[[Image:Splash-static.jpg|right|720px]]<strong><font color="#2603c4" size="4">Electrostatic, Magnetostatic & Thermal Solvers For DC And Low Frequency Simulations</font></strong><table><tr><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.FermaTempo]] is [[image:prop-ico.png | link=EM.CubeTerrano]] [[image:planar-ico.png |link=EM.CUBEPicasso]]'s 3D static solver[[image:metal-ico. It features two distinct electrostatic and magnetostatic simulation engines that can be used to solve a variety of static and lowpng | link=EM.Libera]] [[image:po-frequency electromagnetic problemsico. Both simulation engines are based on finite difference solutions of Poissonpng | link=EM.Illumina]]</td><tr></table>[[Image:Tutorial_icon.png|30px]] 's equation for electric and magnetic potentials''[[EM. Cube#EM.Ferma_Documentation | EM.Ferma Tutorial Gateway]]'''
With [[Image:Back_icon.png|30px]] '''[[EM.Ferma, you can explore the electric fields due Cube | Back 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. You can also use EM.FermaCube Main Page]]'s 2D quasi-static mode to compute the characteristic impedance (Z0) and effective permittivity of transmission line structures with complex cross section profiles.''==Product Overview==
== Methods Of Electrostatics, Magnetostatics & Quasi-Statics = EM.Ferma in a Nutshell ===
EM.Ferma solves 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. 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 the electric scalar potential subject to specified boundary conditions:and magnetic potentials and temperature.
<math>\Delta\PhiWith 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 (\mathbf{r}permeable) = \nabla^2 \Phi(\mathbf{r}) = 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-\frac{\rhostatic mode to compute the characteristic impedance (\mathbf{r}Z0)}{\epsilon}</math>and effective permittivity of transmission line structures with complex cross section profiles.
[[Image:Info_icon.png|30px]] Click here to learn more about the '''[[Electrostatic & Magnetostatic Field Analysis | Theory of Electrostatic and Magnetostatic Methods]]'''.
where Φ(<b>r</b>) is [[Image:Info_icon.png|30px]] Click here to learn more about the electric scalar potential, ρ(<b>r</b>) is the volume charge density, and ε is the permittivity '''[[Steady-State_Thermal_Analysis | Theory of the mediumSteady-State Heat Transfer Methods]]'''.
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[[Image:Magnet lines1.png|thumb|left|400px| Vector plot of magnetic field distribution in a cylindrical permanent magnet.]]
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The electric field boundary conditions at === EM.Ferma as the interface between two material media are:Static Module of EM.Cube ===
<math> \hat{\mathbf{n}} EM. [ \mathbf{D_2(r)} Ferma is the low- \mathbf{D_1(r)} frequency '''Static Module''' of '''[[EM.Cube] = \rho_s (\mathbf{r}) </math>]''', 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|30px]] Click here to learn more about '''[[Getting_Started_with_EM.Cube | EM.Cube Modeling Environment]]'''.
<math> \hat{\mathbf{n}} \times [ \mathbf{E_2(r)} - \mathbf{E_1(r)} ] = 0 </math>== Advantages & Limitations of EM.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 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.
where <mathtable> \hat{\mathbf{n}} </mathtr> is the unit normal vector at the interface pointing from medium 1 towards medium 2,<btd>D[[Image:Ferma L8 Fig title.png|thumb|left|400px| Vector plot of electric field distribution in a coplanar waveguide (rCPW)transmission line.]]</btd> = ε<b>E(r)</btr> is the electric flux density, <b>E(r)</btable> is the electric field vector, and ρ<sub>s</sub> is the surface charge density at the interface.
