[[Image:Splash-static.jpg|right|800px720px]]<strong><font color="#0d10e52603c4" size="4">Electrostatic and , Magnetostatic & Thermal Solvers For DC And Low Frequency Simulations</font></strong>
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<td>[[image:Cube-icon.png | link=Getting_Started_with_EM.Cube]] [[image:cad-ico.png | link=Building_Geometrical_Constructions_in_CubeCAD]] [[image:fdtd-ico.png | link=EM.Tempo]] [[image:prop-ico.png | link=EM.Terrano]] [[image:poplanar-ico.png | link=EM.IlluminaPicasso]] [[image:planarmetal-ico.png | link=EM.PicassoLibera]] [[image:metalpo-ico.png | link=EM.LiberaIllumina]] </td>
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[[Image:Tutorial_icon.png|40px30px]] '''[[EM.Cube#EM.Ferma_Tutorial_Lessons Ferma_Documentation | EM.Ferma Tutorial Gateway]]'''
[[Image:Back_icon.png|40px30px]] '''[[EM.Cube | Back to EM.Cube Main Page]]'''
==Product Overview==
=== EM.Ferma in a Nutshell ===
[[Image:STAT7 11.png|thumb|400px| Vector plot of electric field distribution in a microstrip transmission line.]][[EM.Ferma]] is a 3D static solver. It features two distinct electrostatic and magnetostatic simulation engines and a steady-state thermal simulation engine that can be used to solve a variety of static and low-frequency electromagnetic and thermal problems. Both The thermal solver includes both conduction and convection heat transfer mechanisms. All the three simulation engines are based on finite difference solutions of Poisson's equation for electric and magnetic potentialsand temperature.
With EM.Ferma, you can explore the electric fields due to volume charge distributions or fixed-potential perfect conductors, and magnetic fields due to wire or volume current sources and permanent magnets. Your structure may include dielectric or magnetic (permeable) material blocks. Using the thermal simulator, you can solve for the steady-state temperature distribution of structures that include perfect thermal conductors, insulators and volume heat sources. You can also use EM.Ferma's 2D quasi-static mode to compute the characteristic impedance (Z0) and effective permittivity of transmission line structures with complex cross section profiles.
[[Image:Tutorial_iconInfo_icon.png|40px30px]] Click here to access learn more about the '''[[EMElectrostatic & Magnetostatic Field Analysis | Theory of Electrostatic and Magnetostatic Methods]]'''.Cube#EM [[Image:Info_icon.Ferma_Tutorial_Lessons png| EM.Ferma Tutorial Gateway30px]] Click here to learn more about the '''[[Steady-State_Thermal_Analysis | Theory of Steady-State Heat Transfer Methods]]'''. <table><tr><td>[[Image:Magnet lines1.png|thumb|left|400px| Vector plot of magnetic field distribution in a cylindrical permanent magnet.]]</td></tr></table>
=== EM.Ferma as the Static Module of EM.Cube ===
EM.Ferma is the low-frequency '''Static Module''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Ferma shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as [[Building_Geometrical_Constructions_in_CubeCAD | CubeCAD ]] with all of [[EM.Cube]]'s other computational modules.
[[Image:Info_icon.png|40px30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.
[[Image:Info_icon=== Advantages & Limitations of EM.png|40px]] Click here to learn Ferma's Static Simulator === EM.Ferma computes the electric and magnetic fields independent of each other based on electrostatic and magnetostatic approximations, respectively. As a result, any "electromagnetic" coupling effects or wave retardation effects are ignored in the simulation process. In exchange, static or quasi-static solutions are computationally much more about efficient than the basic functionality full-wave solutions of Maxwell'''s equations. Therefore, for low-frequency electromagnetic modeling problems or for simulation of sub-wavelength devices, EM.Ferma offers a faster alternative to [[Building_Geometrical_Constructions_in_CubeCAD | CubeCADEM.Cube]]'''s full-wave modules like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]]. EM.Ferma currently provides a fixed-cell brick volume mesh generator. To model highly irregular geometries or curved objects, you may have to use very small cell sizes, which may lead to a large computational problem. <table><tr><td>[[Image:Ferma L8 Fig title.png|thumb|left|400px| Vector plot of electric field distribution in a coplanar waveguide (CPW) transmission line.]]</td></tr></table>
== EM.Ferma Features at a Glance ==
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Metal Perfect electric conductor(PEC) solids and surfaces in free space (Electrostatics)</li>
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Dielectric objects in free space (Electrostatics)</li>
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Magnetic (permeable) objects in free space (Magnetostatics)</li> <li> Perfect thermal conductor (PTC) solids and surfaces (Thermal)</li> <li> Insulator objects (Thermal)</li>
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Fixed-potential PEC for maintaining equi-potential metal objects(Electrostatics)</li> <li> Volume charge sources (Electrostatics)</li> <li> Volume current sources (Magnetostatics)</li>
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Volume charge Wire current sources(Magnetostatics)</li>
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Volume current sourcesPermanent magnets (Magnetostatics)</li>
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Wire current sourcesFixed-temperature PTC for maintaining iso-thermal objects (Thermal)</li>
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Permanent magnetsVolume heat sources (Thermal)</li>
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Optimization of transmission line's parameters for impedance design</li>
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=== Steady-State Thermal Simulation ===
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Finite difference solution of Laplace and Poisson equations for the temperature with Dirichlet and Neumann domain boundary conditions </li>
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Calculation of temperature and heat flux density</li>
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Calculation of thermal energy density on field sensor planes</li>
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Calculation of thermal flux over user defined flux boxes</li>
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Calculation of thermal energy</li>
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Electric and magnetic field intensity and vector plots on planes</li>
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Electric and magnetic potential intensity plotson planes</li> <li> Temperature and heat flux intensity and vector plots on planes</li> <li> Electric and magnetic energy density, dissipated power density and thermal energy density plots on planes</li>
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Animation of field and potential plots after parametric sweeps</li>
Custom output parameters defined as mathematical expressions of standard outputs</li>
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[[Image:STAT4 14.png|thumb|left|480px| Vector plot of magnetic field distribution in between two permanent magnets.]]
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== A Static Simulation Primer ==
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=== Static Modeling Methods ===
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Static or quasi-static approximations of Maxwell's equations can be reliably applied in two different cases: at low frequencies from DC to a few Megahertz, or when the total electrical size of your physical structure is a fraction of the wavelength and wave retardation effects are negligible. In the latter case, your physical structure is effectively considered as a lumped device. Under those conditions, the electric and magnetic fields decouple from each other. Electric fields can be computed from charge sources or their equivalents and magnetic fields can be computed from current sources or their equivalents.
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[[Image:Info_icon.png|40px]] Click here to learn more about the '''[[Electrostatic and Magnetostatic Methods | Theory of Electrostatic and Magnetostatic Methods]]'''.
