed into a single consolidated object leading to a contiguous and consistent mesh in the transition and junction areas between connected objects.
* In general, objects of the same CAD category can be "unioned". For example, surface objects can be merged together, and so can solid objects. However, a surface object and a solid in general do not merge.
* In general, objects that belong to different groups on the navigation tree are not merged during mesh generation even if they have the same material composition and physically overlap.
* Only [[EM.Libera]]'s surface mesh generator creates a special junction mesh between overlapping objects that have different material compositions.
* All '''Polymesh''' objects as well as [[EM.Terrano]]'s terrain objects are considered already discretized and are not re-meshed once again by the surface mesh generator.
== Locking the Mesh Density of Object Groups ==
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[[Image:MESH MAN12.png|thumb|left|480px600px|Locking the mesh density in the property dialog of a material group.]]
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[[Image:MESH MAN9.png|thumb|left|640px540px|The geometry of two dielectric spheres with the same material properties but belonging to two different object groups.]]
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[[Image:MESH MAN11.png|thumb|left|640px540px|The FDTD mesh of the two dielectric spheres. The left sphere is meshed using a global density of 20 cells/λ<sub>eff</sub>, while the right sphere is meshed using a locked density of 100 cells/λ<sub>eff</sub>.]]
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[[Image:MESH MAN10.png|thumb|left|640px540px|The top view of the mesh of the two dielectric spheres also showing the XY grid plane.]]
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