== EM.Ferma Features at a Glance ==
In a source-free region, ρ(<b>r</b>) = 0, and Poisson's equation reduces to the familiar Laplace equation: == Physical Structure Definition ===
<mathul>\Delta\Phi <li> Perfect electric conductor(\mathbf{r}PEC) = \nabla^2 \Phisolids and surfaces (\mathbf{r}Electrostatics) = 0</mathli> <li> Dielectric objects (Electrostatics)</li> <li> Magnetic (permeable) objects (Magnetostatics)</li> <li> Perfect thermal conductor (PTC) solids and surfaces (Thermal)</li> <li> Insulator objects (Thermal)</li></ul>
=== Sources ===
Keep in mind that in the absence of an electric charge source, you need to specify a non<ul> <li> Fixed-zero potential somewhere in your structure, PEC for example, on a perfect electric conductor maintaining equi-potential metal objects (PECElectrostatics)</li> <li> Volume charge sources (Electrostatics)</li> <li> Volume current sources (Magnetostatics)</li> <li> Wire current sources (Magnetostatics)</li> <li> Permanent magnets (Magnetostatics)</li> <li> Fixed-temperature PTC for maintaining iso-thermal objects (Thermal)</li> <li> Volume heat sources (Thermal). Otherwise, you will get a trivial zero solution of the Laplace equation. </li></ul>
=== Mesh generation ===
Once the electric scalar potential is computed, the electric field can easily be computed via the equation below: <ul> <li> Fixed-size brick cells</li></ul>
<math> \mathbf{E(r)} = - \nabla \Phi(\mathbf{r})</math>== 3D Electrostatic & Magnetostatic Simulation ===
<ul>
<li>
Finite difference solution of Laplace and Poisson equations for the electric scalar potential with Dirichlet and Neumann domain boundary conditions </li>
<li>
Finite difference solution of Laplace and Poisson equations for the magnetic vector potential with Dirichlet domain boundary conditions </li>
<li>
Calculation of electric scalar potential and electric field</li>
<li>
Calculation of magnetic vector potential and magnetic field</li>
<li>
Calculation of electric flux over user defined flux boxes and capacitance</li>
<li>
Calculation of magnetic flux over user defined flux surfaces and inductance</li>
<li>
Calculation of electric and magnetic energies, Ohmic power loss and resistance</li>
<li>
Parametric sweep with variable object properties or source parameters</li>
</ul>
EM.Ferma also solves the Poisson equation for the magnetic vector potential subject to specified boundary conditions:=== 2D Quasi-Static Simulation ===
<mathul>\Delta \mathbf{A} (\mathbf{r}) = \nabla^2 \mathbf{A}(\mathbf{r}) = - \mu \mathbf{J}(\mathbf{r}) <li> 2D Finite difference solution of cross section of transmission line structures</li> <li> 3D domain solution as well as 2D solution of a longitudinally infinite version of the structure defined on a 2D plane </li> <li> Calculation of electric potential and electric field distribution</li> <li> Parametric sweep of transmission line's geometric and material parameters</li> <li> Optimization of transmission line's parameters for impedance design</li></mathul>
=== Steady-State Thermal Simulation ===
where <bul>A(r) </bli> is Finite difference solution of Laplace and Poisson equations for the magnetic vector potential, temperature with Dirichlet and Neumann domain boundary conditions <b/li>J(r) </bli> is the volume current density, and μ is the permeability Calculation of the medium. The magnetic Poisson equation is vectorial in nature temperature and involves a system heat flux density</li> <li> Calculation of three scalar differential equations corresponding to the three components thermal energy density on field sensor planes</li> <li> Calculation of thermal flux over user defined flux boxes<b/li> <li> Calculation of thermal energy</li>A(r)</bul>.
=== Data Generation & Visualization ===
The <ul> <li> Electric and magnetic field boundary conditions at the interface between two material media are:intensity and vector plots on planes</li> <li> Electric and magnetic potential intensity plots on 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> <li> Animation of field and potential plots after parametric sweeps</li> <li> Graphs of characteristic impedance and effective permittivity of transmission line structures vs. sweep variables</li> <li> Custom output parameters defined as mathematical expressions of standard outputs</li></ul>
<math> \hat{\mathbf{n}} == Building the Physical Structure in EM. [ \mathbf{B_2(r)} - \mathbf{B_1(r)} ] Ferma == 0 </math>
=== Variety of Physical Objects in EM.Ferma ===
<math> \hat{\mathbf{n}} \times [ \mathbf{H_2The 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 (rpermeable)} - \mathbf{H_1material 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 (rFD)} ] = \mathbf{J_s(r)} </math>technique to find a numerical solution of your static boundary value problem.