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=== Advantages & Limitations of EM.Ferma's Static Simulator ===
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EM.Ferma computes the electric and magnetic fields independent of each other based on electrostatic and magnetostatic approximations, respectively. As a result, any "electromagnetic" coupling effects or wave retardation effects are ignored in the simulation process. In exchange, static or quasi-static solutions are computationally much more efficient than the full-wave solutions of Maxwell's equations. Therefore, for low-frequency electromagnetic modeling problems or for simulation of sub-wavelength devices, EM.Ferma offers a faster alternative to [[EM.Cube]]'s full-wave modules like [[EM.Tempo]], [[EM.Picasso]] or [[EM.Libera]]. EM.Ferma currently provides a fixed-cell brick volume mesh generator. To model highly irregular geometries or curved objects, you may have to use very small cell sizes, which may lead to a large computational problem.
== Building the Physical Structure in EM.Ferma ==
[[Image:Static7.png|thumb|270px| EM.Ferma's Navigation Tree.]]The simplest static problems involve a charge source === Variety of Physical Objects in the free space that produces an electric field, or a current source in the free space that produces a magnetic field. In such cases, the only applicable boundary conditions are defined at the computational domain boundary. As soon as you introduce a dielectric object next to a charge source or a magnetic (permeable) material next to a current source, you have to deal with a complex boundary value problem. In other words, you need to solve the electric or magnetic Poisson's equation subject to the domain boundary conditions as well as material interface boundary conditions. EM.Ferma used the Finite Difference technique for numerical solution of your static boundary value problem. ===
=== A Note on Material and Source Types The simplest static problems involve a charge source in the free space that produces an electric field, or a current source in the free space that produces a magnetic field. In such cases, the only applicable boundary conditions are defined at the boundary of the computational domain. As soon as you introduce a dielectric object next to a charge source or a magnetic (permeable) material next to a current source, you have to deal with a complex boundary value problem. In other words, you need to solve the electric or magnetic Poisson equation subject to the domain boundary conditions as well as material interface boundary conditions. The simplest thermal problem involves one or more thermal plates held at fixed temperatures. Once you introduce material blocks, you have to enforce conductive and convective boundary conditions at the interface between different materials and air. EM.Ferma ===uses the Finite Difference (FD) technique to find a numerical solution of your static boundary value problem.
In [[EM.CubeFerma]]'s other modules, material offers the following types are specified under the "Physical Structure" section of the navigation tree, and sources are organized under a separate "Sources" section. In those modules, the physical structure and its various material types typically represent all the CAD objects you draw in your project. Sources are virtual entities that might be associated with certain physical objects and provide the excitation of your boundary value problem. :
In {| class="wikitable"|-! scope="col"| Icon! scope="col"| Physical Object Type! scope="col"| Applications! scope="col"| Geometric Object Types Allowed! scope="col"| Notes & Restrictions|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:200px;" | [[Glossary of EM.FermaCube's Materials, materials Sources, Devices & Other Physical Object Types#Fixed-Potential PEC |Fixed-Potential Perfect Electric Conductor (PEC)]]| style="width:300px;" | Modeling perfect metals with a fixed voltage| style="width:100px;" | Solid and sources are all listed under surface objects| style="width:250px;" | Can be considered an electric source if the fixed voltage is nonzero |-| style="Physical Structurewidth:30px;" | [[File:diel_group_icon.png]]| style="width:200px;" section | [[Glossary of the navigation treeEM. In other wordsCube's Materials, there is no separate "Sources, Devices & Other Physical Object Types#Dielectric Material |Dielectric/Magnetic Material]]| style="width:300px;" | Modeling any homogeneous or inhomogeneous material| style="width:100px;" | Solid objects| style="width:250px;" | non-source material|-| style="width:30px;" section| [[File:aniso_group_icon. For examplepng]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, you can define default zero-potential perfect electric conductors Sources, Devices & Other Physical Object Types#Volume Charge |Volume Charge]]| style="width:300px;" | Modeling volume charge sources with a fixed charge density or an expression in the global coordinates (PECx,y,z) in your project to model metal | style="width:100px;" | Solid objects| style="width:250px;" | Acts as an electric source|-| style="width:30px;" | [[File:voxel_group_icon. You can also define png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Volume Current |Volume Current]]| style="width:300px;" | Modeling volume current sources with a fixed-potential PEC volume current density vector or expressions in the global coordinates (x,y,z) | style="width:100px;" | Solid objects | style="width:250px;" | Acts as a magnetic source|-| style="width:30px;" | [[File:pmc_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Permanent Magnet |Permanent Magnet]]| style="width:300px;" | Modeling permanent magnet sources with a nonzero voltagefixed magnetization vector or expressions in the global coordinates (x, which can effectively act y,z) | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a voltage magnetic source for your boundary value problem|-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:200px;" | [[Glossary of EM. In this caseCube's Materials, you will solve the Lapalce equation subject to the specified nonzero potential boundary valuesSources, Devices & Other Physical Object Types#Wire Current |Wire Current]]| style="width:300px;" | Modeling wire current sources| style="width:100px;" | Line and polyline objects| style="width:250px;" | Acts as a magnetic source|-| style="width:30px;" | [[File:pec_group_icon. Both types png]]| style="width:200px;" | [[Glossary of PEC EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Fixed-Temperature PTC |Fixed-Temperature Perfect Thermal Conductor (PTC)]]| style="width:300px;" | Modeling isothermal surfaces with a fixed temperature| style="width:100px;" | Solid and surface objects are defined from | style="width:250px;" | Can be considered a thermal source if the fixed temperature is different than the ambient temperature (shares the same PEC navigation tree node as PEC object)|-| style="width:30px;" | [[File:diel_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Dielectric Material |Insulator Material]]| style="width:300px;" | Modeling any homogeneous or inhomogeneous material| style="width:100px;" | Solid objects| style="width:250px;" | non-source material (shares the same navigation tree by assigning different voltage valuesnode as dielectric material)|-| style="width:30px;" | [[File:aniso_group_icon. Charge and current png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Volume Heat Source |Volume Heat Source]]| style="width:300px;" | Modeling volume heat sources are defined as CAD with a fixed heat density or an expression in the global coordinates (x,y,z) | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a thermal source (shares the same navigation tree node as volume charge)|-| style="width:30px;" | [[File:Virt_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, and you have Sources, Devices & Other Physical Object Types#Virtual_Object_Group | Virtual Object]]| style="width:300px;" | Used for representing non-physical items | style="width:100px;" | All types of objects| style="width:250px;" | None|}Â Click on each category to draw them learn more details about it in the project workspace just like other material objects[[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].
=== Grouping Objects by Material or Source Type ===
Your physical structure in EM.Ferma is typically made up of some kind of source object either in the free space or in the presence of one or more material objects. EM.Ferma's electrostatic and magnetostatic or thermal simulation engines then discretize the entire computational domain including these source and material objects and solve the Laplace or Poisson equations to find the electric or magnetic fields or temperature everywhere in the computational domain.
