Figure 1: Planar hybrid and triangular meshes for rectangular patches.
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=== Generating A Planar Mesh ===
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The planar MoM mesh generation process involves three steps:
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# Setting the mesh properties
# Creating and viewing the mesh
# Verifying the mesh for integrity
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[[EM.Cube]]âs [[Planar Module]] offers two mesh generation algorithms for discretizing planar structures: Hybrid and Triangular. The hybrid mesh consists of both rectangular and triangular cells. The hybrid mesh generator creates a kind of âobject-centricâ mesh that depends on the geometry of each object. It tries to discretize rectangular objects with rectangular cells as much as possible. In certain connection areas, a few triangular cells might be inserted to provide the mesh transition for current continuity. All the non-rectangular objects (circular, polygonal, etc.) are discretized using triangular cells. The triangular mesh generator, on the other hand, discretizes the planar objects with all triangular cells regardless of their shape. The only exceptions are feed lines that contain gap sources or lumped elements, which are always meshed with rectangular cells.
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You can generate and view a planar mesh by clicking the '''Show Mesh''' [[File:mesh_tool.png]] button of the '''Simulate Toolbar''' or by selecting '''Menu > Simulate > Discretization > Show Mesh''' or using the keyboard shortcut '''Ctrl+M'''. When the mesh of the planar structure is displayed in [[EM.Cube]]âs project workspace, its "Mesh View" mode is enabled. In this mode you can perform view operations like rotate view, pan or zoom, but you cannot create new objects or edit existing ones. To exit the mesh view mode, press the keyboard's '''Esc Key''' or click the '''Show Mesh''' [[File:mesh_tool.png]] button once again.
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Once a mesh is generated, it stays in the memory until the structure is changed or the mesh density or other settings are modified. Every time you view mesh, the one in the memory is displayed. You can force [[EM.Cube]] to create a new mesh from the ground up by selecting '''Menu > Simulate > Discretization > Regenerate Mesh''' or by right clicking on the '''Planar Mesh''' item in the '''Discretization''' section of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.
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=== Mesh Of Connected Trace Objects ===
Using the generated mesh of a planar structure, [[EM.Cube]] creates a set of vectorial basis functions that are passed to the input file of the Planar MoM simulation engine. This engine requires edge-based basis functions. The common edges between adjacent cells are used to define edge-based rooftop or RWG basis functions. These elementary basis functions indeed provide the current flow and warrant the continuity among the mesh cells. Therefore, when two objects overlap or share a common edge, the connection between them must be translated into "bridge" basis functions, which carry the information about current flow to the simulation engine.
Figure 2: Edge-connected rectangular planar objects and their triangular and hybrid planar meshes.
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=== Mesh of Embedded Objects ===
[[EM.Cube]]'s [[Planar Module]] models embedded objects as vertical volume currents. The vectorial basis functions in this case are Z-directed prisms as opposed to rooftop basis functions. If an embedded object is located under or above a metallic trace or connected from both top and bottom, it is critical to create mesh continuity between the embedded object and its connected metallic traces. In other words, the generated mesh must ensure current continuity between the vertical volume currents and horizontal surface currents. [[EM.Cube]]âs planar mesh generator automatically handles situations of this kind and generates all the required connection meshes.
Mesh of a vertical PEC via connecting two horizontal metallic strips. The shorter via has one prismatic cell along the Z direction, while the longer via is discretized into several stacked cells.
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=== Generating A Planar Mesh ===
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The planar MoM mesh generation process involves three steps:
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# Setting the mesh properties
# Creating and viewing the mesh
# Verifying the mesh for integrity
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[[EM.Cube]]âs [[Planar Module]] offers two mesh generation algorithms for discretizing planar structures: Hybrid and Triangular. The hybrid mesh consists of both rectangular and triangular cells. The hybrid mesh generator creates a kind of âobject-centricâ mesh that depends on the geometry of each object. It tries to discretize rectangular objects with rectangular cells as much as possible. In certain connection areas, a few triangular cells might be inserted to provide the mesh transition for current continuity. All the non-rectangular objects (circular, polygonal, etc.) are discretized using triangular cells. The triangular mesh generator, on the other hand, discretizes the planar objects with all triangular cells regardless of their shape. The only exceptions are feed lines that contain gap sources or lumped elements, which are always meshed with rectangular cells.
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You can generate and view a planar mesh by clicking the '''Show Mesh''' [[File:mesh_tool.png]] button of the '''Simulate Toolbar''' or by selecting '''Menu > Simulate > Discretization > Show Mesh''' or using the keyboard shortcut '''Ctrl+M'''. When the mesh of the planar structure is displayed in [[EM.Cube]]âs project workspace, its "Mesh View" mode is enabled. In this mode you can perform view operations like rotate view, pan or zoom, but you cannot create new objects or edit existing ones. To exit the mesh view mode, press the keyboard's '''Esc Key''' or click the '''Show Mesh''' [[File:mesh_tool.png]] button once again.
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Once a mesh is generated, it stays in the memory until the structure is changed or the mesh density or other settings are modified. Every time you view mesh, the one in the memory is displayed. You can force [[EM.Cube]] to create a new mesh from the ground up by selecting '''Menu > Simulate > Discretization > Regenerate Mesh''' or by right clicking on the '''Planar Mesh''' item in the '''Discretization''' section of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.
=== Planar Mesh Density ===