[[EM.Ferma]] offers the following types of physical objects:
where <math> \hat{\mathbf{n}} </math> is the unit normal vector at the interface pointing from medium 1 towards medium 2,| class="wikitable"<b>B|-! 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.Cube's Materials, Sources, Devices & Other Physical Object Types#Fixed-Potential PEC |Fixed-Potential Perfect Electric Conductor (rPEC)<]]| style="width:300px;" | Modeling perfect metals with a fixed voltage| style="width:100px;" | Solid and surface objects| style="width:250px;" | Can be considered an electric source if the fixed voltage is nonzero |-| 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 |Dielectric/b> 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;" | [[File:aniso_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices &muOther Physical Object Types#Volume Charge |Volume Charge]]| style="width:300px;<b>H" | Modeling volume charge sources with a fixed charge density or an expression in the global coordinates (rx,y,z)</b> is | style="width:100px;" | Solid objects| style="width:250px;" | Acts as an electric source|-| style="width:30px;" | [[File:voxel_group_icon.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 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 flux densitysource|-| style="width:30px;" | [[File:pmc_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, <b>HSources, Devices & Other Physical Object Types#Permanent Magnet |Permanent Magnet]]| style="width:300px;" | Modeling permanent magnet sources with a fixed magnetization vector or expressions in the global coordinates (rx,y,z)</b> is the | style="width:100px;" | Solid objects| style="width:250px;" | Acts as a magnetic field vectorsource|-| style="width:30px;" | [[File:thin_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types#Wire Current |Wire Current]]| style="width:300px;" | Modeling wire current sources| style="width:100px;" | Line and <b>J<sub>polyline objects| style="width:250px;" | Acts as a magnetic source|-| style="width:30px;" | [[File:pec_group_icon.png]]| style="width:200px;" | [[Glossary of EM.Cube's</sub></b> 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| style="width:250px;" | Can be considered a thermal source if the fixed temperature is different than the surface current ambient temperature (shares the same 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 node as dielectric material)|-| style="width:30px;" | [[File:aniso_group_icon.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 with a fixed heat density at or an expression in the interfaceglobal 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, 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|}
Click on each category to learn more details about it in the [[Glossary of EM.Cube's Materials, Sources, Devices & Other Physical Object Types]].
Once the magnetic vector potential is computed, the magnetic field can easily be computed via the equation below: === Grouping Objects by Material or Source Type ===
<math> \mathbf{H(r)} = \frac{1}{\mu} \nabla \times \mathbf{A} (\mathbf{r})</math>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 geometric objects in the project workspace are organized together into object groups which share the same properties including color and electric or magnetic parameters. It is recommended that you first create object groups, and then draw new objects under the active group. To create a new object group, right-click on its category name in the "Physical Structure" section of the navigation tree and select one of the "Insert New Group..." items from the contextual menu. 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 geometric object.
== A Note on Material It is important to note that there is a one-to-one correspondence between electrostatic and Source Types in EM.Ferma ==thermal simulation entities:
In [[EM.Cube]]'s other modules, material types are specified under the {| class="Physical Structurewikitable" section of the Navigation Tree, and sources are organized under a separate |-! scope="Sourcescol" 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. | 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:200px;" | Volume Heat Source|}
In [[EM.Cube]]'s Static Module, materials {{Note|Electrostatic and sources are all listed under thermal solvers share the "Physical Structure" section of same material categories on the Navigation Tree, and there is no separate "Sources" sectionnavigation tree. For example, you can define default zero-potential perfect electric conductors (This means that PEC) in your project to model metal objects. You can also define fixed-potential PEC are treated as PTC objects with a nonzero voltage, which can effectively act dielectric objects are treated 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 insulator objects are defined from the same PEC node of the Navigation Tree by assigning different voltage values. Charge and current sources volume charges are defined treated as CAD objects that you must draw in volume heat sources when the project workspacethermal solver is enabled.}}
== Sources Once a new object group node has been created in EMthe navigation tree, it becomes and remains the "Active" object group, which is always listed in bold letters. When you draw a new geometric object such as a box or a sphere, its name is added under the currently active object group. There is only one object group that is active at any time. Any group can be made active by right-clicking on its name in the navigation tree and selecting the '''Activate''' item of the contextual menu.Ferma ==
For static analysis, the model can be excited with any number of Voltage Sources, Charge Sources, or Current Sources[[Image:Info_icon. For Quasistatic analysis, only Voltage Sources are of practical usepng|30px]] Click here to learn more about '''[[Building Geometrical Constructions in CubeCAD#Transferring Objects Among Different Groups or Modules | Moving Objects among Different Groups]]'''.