All the CAD geometric objects in the project workspace are organized together into object groups which share the same properties including color and electric or magnetic [[parameters]]. Once a new It is recommended that you first create object group node has been created on the navigation treegroups, it becomes the "Active" object group of the project workspace, which is always listed in bold letters. When you and then draw a new CAD object such as a Box or a Sphere, it is inserted objects under the currently active surface typegroup. There is only one To create a new object group that is active at any time. Any group can be made active by , right clicking -click on its category name in the "Physical Structure" section of the navigation tree and selecting the '''Activate''' item select one of the "Insert New Group..." items from the contextual menu. It is recommended that you first create object groups, and then draw new objects under the active surface group. However, if you start a new EM.Ferma project from scratch, and start drawing a new object without having previously defined any object groups, a new default "Fixed-Potential PEC " object group with a zero voltage is created and added to the navigation tree to hold your new CAD geometric object.
[[Image:Info_icon.png|40px]] Click here It is important to learn more about '''[[Defining_Materials_in_EM.Cube#Defining_a_New_Material_Group | Defining note that there is a New Object Group]]'''.one-to-one correspondence between electrostatic and thermal simulation entities:
[[Image{| class="wikitable"|-! scope="col"| Electrostatic Item! scope="col"| Corresponding Thermal Item|-| style="width:200px;" | Electric Scalar Potential| style="width:200px;" | Temperature|-| style="width:200px;" | Electric Field| style="width:200px;" | Heat Flux Density|-| style="width:200px;" | Perfect Electric Conductor| style="width:200px;" | Perfect Thermal Conductor|-| style="width:200px;" | Dielectric Material| style="width:200px;" | Insulator Material|-| style="width:200px;" | Volume Charge| style="width:Info_icon.png200px;" |40px]] Click here to learn more about '''[[Defining_Materials_in_EM.Cube#Moving_Objects_among_Material_Groups Volume Heat Source| Moving Objects among Different Groups]]'''.}
=== Variety of Material Objects ==={{Note|Electrostatic and thermal solvers share the same material categories on the navigation tree. This means that PEC objects are treated as PTC objects, dielectric objects are treated as insulator objects and volume charges are treated as volume heat sources when the thermal solver is enabled.}}
[[Image:Static1Once a new object group node has been created in the navigation tree, it becomes and remains the "Active" object group, which is always listed in bold letters.png|thumb|330px| EMWhen you draw a new geometric object such as a box or a sphere, its name is added under the currently active object group.Ferma's PEC dialogThere is only one object group that is active at any time.]] EM.Ferma offers Any group can be made active by right-clicking on its name in the following types navigation tree and selecting the '''Activate''' item of material objects for construction of your physical structure (click on each type to learn more about it):the contextual menu.
* '''[[Defining_Materials_in_EM.Cube#Perfect_Electric_Conductors_.26_Metal_Traces | Perfect Electric Conductors (PEC)]]''': A perfect electric conductor (PEC) is a material with ε<sub>r</sub> = 1 and σ = ∞. * '''[[Defining_Materials_in_EM.Cube#Defining_Dielectric_Materials | Dielectric/Magnetic Materials]]''': You can define dielectric materials with the relative permittivity ε<sub>r</sub> and electric conductivity σ for electrostatic analysis or magnetic (permeable) materials with the relative permeability μ<sub>r</sub> for magnetostatic analysis. [[Image:Info_icon.png|40px30px]] Click here for a general discussion of to learn more about '''[[Defining Materials Building Geometrical Constructions in EM.Cube]]'''. {{Note| You can define any solid CubeCAD#Transferring Objects Among Different Groups or surface object as a fixed-potential PEC object.}} {{NoteModules | Excluding surface and curve CAD objects, you can define any solid CAD object as a dielectric or magnetic material object.}} === Variety of Source Objects === EM.Ferma also offers the following types of source objects for excitation of your physical structure: * '''[[#Using_Fixed-Potential_PEC_Objects_as_Voltage_Sources | Fixed-Potential PEC Moving Objectsamong Different Groups]]'''* '''Volume Charges''': For volume charge sources you need to specify a positive or negative charge density in C/m<sup>3</sup>. You can draw all kinds of solid CAD objects under this group.* '''Volume Currents''': For volume current sources you need to specify a current density in A/m<sup>2</sup>. You can draw all kinds of solid CAD objects under this group. Note that current density is a vectorial quantity and has a magnitude and a unit direction vector.* '''[[#Wire_Current_Sources | Wire Currents]]'''* '''[[#Permanent_Magnets | Permanent Magnets]]'''
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<td> [[Image:Static3STAT MAN1.png|thumb|330pxleft| EM.Ferma's Charge Source dialog.]] </td><td> [[Image:Static5.png|thumb|330px480px| EM.Ferma's Volume Current Source dialognavigation tree.]] </td>
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=== Using Fixed-Potential PEC Objects as Voltage Sources A Note on Material and Source Types in EM.Ferma ===
In [[Image:Static4.png|thumb|330px| EM.FermaCube]]'s Wire Current Source dialog.]] Under the static conditionother modules, every point on a PEC object has material types are categorized under the same electric potential. By default"Physical Structure" section of the navigation tree, this is and sources are organized under a zero potential, meaning the PEC object is separate "groundedSources"section. In EM.Ferma, a PEC group has a ''Fixed Potential''' property, which is expressed in Volts and has a zero default value. If you define a new PEC group and keep its default zero voltagethose modules, all the geometric objects belonging to that group will simply act as metal objects of you draw in your physical structureproject workspace typically represent material bodies. However, you can define a nonzero voltage value All of [[EM.Cube]] modules except for a PEC groupEM. You can do in Ferma require at least one excitation source to be selected from the property dialog "Sources" section of the PEC group, which navigation tree before you can access by right-clicking on the group's name in the navigation tree and selecting '''Properties...''' from the contextual menu. In the case of run a nonzero voltage, all the PEC objects belonging to that group effectively turn into voltage sources. For example, two parallel PEC plates, one with a zero potential and the other with a nonzero potential represent a simple air-filled capacitor. Note that the voltage value can be positive or negativesimulation.
=== Wire Current In EM.Ferma, materials and sources are all lumped together and listed under the "Physical Structure" section of the navigation tree. In other words, there is no separate "Sources ===" section. For example, you can define default zero-potential perfect electric conductors (PEC) in your project to model metal objects. You can also define fixed-potential PEC objects with a nonzero voltage, which can effectively act as a voltage source for your boundary value problem. In this case, you will solve the Lapalce equation subject to the specified nonzero potential boundary values. Both types of PEC objects are defined from the same PEC node of the navigation tree by assigning different voltage values. Charge and current sources are also defined as geometric objects, and you have to draw them in the project workspace just like other material objects.
