[[Image:Info_icon.png|30px]] Click here to access '''[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]]'''.
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== Discretizing a Physical Structure Using a Mesh Generator in EM.Cube ==
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In order to transform a physical modeling problem into a computational problem that can be solved using a numerical technique, your physical structure must first be discretized into simple canonical elements or mesh cells.
[[EM.Cube]]'s computational modules use a number of different mesh generation schemes to discretize physical structures. Even [[Building Geometrical Constructions in CubeCAD | CubeCAD]] provides several tools for object discretization. In general, all of [[EM.Cube]]'s mesh generation schemes can be grouped into three categories based on dimensionality:
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#Linear Mesh
#Surface Mesh
#Volume Mesh
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The linear mesh, also known as the wireframe mesh, is used by [[EM.Libera]] to discretize the physical structure for Wire MoM simulation. [[EM.Cube]] offers two types of surface mesh: triangular surface mesh and hybrid surface mesh. As its name implies, a triangular surface mesh is made up of interconnected triangular cells. [[EM.Terrano]], [[EM.Illumina]], [[EM.Libera]] and [[EM.Picasso]] all use triangular surface mesh generators to discretize surface geometric objects as well as the surface of solid geometric objects. The hybrid surface mesh is [[EM.Picasso]]'s default mesh. It combines rectangular and triangular cells to discretize planar structures. The hybrid surface mesh generator tries to produce as many identical rectangular cells as possible in rectangular regions of your planar structure.
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[[EM.Cube]] provides two types of brick mesh, also known as voxel mesh, to discretize the volume of your computational domain. Brick meshes are entire-domain volume meshes and are made up of cubic cells. They are generated by a three-dimensional arrangement of grid lines along the X, Y and Z axes. [[EM.Tempo]] offers an "Adaptive" brick mesh as well as a "Fixed-Cell" brick mesh for the FDTD simulation of your physical structure. [[EM.Ferma]] offers only a fixed-mesh brick mesh for the solution of electrostatic and magnetostatic Laplace/Poisson equations.
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<table>
<tr>
<td> [[Image:Mesh1_new.png|thumb|left|240px|The geometry of a metallic torus.]] </td>
<td> [[Image:Mesh2_new.png|thumb|left|240px|The brick volume mesh of the metallic torus.]] </td>
<td> [[Image:Mesh3_new.png|thumb|left|240px|The triangular surface mesh of the metallic torus.]] </td>
</tr>
</table>
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The objects of your physical structure are discretized based on a specified mesh density. The default mesh densities of [[EM.Tempo]], [[EM.Picasso]], [[EM.Libera]] and [[EM.Illumina]] are expressed as the number of cells per effective wavelength. Therefore, the resolution of the default mesh in these modules is frequency-dependent. You can also define the mesh resolution using a fixed cell size or fixed edge length specified in project units. The mesh density of [[EM.Terrano]] is always expressed in terms of cell edge length. The mesh resolution of [[EM.Ferma]] is always specified as the fixed cell size. All of [[EM.Cube]]'s computational modules have default mesh settings that usually work well for most simulations.
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The accuracy of the numerical solution of an electromagnet problem depends very much on the quality and resolution of the generated mesh. As a rule of thumb, a mesh density of about 10-25 cells per effective wavelength usually yields satisfactory results. Yet, for structures with lots of fine geometrical details or for highly resonant structures, higher mesh densities may be required. The particular simulation data you seek in a project also influences your choice of mesh resolution. For example, far-field characteristics like radiation patterns are less sensitive to the mesh density than the near-field distributions on a structure with a highly irregular shape and a rugged boundary.
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The table below compares [[EM.Cube]]'s computational modules with regards to their mesh generator types:
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{| class="wikitable"
|-
! scope="col"|
! scope="col"| Module Name
! scope="col"| Mesh Type
|-
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:450px;" | Adaptive and fixed-cell volumetric brick (voxel) mesh
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:450px;" | Triangular facet mesh
|-
| style="width:40px;" | [[image:static-ico.png | link=[[EM.Ferma]]]]
| [[EM.Ferma]]
| style="width:450px;" | Fixed-cell volumetric brick mesh
|-
| style="width:40px;" | [[image:planar-ico.png | link=[[EM.Picasso]]]]
| [[EM.Picasso]]
| style="width:450px;" | Hybrid rectangular-triangular surface mesh
|-
| style="width:40px;" | [[image:metal-ico.png | link=[[EM.Libera]]]]
| [[EM.Libera]]
| style="width:450px;" | Wireframe and triangular surface mesh
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:450px;" | Triangular surface mesh
|}
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[[Image:Info_icon.png|30px]] Click here to access '''[[Glossary of EM.Cube's Mesh Generators & Simulation-Related Operations]]'''.
== Defining Simulation Observables in EM.Cube ==
[[Image:Info_icon.png|30px]] Click here to access '''[[Glossary of EM.Cube's Simulation Observables]]'''.