=== Voltage Sources ===<table><tr><td> [[Image:STAT MAN1.png|thumb|left|480px|EM.Ferma's navigation tree.]] </td></tr></table>
In === A Note on Material and Source Types in EM.Ferma, Voltage Sources are applied to a specified PEC material group that exists in [[EM.Cube|EM.CUBE]]'s navigation tree. All CAD objects under the specified PEC group will act as Voltage Sources.===
To add a new Voltage Source to a projectIn [[EM.Cube]]'s other modules, right-click on material types are categorized under the "Voltage SourcesPhysical Structure" on section of the navigation tree, and select sources are organized under a separate "Insert Voltage Source...Sources"section. In the Voltage Source dialogthose modules, select all the PEC group geometric objects you draw in your project workspace typically represent material bodies. All of [[EM.Cube]] modules except for EM.Ferma require at least one excitation source to which the specified voltage will be applied. Enter any string as selected from the Voltage -- a text string will be interpreted as a variable which "Sources" section of the navigation tree before you can be used for parametric design, or run a parameter sweepsimulation.
=== Charge 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.
Charge Sources in == EM.Ferma apply a charge (or charge density) to a region defined by any of [[EM.Cube|EM.CUBE]]'s CAD objects.Computational Domain ==
Adding a new Charge Source is very similar to adding a new material in [[EM.Cube|EM.CUBE]]. Find the "Charge Source" group label in the navigation tree and select "Insert New Charge Source..." A dialog will prompt the user to decide whether charge for this group will be defined in terms of total charge or charge density. If charge density is chosen, the specified charge density will be applied to all CAD objects defined in the present Charge Source group. If total charge is selected, the specified total charge will be distributed amongst the total volume of all objects under the present material group.===The Domain Box===
=== Current Sources ===In EM.Ferma, the Poisson or Laplace equations are solved subject to boundary conditions using the Finite Difference technique. As a result, you need to specify a finite computational domain and then specify the domain boundary conditions. EM.Ferma's computational domain defines where the domain boundary condition will be specified. A default domain box is always placed in the project workspace as soon as you draw your first object. The domain can be seen as a blue cubic wireframe that surrounds all of the CAD objects in the project workspace.
Current Sources 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 EMtwo different ways: Default and Custom.Ferma apply The default type places an enclosing box with a specified current to any number offset from the largest bounding box of one-dimensional your project's CAD objects, such as Lines, Polylines, or Spirals. For any curveThe default offset value is 20 project units, such as but you can change this value arbitrarily. The custom type defines a Parabola or a Circle, fixed domain box by specifying the user will be prompted to perform a one-time conversion to a Polyline just before running a simulationcoordinates of its two opposite corners labeled Min and Max in the world coordinate system.
Adding a new Current Source is very similar to adding a new Charge Source<table><tr> <td> [[Image:Qsource5. Keep in mind only one-dimensional objects can be drawn under this material grouppng|thumb|left|480px|EM.Ferma's Domain Settings dialog.]] </td></tr></table>
{| border="0"|-| valign="top"|[[File:vsource.png|thumb|left|250px|EM.Ferma's Voltage Source Dialog]]| valign="bottom"|[[File:qsource.png|thumb|left|250px|EM.Ferma's Charge Source Dialog]]| valignDomain Boundary Conditions==="top"|[[File:isource.png|thumb|left|250px|EM.Ferma's Current Source Dialog]]|-|}
== Observables in *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 a constant normal electric field component on the domain walls and its value is specified in V/m.