EM.Ferma allows you to define idealized wire current sources. You can use this source type to model filament currents or coils. Wire currents are defined using only line and polyline objects. You also need to define a current value I in Amperes and a wire radius r in the project units. The line or polyline object is then approximated as a volume current with a current density of J = I/(πr<sup>2</sup>) flowing along the line or polyline side's direction. All the wire current sources belonging to the same group have the same color, same current value and same wire radius. The direction of the current can be reversed in wire current sources.  To add a new wire current source group to a project, right-click on "Wire Currents" on the Navigation Tree, and select "Insert New Current Source..." From the Wire Current Source Dialog, you can change the default brown color of the source group or set the values of the Current and Wire Radius. There is also a check box for "Reverse Current Direction". Note that this will reverse the direction of all the wire currents belonging to the same group. When you draw a line or polyline object under a wire current group in the Navigation Tree, you will notice that direction arrows are placed on the drawn CAD object. You can draw any curve object in the project workspace and convert it to a polyline using [[EM.Cube]]'s Polygonize Tool.  {{Note| If you draw curve CAD objects under a wire current group, they will be permanently converted to polyline objects before running the simulation engine.}}  === Permanent Magnets=== [[Image:Static6.png|thumb|330px| EM.Ferma's Permanent Magnet Source dialog.]]A permanent magnet is typically a ferromagnetic material with a fixed inherent magnetization vector. As a result, it can be used as a source in an magnetostatic problem. When a permeable material has a permanent magnetization, the following relationship holds:  <math> \mathbf{B(r)} = {\mu} (\mathbf{H(r)} + \mathbf{M(r)} ) </math> where <b>M(r)</b> is the magnetization vector. In SI units system, the magnetic field <b>H</b> and magnetization <b>M</b> both have the same units of A/m.  It can be shown that for magnetostatic analysis, the effect of the permanent magnetization can be modeled as an equivalent volume current source: <math> \mathbf{J_{eq}(r)} = \nabla \times \mathbf{M(r)} </math> If the magnetization vector is uniform and constant inside the volume, then its curl is zero everywhere inside the volume except on its boundary surface. In this case, the permanent magnetic can be effectively modeled by an equivalent surface current density on the surface of the permanent magnetic object:  <math> \mathbf{J_{s,eq}(r)} = \mathbf{M(r)} \times \hat{\mathbf{n}} </math> where <math> \hat{\mathbf{n}} </math> is the unit outward normal vector at the surface of the permanent magnet object. Note that the volume of the permanent magnet still acts as a permeable material in the magnetostatic analysis.  To add a new permanent magnet source group to a project, right-click on "Permanent Magnets" on the Navigation Tree, and select "Insert New Permanent Magnet Source..." From the Permanent Magnet Source Dialog, you can change the default purple color of the source group or set the values of the relative permeability, Magnetization magnitude and unit direction vector components. The default direction vector is z-directed. == Computational Domain and Discretization==
===The Domain Box===
To modify the domain settings, click the Domain button of the Simulate Toolbar or right-click on "3D Static Domain" entry in the Navigation Tree and select "Domain Settings..." from the contextual menu. In the Domain Settings Dialog, the computational domain can be defined in two different ways: Default and Custom. The default type places an enclosing box with a specified offset from the largest bounding box of your project's CAD objects. The default offset value is 20 project units, but you can change this value arbitrarily. The custom type defines a fixed domain box by specifying the coordinates of its two opposite corners labeled Min and Max in the world coordinate system.
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===Domain Boundary Conditions===
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EM.Ferma allows you to specify the electric potential boundary conditions on the domain box. Two options are available. The Dirichlet boundary condition is the default option and is specified as a fixed potential value on the surface of the domain walls. By default, this value is 0 Volts. The Neumann boundary condition specifies the normal derivative of the electric scalar potential on the surface of the domain walls. This is equivalent to the normal electric field component on the domain walls and its value is specified in V/m. The magnetostatic simulation engine always assumes Dirichlet domain boundary conditions and sets the values of the magnetic vector potential to zero on all the domain walls. To modify the boundary conditions, right-click on "Boundary Conditions" in the Navigation Tree, and select "Boundary Conditions..." from the contextual menu to open the Boundary Conditions Dialog.
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<td> [[Image:Qsource5.png|thumb|350pxleft|480px|EM.Ferma's Domain Settings dialog.]] </td><td> [[Image:fermbc.png|thumb|350px|EM.Ferma's Boundary Conditions dialog.]] </td>
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[[Image:Qsource4.png|thumb|350px|EM.Ferma's Mesh Settings dialog.]]===The Static MeshDomain Boundary Conditions===
The Finite Difference technique discretizes *EM.Ferma allows you to specify the electric potential boundary conditions on the computational domain using a 3D rectangular gridbox. EMTwo options are available.Ferma generates The Dirichlet boundary condition is the default option and is specified as a fixed-cell meshpotential value on the surface of the domain walls. By default, this value is 0 Volts. The Neumann boundary condition specifies the normal derivative of the electric scalar potential on the surface of the domain walls. This means that is equivalent to a constant normal electric field component on the extents domain walls and its value is specified in V/m.  *The magnetostatic simulation engine always assumes Dirichlet domain boundary conditions and sets the values of the mesh cells along magnetic vector potential to zero on all the principal axes are domain walls.  *EM.Ferma provides two options for thermal boundary conditions on the domain box. The Dirichlet boundary condition is the default option and is specified as a fixed: Δx, Δy, Δztemperature value on the surface of the domain walls. By default, this value is 0°C. The Neumann boundary condition specifies the mesh cell size normal derivative of the temperature on the surface of the domain walls. This is set equivalent to one unit project along all a constant heat flux passing through the three directions (with Δx = Δy = Δz)domain walls and its value is specified in W/m<sup>2</sup>. A zero heat flux means a perfectly insulated domain box and is known as the adiabatic boundary condition. To modify the cell sizeboundary conditions, click the Mesh Settings button of the Simulate Toolbar or right-click on "Static MeshBoundary Conditions" in the Navigation Treenavigation tree, and select "Mesh SettingsBoundary Conditions..." from the contextual menu to open the Mesh Settings Boundary Conditions Dialog. {{Note|To obtain accurate resultsWhen you switch from the electrostatic-magnetostatic solver to the thermal solver in EM.Ferma's Run Simulation dialog, it automatically checks the box labeled '''Treat as a Thermal Structure''' in the Boundary Conditions dialog. Conversely, if you check this box in the Boundary Conditions dialog, the solver type is highly recommended set to use a square mesh as much as possiblethe thermal solver in the Simulation Run dialog.}}In the "Global Thermal Properties" section of the Boundary Conditions dialog, you can set the values of the ambient temperature in °C, thermal conductivity of the environment in W/(m.K) and the convective coefficient in W/(m<sup>2</sup>.K). You can also disable the enforcement of the convective boundary condition on the surface of solid insulator objects.