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== Discretizing a Physical Structure Using a Mesh Generator in EM.Cube ==
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In order to transform a physical modeling problem into a computational problem that can be solved using a numerical technique, your physical structure must first be discretized into simple canonical elements or mesh cells.
[[EM.Cube]]'s computational modules use a number of different mesh generation schemes to discretize physical structures. Even [[Building Geometrical Constructions in CubeCAD | CubeCAD]] provides several tools for object discretization. In general, all of [[EM.Cube]]'s mesh generation schemes can be grouped into three categories based on dimensionality:
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#Linear Mesh
#Surface Mesh
#Volume Mesh
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The linear mesh, also known as the wireframe mesh, is used by [[EM.Libera]] to discretize the physical structure for Wire MoM simulation. [[EM.Cube]] offers two types of surface mesh: triangular surface mesh and hybrid surface mesh. As its name implies, a triangular surface mesh is made up of interconnected triangular cells. [[EM.Terrano]], [[EM.Illumina]], [[EM.Libera]] and [[EM.Picasso]] all use triangular surface mesh generators to discretize surface geometric objects as well as the surface of solid geometric objects. The hybrid surface mesh is [[EM.Picasso]]'s default mesh. It combines rectangular and triangular cells to discretize planar structures. The hybrid surface mesh generator tries to produce as many identical rectangular cells as possible in rectangular regions of your planar structure.
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[[EM.Cube]] provides two types of brick mesh, also known as voxel mesh, to discretize the volume of your computational domain. Brick meshes are entire-domain volume meshes and are made up of cubic cells. They are generated by a three-dimensional arrangement of grid lines along the X, Y and Z axes. [[EM.Tempo]] offers an "Adaptive" brick mesh as well as a "Fixed-Cell" brick mesh for the FDTD simulation of your physical structure. [[EM.Ferma]] offers only a fixed-mesh brick mesh for the solution of electrostatic and magnetostatic Laplace/Poisson equations.
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<table>
<tr>
<td> [[Image:Mesh1_new.png|thumb|left|240px|The geometry of a metallic torus.]] </td>
<td> [[Image:Mesh2_new.png|thumb|left|240px|The brick volume mesh of the metallic torus.]] </td>
<td> [[Image:Mesh3_new.png|thumb|left|240px|The triangular surface mesh of the metallic torus.]] </td>
</tr>
</table>
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The objects of your physical structure are discretized based on a specified mesh density. The default mesh densities of [[EM.Tempo]], [[EM.Picasso]], [[EM.Libera]] and [[EM.Illumina]] are expressed as the number of cells per effective wavelength. Therefore, the resolution of the default mesh in these modules is frequency-dependent. You can also define the mesh resolution using a fixed cell size or fixed edge length specified in project units. The mesh density of [[EM.Terrano]] is always expressed in terms of cell edge length. The mesh resolution of [[EM.Ferma]] is always specified as the fixed cell size. All of [[EM.Cube]]'s computational modules have default mesh settings that usually work well for most simulations.
Â
The accuracy of the numerical solution of an electromagnet problem depends very much on the quality and resolution of the generated mesh. As a rule of thumb, a mesh density of about 10-25 cells per effective wavelength usually yields satisfactory results. Yet, for structures with lots of fine geometrical details or for highly resonant structures, higher mesh densities may be required. The particular simulation data you seek in a project also influences your choice of mesh resolution. For example, far-field characteristics like radiation patterns are less sensitive to the mesh density than the near-field distributions on a structure with a highly irregular shape and a rugged boundary.
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The table below compares [[EM.Cube]]'s computational modules with regards to their mesh generator types:
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{| class="wikitable"
|-
! scope="col"|
! scope="col"| Module Name
! scope="col"| Mesh Type
|-
| style="width:40px;" | [[image:fdtd-ico.png | link=[[EM.Tempo]]]]
| [[EM.Tempo]]
| style="width:450px;" | Adaptive and fixed-cell volumetric brick (voxel) mesh
|-
| style="width:40px;" | [[image:prop-ico.png | link=[[EM.Terrano]]]]
| [[EM.Terrano]]
| style="width:450px;" | Triangular facet mesh
|-
| style="width:40px;" | [[image:static-ico.png | link=[[EM.Ferma]]]]
| [[EM.Ferma]]
| style="width:450px;" | Fixed-cell volumetric brick mesh
|-
| style="width:40px;" | [[image:planar-ico.png | link=[[EM.Picasso]]]]
| [[EM.Picasso]]
| style="width:450px;" | Hybrid rectangular-triangular surface mesh
|-
| style="width:40px;" | [[image:metal-ico.png | link=[[EM.Libera]]]]
| [[EM.Libera]]
| style="width:450px;" | Wireframe and triangular surface mesh
|-
| style="width:40px;" | [[image:po-ico.png | link=[[EM.Illumina]]]]
| [[EM.Illumina]]
| style="width:450px;" | Triangular surface mesh
|}
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[[Image:Info_icon.png|30px]] Click here to access '''[[Glossary of EM.Cube's Mesh Generators & Simulation-Related Operations]]'''.
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