=== Field Sensor ===*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.
Just like other [[EM.Cube|EM.CUBE]] Modules, *EM.Ferma has a standard Field Sensor observableprovides two options for thermal boundary conditions on the domain box. To specify The Dirichlet boundary condition is the default option and is specified as a Field Sensor, right-click fixed temperature value on "Field Sensors" in the navigation tree and click "Add Newsurface of the domain walls.By default, this value is 0°C..". The Field Sensor dialog allows Neumann boundary condition specifies the user to select normal derivative of the direction temperature on the surface of the sensor, visualization type, domain walls. This is equivalent to a constant heat flux passing through the domain walls and whether E-field output or H-field output will be shown during its value is specified in W/m<sup>2</sup>. A zero heat flux means a sweep analysisperfectly insulated domain box and is known as the adiabatic boundary condition.
In EM.FermaTo modify the boundary conditions, Field Sensors are also used right-click on "Boundary Conditions" in the navigation tree, and select "Boundary Conditions..." from the contextual menu to open the Boundary Conditions Dialog. When you switch from the electrostatic-magnetostatic solver to specify 2D solution planes for the thermal solver in EM.Ferma's 2D solution modeRun Simulation dialog, it automatically checks the box labeled '''Treat as a Thermal Structure''' in the Boundary Conditions dialog. This will be detailed shortlyConversely, if you check this box in the Boundary Conditions dialog, the solver type is set to the 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.
The E-fields and H-fields are computed at each mesh node within the specified 2D Field Sensor plane<table><tr> <td> [[Image:fermbc. In other words, the resolution of the Field Sensor is controlled by the mesh resolutionpng|thumb|left|480px|EM.Ferma's Boundary Conditions dialog.]] </td></tr></table>
=== Transmission Line Characteristics =EM.Ferma's Simulation Data & Observables ==
In EM.Ferma's quasistatic modeAt the end of an electrostatic simulation, transmission-line [[parameters]] Z0 the electric field vector and EpsEff electric scalar potential values are computed, in addition to output due to at all the Field Sensormesh grid points of the entire computational domain. At the end of an magnetostatic simulation, which is required to define the 2D solution planemagnetic field vector and magnetic vector potential values are computed at all the grid nodes. Text files corresponding to these observables will be placed in At the end of a thermal simulation, the temperature and heat flux vector are computed at all the mesh grid points of the project's working directory after each analysisentire computational domain.
== Domain Besides the electric and Boundary Conditions ==magnetic fields and temperature, EM.Ferma can compute a number of field integral quantities such as voltage, current, flux, energy, etc. The field components, potential values and field 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. In the absence of any observable defined in the navigation tree, the static simulation will be carried out and completed, but no output simulation data will be generated.
[[Image:fermbc.png|thumb|200px|Boundary Condition Dialog]]In EM.Ferma, offers the Laplace equation is solved subject to boundary conditions. Here, we will discuss how to specify these boundary conditions.following types of output simulation data:
{| class="wikitable"|-! scope="col"| Icon! scope= 3D Domain "col"| Simulation Data Type! scope="col"| Observable Type! scope="col"| Applications|-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Near-Field Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing electric and magnetic field components, electric scalar potential and magnitude of magnetic vector potential on a planar cross section of the computational domain |-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Electric and Magnetic Energy and Dissipated Power Density Maps | style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-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 computational domain |-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Temperature and Heat Flux Distribution Maps| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing temperature and heat flux components on a planar cross section of the computational domain |-| style="width:30px;" | [[File:fieldsensor_icon.png]]| style="width:150px;" | Thermal Energy Density Maps | style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Near-Field_Sensor_Observable |Near-Field Sensor]] | style="width:450px;" | Computing thermal energy density on a planar cross section of the computational domain |-| style="width:30px;" | [[File:field_integ_icon.png]]| style="width:150px;" | Field Integral Quantities| style="width:150px;" | [[Glossary of EM.Cube's Simulation Observables & Graph Types#Static_Field_Integral_Observable | Static Field Integral]] | style="width:450px;" | Computing line, surface and volume integrals of the electric and magnetic fields and heat flux |}
Click on each category to learn more details about it in the [[Image:qsource2.png|thumb|200px|The green wireframe around the CAD objects defines the extents Glossary of the computational domain. The specified boundary conditions are applied on the domain wallsEM. Cube's Simulation Observables & Graph Types]].