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<td> [[Image:Qsource2fermbc.png|thumb|360pxleft|Geometry of a spherical charge source and the enclosing domain box480px|EM.]] </td><td> [[Image:Qsource3.png|thumb|360px|Fixed-cel mesh of the spherical charge objectFerma's Boundary Conditions dialog.]] </td>
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== Running Static Simulations in EM.Ferma 's Simulation Data & Observables ==
[[Image:Qsource6At the end of an electrostatic simulation, the electric field vector and electric scalar potential values are computed at all the mesh grid points of the entire computational domain.png|thumb|400px|EMAt the end of an magnetostatic simulation, the magnetic field vector and magnetic vector potential values are computed at all the grid nodes.Ferma's Simulation Run dialogAt the end of a thermal simulation, the temperature and heat flux vector are computed at all the mesh grid points of the entire computational domain.]] ===Two Simulation Engines===
Besides the electric and magnetic fields and temperature, EM.Ferma has two independent but functionally similar static simulation engines: Electrostatic and Magnetostaticcan compute a number of field integral quantities such as voltage, current, flux, energy, etc. The electrostatic engine solves the electric form of Poisson's equation for electric scalar potential subject to electric field boundary conditionscomponents, in the presence of electric sources (volume charges and fixed-potential PEC blocks) values and dielectric material mediafield integrals are written into output data files and can be visualized on the screen or graphed in Data Manager only if you define a field sensor or a field integral observable. The magnetostatic engine solves In the magnetic form absence of Poisson's equation for magnetic vector potential subject to magnetic field boundary conditions, any observable defined in the presence of magnetic sources (wire navigation tree, the static simulation will be carried out and volume currents and permanent magnetic blocks) and magnetic material mediacompleted, but no output simulation data will be generated.
In EM.Ferma you don't have to select any specific simulation engine. The program looks at offers the following types sources and material objects present in your project workspace and then it determines whether an electrostatic analysis or a magnetostatic analysis or possibly both should be performed. When there are only electric sources present, you will get nonzero electric fields and zero magnetic fields. When there are only magnetic sources present, you will get nonzero magnetic fields and zero electric fields.of output simulation data:
To run a static simulation, first you have to open the Run Dialog. This is done by clicking the {| class="Runwikitable" button of the Simulate Toolbar, or by selecting the |-! scope="Runcol" item of the Simulate Menu, or simply using the keyboard shortcut | Icon! scope="Ctrl+Rcol". The only available simulation engine is | Simulation Data Type! scope="Staticcol". Clicking the Run button of this dialog starts a static analysis. A separate window pops up which reports the progress of the current simulation. | Observable Type === Simulation Modes ==! scope="col"| Applications|-EM.Ferma currently offers three different simulation modes| style="width: Analysis, Parametric Sweep and Optimization30px;" | [[File:fieldsensor_icon. An png]]| style="Analysiswidth:150px;" is a single| Near-shot finite difference solution Field Distribution Maps| style="width:150px;" | [[Glossary of your static structureEM. The structure is first discretized using a fixedCube's Simulation Observables & Graph Types#Near-cell mesh Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing electric and the Poisson equation is solved numerically everywhere in your computational domain. The magnetic field and components, electric scalar potential values at each mesh node are computed and magnitude of magnetic vector potential on a planar cross section of the specified observables are written into data files.computational domain |-In a | style="Parametric Sweepwidth:30px;", one ore more variables are varied at the specified steps(s). This means that you must first define one or more variables in your projects. | [[VariablesFile:fieldsensor_icon.png]] can be associated with CAD object properties like dimensions, coordinates, rotation angles, etc. or with material properties or source properties. For each single variable sample or each combination of variable samples, first all the associated CAD object properties, material properties or source properties are updated in the project workspace. Then is a finite difference solution of your updated static structure is computed | style="width:150px;" | Electric and parametric sweep proceeds to the next variable sample or combination.Magnetic Energy and Dissipated Power Density Maps  The optimization mode requires definition | style="width:150px;" | [[Glossary of one or more objectives based on the standard output quantitiesEM. At the present time, the optimization mode is only available for the 2D QuasiCube's Simulation Observables & Graph Types#Near-Static Mode Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing electric and magnetic energy densities and dissipated power density on a planar cross section of the EM.Ferma, which will be discussed separately later. computational domain |-| style="width:30px;" | [[ImageFile:Qsource7fieldsensor_icon.png]]|thumbstyle="width:150px;" |400pxTemperature and Heat Flux Distribution Maps|style="width:150px;" | [[Glossary of EM.FermaCube's Static Engine Settings dialog.Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] =| style==Static Simulation Engine Settings=== EM.Ferma currently uses a single iterative linear system solver based "width:450px;" | Computing temperature and heat flux components on a planar cross section of the stabilized Bicomputational domain |-Conjugate Gradient (BiCG) method to solve the matrix equations which result from the discretization of Poisson's equation. You can specify some numerical | style="width:30px;" | [[parametersFile:fieldsensor_icon.png]] related to the Bi-CG solver. To do that, you need to open the Simulation Engine Settings Dialog by clicking the | style="Settingswidth:150px;" button located next to the | Thermal Energy Density Maps | style="Select Enginewidth:150px;" drop-down list. From this dialog you can set the maximum number | [[Glossary of BiCG iterations, which has a default value of 10,000EM. You can also set a value for Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="Convergence Errorwidth:450px;". The default value for electrostatic analysis is 0.001. For magnetostatic analysis, the specified value of convergence error is reduced by | Computing thermal energy density on a factor 1000 automatically. Therefore, planar cross section of the default convergence error in this case is 1ecomputational domain |-6| style="width:30px;" | [[File:field_integ_icon. png]]| style="width:150px;" | Field Integral Quantities{{Note|The value style="width:150px;" | [[Glossary of convergence error affect the accuracy of your simulation resultsEM. For most practical scenariosCube's Simulation Observables & Graph Types#Static_Field_Integral_Observable | Static Field Integral]] | style="width:450px;" | Computing line, the default values are adequate. You can reduce the convergence error for better accuracy at the expense surface and volume integrals of longer computation time.}}the electric and magnetic fields and heat flux == Working with Static Simulation Data ==|}
At the end of an electrostatic simulation, the electric field and electric scalar potential values are computed at all the mesh grid points of the entire computational domain. At the end of an magnetostatic simulation, the magnetic field and magnetic vector potential values are computed at all the grid nodes. The field and potential values are written into output data files and can be visualized Click on the screen only if you define a field sensor observable. In the absence of a defined observable, the static simulation will be carried out and completed, but to action will take place.  === Defining Field Sensors === [[Image:Qsource8.png|thumb|350px|EM.Ferma's Field Sensor dialog.]] Just like other [[EM.Cube|EM.CUBE]] Modules, EM.Ferma has a Field Sensor observable, which plots 3D visualizations of electric and magnetic field components on a specified plane. However, unlike the other modules, EM.Ferma field sensors have two additional plots for electric scalar potential and magnitude of the magnetic vector potential. These are called the "EPot" and "HPot" nodes on the navigation tree. To define a Field Sensor, right-click on "Field Sensors" in the Navigation Tree and select "Insert New Observable..." from the contextual menu. The Field Sensor dialog allows the user to select the direction of the sensor (X, Y, Z), visualization type, and whether E-field output or H-field output will be shown during a sweep analysis. The E-fields and H-fields are computed at each mesh node within the specified 2D Field Sensor plane. In other words, the resolution of the Field Sensor is controlled by the mesh resolution. [[Image:Info_icon.png|40px]] Click here category to learn more details about defining '''it in the [[Data_Visualization_and_Processing#The_Field_Sensor_Observable | Field Sensor Observables]]'''Glossary of EM. [[Image:Info_icon.png|40px]] Click here to learn more about Cube'''[[Data_Visualization_and_Processing#Visualizing_3D_Near-Field_Maps | Visualizing 3D Near-Field Mapss Simulation Observables & Graph Types]]'''. [[Image:Info_icon.png|40px]] Click here to learn more about '''[[Data_Visualization_and_Processing#Plotting_Field_Distribution_Graphs_Along_Lines | Plotting Field Distribution Graphs Along Lines]]'''.