EM.<table><tr> <td> [[Image:Ferma's computational domain defines where the boundary condition will be specifiedL1 Fig15. The domain can be seen as png|thumb|left|640px|Electric field distribution of a green cubic wireframe that surrounds all of the CAD objects in the model. To modify the domain boundary, find the "3D Static Domain" entry in the navigation tree, right-click spherical charge on it, and select "Domain Settingsa horizontal field sensor plane.]] </td></tr> <tr> <td> [[Image:Ferma L1 Fig16..". The domain dialog will appear. In the domain dialog, the domain boundary can be specified in terms png|thumb|left|640px|Electric scalar potential distribution of either a custom, fixed location, or as custom offsets from CAD objects in the scenespherical charge on a horizontal field sensor plane.]] </td></tr></table>
=== Boundary Condition ===The table below list the different types of field integrals and their definitions:
EM{| class="wikitable"|-! scope="col"| Field Integral! scope="col"| Definition! scope="col"| Output Data File|-! scope="row"| Voltage| <math> V = - \int_C \mathbf{E(r)} .Ferma allows the user to either specify the potential on the boundary \mathbf{dl} </math>| voltage.DAT|-! scope="row"| Current| <math> I = \oint_{C_o} \mathbf{H(Dirichlet boundary conditionr), or specify the normal derivative on the boundary } . \mathbf{dl} </math>| current.DAT|-! scope="row"| Conduction Current| <math> I_{cond} = \int\int_S \mathbf{J(Neumann boundary conditionr) via a specified field strength} . \mathbf{ds} = \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} </math>| conduction_current.DAT|-! scope="row"| Electric Flux| <math> \Phi_E = \int\int_{S_o} \mathbf{D(r)} . \mathbf{ds} = \int\int_{S_o} \epsilon \mathbf{E(r)} . \mathbf{ds} </math>| flux_E.DAT|-! scope="row"| Magnetic Flux| <math> \Phi_H = \int\int_S \mathbf{B(r)} . \mathbf{ds} = \int\int_S \mu \mathbf{H(r)} . \mathbf{ds} </math>| flux_H.DAT|-! scope="row"| Electric Energy| <math> W_E = \frac{1}{2} \int \int \int_V \epsilon To modify the boundary condition, find \vert \mathbf{E(r)} \vert ^2 dv </math>| energy_E.DAT|-! scope="Boundary Conditionsrow" on the navigation tree, and select | Magnetic Energy| <math> W_H = \frac{1}{2} \int\int\int_V \mu \vert \mathbf{H(r)} \vert ^2 dv </math>| energy_H.DAT|-! scope="Boundary Conditionsrow"| Ohmic Power Loss| <math> P_{ohmic} = \int\int\int_V \sigma \vert \mathbf{E(r)} \vert ^2 dv </math>| ohmic.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 The user will be prompted with the dialog seen at \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>| mutual_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|}
== 2D Solution Planes <table><tr> <td> [[Image:Qsource13.png|thumb|left|480px|Defining the capacitance observable in EMthe 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> <tr> <td> [[Image:Qsource12.png|thumb|left|480px|A line defining the voltage path for calculation of voltage between capacitor plates.Ferma ==]] </td></tr></table>
[[Image:qstatic.png|thumb|300px|Setting up a Transmission Line simulation.]]== Discretizing the Physical Structure in EM.Ferma features a 2D solution mode where the model is treated as a longitudinally infinite structure at a list of specified 2D Solution Planes. The 2D planes are defined by a Field Sensor definition that already exists in the project.==
To explore EM.Ferma's 2D mode, right-click on "2D Solution Planes" in the navigation tree and select "2D Domain Settings...". In the 2D Static Domain dialog, enable the checkbox labeled "Treat Structure as Longitudinally Infinite across Each 2D Plane Specified Below". ===The user is then able to Add or Edit 2D Solution Plane definitions to the solution list. Static Mesh===
The Finite Difference technique discretizes the computational domain using a 3D rectangular grid. EM.Ferma generates a fixed-cell mesh. This means that the extents of the mesh cells along the principal axes are fixed: Δx, Δy, Δz. By default, the mesh cell size is set to one unit project along all the three directions (with Δx =Δy == Setting up Δz). To modify the cell size, click the Mesh Settings button of the Simulate Toolbar or right-click on "Static Mesh" in the Navigation 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 Transmission Line Simulation ===square mesh as much as possible.}}
To perform a Transmission Line simulation, first turn on Quasistatic simulation mode for a selected 2D Solution Plane, as shown in the figure at right[[Image:Info_icon. If an analysis is run with this option checked, the characteristic impedance (Z0) and Effective Epsilon will be computed for the corresponding 2D Solution Plane. This output can be found in appropriately-named text files in the project directory upon completion of the simulation. Fields and potentials at the selected 2D plane will still be computed. Many 2D quasistatic solutions can be obtained in the same analysis, if for example, your design contains many types of png|30px]] Click here to learn more about '''[[Transmission LinesPreparing_Physical_Structures_for_Electromagnetic_Simulation#Working_with_EM.Cube.27s_Mesh_Generators |transmission linesWorking with Mesh Generator]]'''.
Quasistatic analysis can only be performed with a Dirichlet boundary condition with 0V specified on [[Image:Info_icon.png|30px]] Click here to learn more about the boundariesproperties of '''[[Glossary_of_EM.Cube%27s_Simulation-Related_Operations#Fixed-Cell_Brick_Mesh | EM.Ferma's Fixed-Cell Brick Mesh Generator]]'''.
For a step-by-step demonstration (including transmission line <table><tr> <td> [[optimizationImage:Qsource4.png|thumb|350px|EM.Ferma's Mesh Settings dialog.]]), take a look at this video on our YouTube channel: [http:</td></www.youtube.comtr></watch?v=Iiu9rQf1QI4 EM.CUBE Microstrip Optimization]table>
== Simulation Modes ==<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>
== Running Static Simulations in EM.Ferma currently offers Analysis, Parametric Sweep, and [[Optimization]] simulation modes. More information about these simulation modes can be found on the [[Optimization]] page.==
{{Note|All of these simulation modes are subject to 2D Solution mode being disabled or enabled=== EM. Before starting a simulation, you may wish to review the current state of this settings in the 2D Domain dialog.}}Ferma's Simulation Modes ===
== Simulation Examples / Gallery ==[[EM.Ferma]] currently offers three different simulation modes as follows:
{| borderclass="0wikitable"
|-
| valign! scope="topcol"|Simulation Mode[[File:ScreenCapture1.png|thumb|left! scope="col"|350px|Classic Example: Two oppositely charged spheres.]]Usage! scope="col"| valignNumber of Engine Runs! scope="topcol"|Frequency [[File:iarray.png|thumb|left! scope="col"|350px|H-Field from array of current loops.]]Restrictions
|-
|}style="width:120px;" | [[#Running an Electrostatic or Magnetostatic Analysis | Analysis]]{| borderstyle="0width:270px;"| Simulates the physical structure "As Is"| style="width:100px;" | Single run| style="width:200px;" | N/A| style="width:150px;" | None
|-
| valignstyle="topwidth:120px;"|[[File:ustripParametric_Modeling_%26_Simulation_Modes_in_EM.png|thumb|leftCube#Running_Parametric_Sweep_Simulations_in_EM.Cube |350px|Potential near microstrip conductor from a quasistatic simulation.Parametric Sweep]]| valignstyle="topwidth:270px;"|Varies the value(s) of one or more project variables[[File| style="width:ustrip2.png100px;" |thumbMultiple runs|leftstyle="width:200px;" |350pxN/A|Electric field near microstrip conductor from a quasistatic simulation. This Field Sensor's view mode has been set to Vector mode.]]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
|}