<table>
<tr>
<td> [[Image:Qsource9Ferma L1 Fig15.png|thumb|360pxleft|640px|Electric field distribution of a spherical charge on a horizontal field sensor plane.]] </td></tr> <tr><td> [[Image:Qsource10Ferma L1 Fig16.png|thumb|360pxleft|640px|Electric scalar potential distribution of a spherical charge on a horizontal field sensor plane.]] </td>
</tr>
</table>
=== Defining Field Integrals ===Â It is often needed to compute integrals of the electric or magnetic fields to define other related quantities. The following table shows some below list the different types of widely used field integrals in electrostatics and magnetostatics. In EM.Ferma, you can define a path integral along a line segment that is parallel to one of the three principal axes, or a loop integral on a rectangle that is parallel to one of the principal planes. You can also define flux planes or flux boxes. All this is done from the same Field Integral Dialog. To define a Field Integral, right-click on "Field Integrals" in the Navigation Tree and select "Insert New Observable..." from the contextual menu. The Integral Type drop-down list gives nine options as listed in the table belowtheir definitions:Â
{| class="wikitable"
| <math> P_{ohmic} = \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv </math>
| ohmic.DAT
|-
! scope="row"| Resistance
| <math> R = V/I_{cond} = - \int_C \mathbf{E(r)} . \mathbf{dl} / \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} </math>
| resistance.DAT
|-
! scope="row"| Capacitance
| <math> C = \Phi_E/V = \int\int_{S_o} \epsilon \mathbf{E(r)} . \mathbf{ds} / \int_C \mathbf{E(r)} . \mathbf{dl} </math>
| capacitance.DAT
|-
! scope="row"| Capacitance (Alternative)
| <math> C = 2W_E/V^2 = 2 \int \int \int_V \epsilon \vert \mathbf{E(r)} \vert ^2 dv / \left( \int_C \mathbf{E(r)} . \mathbf{dl} \right)^2</math>
| capacitance.DAT
|-
! scope="row"| Self-Inductance
| <math> L = \Phi_H/I = \int\int_S \mu \mathbf{H(r)} . \mathbf{ds} / \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| inductance.DAT
|-
! scope="row"| Self-Inductance (Alternative)
| <math> L = 2W_M/I^2 = 2 \int \int \int_V \mu \vert \mathbf{H(r)} \vert ^2 dv / \left( \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} \right)^2</math>
| inductance.DAT
|-
! scope="row"| Mutual Inductance
| <math> M = \Phi_H^{\prime}/I = \int\int_{S^{\prime}} \mu \mathbf{H(r)} . \mathbf{ds} / \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| inductancemutual_inductance.DAT|-! scope="row"| Resistance| <math> R = V/I_{cond} = - \int_C \mathbf{E(r)} . \mathbf{dl} / \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} </math>| resistance.DAT|-! scope="row"| Resistance (Alternative 1)| <math> R = V^2/P_{ohmic} = \left( \int_C \mathbf{E(r)} . \mathbf{dl} \right)^2 / \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv </math>| resistance.DAT|-! scope="row"| Resistance (Alternative 2)| <math> R = P_{ohmic}/I_{cond}^2 = \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv / \left( \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} \right)^2</math>| resistance.DAT|-! scope="row"| Thermal Flux| <math> \Phi_T = \int\int_{S_o} \mathbf{q(r)} . \mathbf{ds} </math>| flux_T.DAT|-! scope="row"| Thermal Energy| <math> W_T = Q = \int \int \int_V \rho_V c_p \left( T\mathbf{(r)} - T_{env} \right) dv </math>| energy_T.DAT
|}
<table>
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<td>
[[Image:Qsource13.png|thumb|left|480px|Defining the capacitance observable in the field integral dialog.]]
</td>
</tr>
<tr>
<tr>
<td>
[[Image:Qsource11.png|thumb|left|480px|The electric flux box for calculation of charge around a capacitor.]]
</td>
</tr>
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<td>
[[Image:Qsource12.png|thumb|left|480px|A line defining the voltage path for calculation of voltage between capacitor plates.]]
</td>
</tr>
</table>
[[Image:Qsource13.png|thumb|400px|Defining == Discretizing the capacitance observable Physical Structure in the Field Integral dialogEM.]]Ferma ==In ===The Static Mesh===Â The Finite Difference technique discretizes the above table, C represents an open curve (path), C<sub>o</sub> represents computational domain using a closed curve (loop), S represents an open surface like a plane, S<sub>o</sub> represents 3D rectangular grid. EM.Ferma generates a closed surface like a box, and V represents a volumefixed-cell mesh. In This means that the case extents of mutual inductance, S' represents an open surface or plane passing through the second (coupled) inductormesh cells along the principal axes are fixed: Δx, and &PhiDelta;'<sub>H</sub> represents y, Δz. By default, the magnetic flux linkage due mesh cell size is set to one unit project along all the magnetic field three directions (with Δx = Δy = Δz). To modify the cell size, click the Mesh Settings button of the first inductor passing through Simulate Toolbar or right-click on "Static Mesh" in the second inductorNavigation Tree, and select "Mesh Settings..." from the contextual menu to open the Mesh Settings Dialog. {{Note|To obtain accurate results, it is highly recommended to use a square mesh as much as possible. }}
The domain of the field integral is set using the "Integration Box Coordinates" section of the Field Integral dialog[[Image:Info_icon. Box domains are specified by the coordinates of two opposite cornerspng|30px]] Click here to learn more about '''[[Preparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM. Voltage Path requires a line; therefore, two of the coordinates of the two corners must be identicalCube. Otherwise, an error message will pop up. For example, (0, 0, 0) for Corner 1 and (10, 0, 0) for Corner 2 define a Z-directed line segment. Current Loop requires a rectangle; therefore, one of the coordinates of the two corners must be identical. For example, (0, 0, 0) for Corner 1 and (10, 10, 0) for Corner 2 define a rectangle in the XY plane27s_Mesh_Generators | Working with Mesh Generator]]'''.
After [[Image:Info_icon.png|30px]] Click here to learn more about the completion properties of a static simulation, the result of the field integrals are written into ".DAT" data files. These files can be accessed using '''[[EMGlossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh | EM.Ferma's Fixed-Cell Brick Mesh Generator]]'s Data Manager''.
<table>
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<td> [[Image:Qsource11Qsource4.png|thumb|360px350px|The electric flux box for calculation of charge around a capacitorEM.]] </td><td> [[Image:Qsource12.png|thumb|360px|A line defining the voltage path for calculation of voltage between capacitor platesFerma's Mesh Settings dialog.]] </td>
</tr>
</table>
== The 2D Electrostatic Simulation Mode==<table><tr> <td> [[Image:Qsource2.png|thumb|360px|Geometry of a spherical charge source and the enclosing domain box.]] </td><td> [[Image:Qsource3.png|thumb|360px|Fixed-cel mesh of the spherical charge object.]] </td></tr></table>
=== Using Running Static Simulations in EM.Ferma to Simulate 2D Transmission Lines ===
[[Image:Qsource16.png|thumb|400px|A field sensor and 2D solution plane defined for a microstrip line.]]You can use [[=== EM.Ferma]] to perform a quasi-static analysis of multi-conductor transmission line structures, which usually provides good results at lower microwave frequencies (f < 10GHz). [[EM.Ferma]] computes the characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub> of your TEM or quasi-TEM transmission line. The "quasi-static approach" involves two steps as described above, which [[EM.Ferma]]'s 2D Quasi-Static mode automatically performs to calculate ε<sub>eff</sub> and Z<sub>0</sub>. Simulation Modes ===
To perform a transmission line [[EM.Ferma]] currently offers three different simulation, first draw your structure in the project workspace just like a typical 3D structure. Define a "Field Sensor" observable in the navigation tree so modes as to capture the cross section of your structure as your desired transmission line profile. follows:
Next, define a {| class="2D Solution Planewikitable" in the navigation tree based on your existing field sensor. When defining the 2D plane, check the box labeled "Perform 2D Quasi|-Static ! scope="col"| SimulationMode! scope=". If col"| Usage! scope="col"| Number of Engine Runs! scope="col"| Frequency ! scope="col"| Restrictions|-| style="width:120px;" | [[#Running an analysis is run with this option checked, Electrostatic or Magnetostatic Analysis | Analysis]]| style="width:270px;" | Simulates the characteristic impedance Z<sub>0</sub> and effective permittivity &epsilonphysical structure "As Is"| style="width:100px;<sub>eff<" | Single run| style="width:200px;" | N/sub> will be computed for the corresponding 2D Solution Plane. The results are written to two output data files named A| style="solution_plane_Z0.DATwidth:150px;" and | None|-| style="solution_plane_EpsEffwidth:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM.DATCube#Running_Parametric_Sweep_Simulations_in_EM.Cube | Parametric Sweep]]| style=", respectively, where width:270px;"solution_plane" is | Varies the default name value(s) of your 2D planeone or more project variables| style="width:100px;" | Multiple runs| style="width:200px;" | N/A| style="width:150px;" | None|-| style="width:120px;" | [[Parametric_Modeling_%26_Simulation_Modes_in_EM. Cube#Performing_Optimization_in_EM.Cube | Optimization]]| style="width:270px;" | Optimizes the value(s) of one or more project variables to achieve a design goal | style="width:100px;" | Multiple runs | style="width:200px;" | N/A| style="width:150px;" | None|}
Many 2D quasi-static solutions can be obtained in the same analysis=== Running an Electrostatic, for example, when your design contains many types of transmission lines. At the end of a quasi-static analysis, the electric field components and scalar potential at the selected 2D planes will still be computed and can be visualized. In the case of a parametric sweep, the data files will contain multiple data entries listed against the corresponding variable samples. Such data files can be plotted in EM.Grid.Magnetostatic or Thermal Analysis ===
[[EM.Ferma's electrostatic ]] has three independent but functionally similar static simulation engines: Electrostatic, Magnetostatic and Thermal. The electrostatic engine features a 2D solution mode where your physical model is treated as a longitudinally infinite structure in solves the direction normal electric form of Poisson's equation for electric scalar potential subject to specified "2D Solution Plane"electric field boundary conditions, in the presence of electric sources (volume charges and fixed-potential PEC blocks) and dielectric material media. More than one 2D solution plane may be defined. In that caseThe magnetostatic engine solves the magnetic form of Poisson's equation for magnetic vector potential subject to magnetic field boundary conditions, multiple 2D solutions are obtainedin the presence of magnetic sources (wire and volume currents and permanent magnetic blocks) and magnetic material media. A 2D solution plane is defined based on a "Field Sensor" definition that already exists The thermal engine solves the thermal form of Poisson's equation for steady-state temperature subject to thermal boundary conditions, in your projectthe presence of heat sources (volume sources and fixed-temperature PTC blocks) and insulator material media.
To explore EM.Ferma's 2D moderun a static simulation, right-click on '''2D Solution Planes''' in first you have to open the Run Dialog. This is done by clicking the "Computational DomainRun" section button of the navigation tree and select '''2D Domain Settings...''' from the contextual menu. In the 2D Static Domain dialogSimulate Toolbar, check or by selecting the checkbox labeled "Treat Structure as Longitudinally Infinite across Each 2D Plane Specified BelowRun". This would enable you to add new 2D Solution Plane definitions to item of the list Simulate Menu, or edit simply using the existing oneskeyboard shortcut "Ctrl+R". In There are two available options for the Add/Edit 2D Solution Plane dialog, you can choose a name other than the default name simulation engine: '''Electrostatic-Magnetostatic Solver''' and select one of the available field sensor definitions in your project'''Steady-State Thermal Solver'''. At Clicking the end Run button of this dialog starts a 2D electrostatic static analysis, you can view the electric field and potential results on the respective field sensor planes. It is assumed that your structure is invariant along A separate window pops up which reports the direction normal to the 2D solution plane. Therefore, your computed field and potential profiles must be valid at all the planes perpendicular to progress of the specified longitudinal directioncurrent simulation.
<table>
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<td> [[Image:Qsource14Ferma L1 Fig11.png|thumb|420pxleft|The 2D Static Domain dialog600px|EM.]] </td><td> [[Image:Qsource15.png|thumb|300px|A Add/Edit 2D Solution Plane Ferma's Simulation Run dialog.]] </td>
</tr>
</table>
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In EM.Ferma you don't have to choose between the electrostatic or magnetostatic simulation engines. The program looks at the types of sources and material objects present in your project workspace and then it determines whether an electrostatic analysis or a magnetostatic analysis or possibly both should be performed. When there are only electric sources present, you will get nonzero electric fields and zero magnetic fields. When there are only magnetic sources present, you will get nonzero magnetic fields and zero electric fields. On the other hand, since the electrostatic and thermal solvers share the same navigation resources, you can run only one of the two engines at a time. By default, the electrostatic solver is enabled.
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An "Analysis" is the simplest simulation mode of EM.Ferma. It is a single-shot finite difference solution of your static problem. The physical structure of your project workspace is first discretized using a fixed-cell mesh and the Poisson equation is solved numerically everywhere in the computational domain. The field and potential values at each mesh node are computed, and the specified observables are written into data files. The other available simulation modes, parametric sweep and optimization, involve multiple runs of the static solvers.
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===Static Simulation Engine Settings===
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EM.Ferma offers two different types of linear system solver for solving the matrix equations that result from discretization of Poisson's equation: an iterative solver based on the stabilized Bi-Conjugate Gradient (BiCG) method and a Gauss-Seidel solver. The default solver type is BiCG. You can specify some numerical parameters related to the BiCG solver. To do that, you need to open the Simulation Engine Settings Dialog by clicking the "Settings" button located next to the "Select Engine" drop-down list. From this dialog you can set the maximum number of BiCG iterations, which has a default value of 10,000. You can also set a value for "Convergence Error". The default value for electrostatic analysis is 0.001. For magnetostatic analysis, the specified value of convergence error is reduced by a factor 1000 automatically. Therefore, the default convergence error in this case is 10<sup>-6</sup>.
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{{Note|The value of convergence error affect the accuracy of your simulation results. For most practical scenarios, the default values are adequate. You can reduce the convergence error for better accuracy at the expense of longer computation time.}}
<table>
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<td> [[Image:Qsource17Qsource7.png|thumb|360pxleft|Electric field distribution of the microstrip line on the 2D solution plane480px|EM.Ferma's Static Engine Settings dialog.]] </td><td> [[Image:Qsource18.png|thumb|360px|Electric scalar potential distribution of the microstrip line on the 2D solution plane.]] </td>
</tr>
</table>
You can also use EM.Ferma to perform a quasi-static analysis of multi-conductor transmission line structures, which usually provides good results at lower microwave frequencies (f < 10GHz). For that purpose, check the box labeled "Perform == The 2D Quasi-Static Simulation" when defining the 2D solution plane. EM.Ferma computes the characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub> of your TEM or quasi-TEM transmission line. The results are written to two output data files named "solution_plane_Z0.DAT" and "solution_plane_EpsEff.DAT", respectively, where "solution_plane" is the default name of your 2D plane. At the end of a quasi-static analysis, the electric field components and scalar potential at the selected 2D planes will still be computed and can be visualized. In the case of a parametric sweep, the data files will contain multiple data entries listed against the corresponding variable samples. Such data files can be plotted in EM.Grid.Mode==
[[Image:Info_iconEM.png|40px]] Click here Ferma's electrostatic simulation engine features a 2D solution mode where your physical model is treated as a longitudinally infinite structure in the direction normal to learn more about specified "2D Solution Plane". A 2D solution plane is defined based on a "Field Sensor" definition that already exists in your project. To explore EM.Ferma's 2D mode, right-click on '''2D Solution Planes''' in the theory "Computational Domain" section of the navigation tree and select '''[[Modeling_Lumped_Elements,_Circuits_%26_Devices_in_EM.Cube#2D_Quasi-Static_Solution_of_TEM_Line_Structures| 2D Quasi-Static Analysis of Transmission Lines]]Domain Settings...'''from the contextual menu. In the 2D Static Domain dialog, check the checkbox labeled "Reduce the 3D Domain to a 2D Solution Plane". The first field sensor observable in the navigation tree is used for the definition of the 2D solution plane.
[[Image:Info_iconAt the end of a 2D electrostatic analysis, you can view the electric field and potential results on the field sensor plane.png|40px]] Click here It is assumed that your structure is invariant along the direction normal to learn more about '''[[Modeling_Lumped_Elementsthe 2D solution plane. Therefore,_Circuits_%26_Devices_in_EMyour computed field and potential profiles must be valid at all the planes perpendicular to the specified longitudinal direction.Cube#Using_EMA 2D structure of this type can be considered to represent a transmission line of infinite length.Ferma_to_Simulate_2D_Transmission_Lines | Modeling Transmission Lines Using EM.Ferma]]'''also performs a quasi-static analysis of the transmission line structure, and usually provides good results at lower microwave frequencies (f < 10GHz). It computes the characteristics impedance Z<sub>0</sub> and effective permittivity ε<sub>eff</sub> of the multi-conductor TEM or quasi-TEM transmission line. The results are written to two output data files named "solution_plane_Z0.DAT" and "solution_plane_EpsEff.DAT", respectively.
The quantities ε<subtable>eff</subtr> and Z<subtd>0</sub> are two of EM[[Image:Qsource14.Ferma's standard output parameterspng|thumb|left|450px|The 2D static domain dialog. You can use them to optimize a transmission line structure. Two possible objectives are "Z]] <sub/td>0</subtr> == 50" or "sqrt(ε<sub>eff</subtable>) == 1.5".
[[Image:Info_icon.png|40px30px]] Click here for a discussion to learn more about the theory of '''[[Parametric_Modeling,_Sweep_Electrostatic_%26_Optimization26_Magnetostatic_Field_Analysis#Optimization 2D_Quasi-Static_Solution_of_TEM_Transmission_Line_Structures | Optimization in EM.Cube2D Quasi-Static Analysis of Transmission Lines]]'''.
For a step-by-step demonstration (including transmission line optimization), take a look at this video on our YouTube channel: <table><tr> <td> [[httpImage://wwwQsource16.youtubepng|thumb|left|480px|A field sensor and 2D solution plane defined for a microstrip line.com/watch?v=Iiu9rQf1QI4 EM.CUBE Microstrip Optimization]]</td></tr><!--== Simulation Examples / Gallery ==table>
{| border="0"<table>|-| valign="top"|<tr> <td> [[FileImage:ScreenCapture1Qsource17.png|thumb|left|350px480px|Classic Example: Two oppositely charged spheres.]]| valign="top"|[[File:iarray.png|thumb|left|350px|H-Field from array Electric field distribution of current loopsthe microstrip line on the 2D solution plane.]]</td>|-</tr> |}{| border="0"|-| valign="top"|<tr> <td> [[FileImage:ustripQsource18.png|thumb|left|350px|Potential near microstrip conductor from a quasistatic simulation.]]| valign="top"|[[File:ustrip2.png|thumb|left|350px480px|Electric field near scalar potential distribution of the microstrip conductor from a quasistatic simulation. This Field Sensor's view mode has been set to Vector modeline on the 2D solution plane.]]</td>|-</tr>|}--</table>Â == Version History ==Â * First available in [[EM.Cube|EM.CUBE]] 14.2
== More Resources ==<br />
* [http://en.wikipedia.org/wiki/Electrostatics Wikipedia: Electrostatics.]* [http://www.youtube.com/watch?v=Iiu9rQf1QI4 YouTube: EM.Ferma Optimization Example.]* [http://www.emagtech.com/content/emferma More about EM.Ferma.]<hr>
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