== Version History =Running an Electrostatic, Magnetostatic or Thermal Analysis === [[EM.Ferma]] has three independent but functionally similar static simulation engines: Electrostatic, Magnetostatic and Thermal. The electrostatic engine solves the electric form of Poisson's equation for electric scalar potential subject to electric field boundary conditions, in the presence of electric sources (volume charges and fixed-potential PEC blocks) and dielectric material media. The magnetostatic engine solves the magnetic form of Poisson's equation for magnetic vector potential subject to magnetic field boundary conditions, in the presence of magnetic sources (wire and volume currents and permanent magnetic blocks) and magnetic material media. The thermal engine solves the thermal form of Poisson's equation for steady-state temperature subject to thermal boundary conditions, in the presence of heat sources (volume sources and fixed-temperature PTC blocks) and insulator material media.  To run a static simulation, first you have to open the Run Dialog. This is done by clicking the "Run" button of the Simulate Toolbar, or by selecting the "Run" item of the Simulate Menu, or simply using the keyboard shortcut "Ctrl+R". There are two available options for the simulation engine: '''Electrostatic-Magnetostatic Solver''' and '''Steady-State Thermal Solver'''. Clicking the Run button of this dialog starts a static analysis. A separate window pops up which reports the progress of the current simulation.  <table><tr> <td> [[Image:Ferma L1 Fig11.png|thumb|left|600px|EM.Ferma's Simulation Run dialog.]] </td></tr></table> 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.  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. ===Static Simulation Engine Settings=== 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>.  {{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><tr> <td> [[Image:Qsource7.png|thumb|left|480px|EM.Ferma's Static Engine Settings dialog.]]</td></tr></table> == The 2D Quasi-Static Simulation Mode== EM.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 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 "Computational Domain" section of the navigation tree and select '''2D 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.  At the end of a 2D electrostatic analysis, you can view the electric field and potential results on the field sensor plane. It is assumed that your structure is invariant along the direction normal to the 2D solution plane. Therefore, your computed field and potential profiles must be valid at all the planes perpendicular to the specified longitudinal direction. A 2D structure of this type can be considered to represent a transmission line of infinite length. 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.  <table><tr> <td> [[Image:Qsource14.png|thumb|left|450px|The 2D static domain dialog.]] </td></tr> </table> [[Image:Info_icon.png|30px]] Click here to learn more about the theory of '''[[Electrostatic_%26_Magnetostatic_Field_Analysis#2D_Quasi-Static_Solution_of_TEM_Transmission_Line_Structures | 2D Quasi-Static Analysis of Transmission Lines]]'''. <table><tr> <td> [[Image:Qsource16.png|thumb|left|480px|A field sensor and 2D solution plane defined for a microstrip line.]]</td></tr></table> <table><tr> <td> [[Image:Qsource17.png|thumb|left|480px|Electric field distribution of the microstrip line on the 2D solution plane.]] </td></tr> <tr> <td> [[Image:Qsource18.png|thumb|left|480px|Electric scalar potential distribution of the microstrip line on the 2D solution plane.]] </td></tr></table> <br /> <hr>
* First available in [[EMImage:Top_icon.Cubepng|30px]] '''[[EM.CUBEFerma#Product_Overview | Back to the Top of the Page]] 14.2'''
== More Resources ==[[Image:Tutorial_icon.png|30px]] '''[[EM.Cube#EM.Ferma_Documentation | EM.Ferma Tutorial Gateway]]'''
* [http[Image://en.wikipedia.org/wiki/Electrostatics Wikipedia: ElectrostaticsBack_icon.png|30px]]* '''[http://www[EM.youtube.com/watch?v=Iiu9rQf1QI4 YouTube: Cube | Back to EM.Ferma Optimization Example.Cube Main Page]* [http://www.emagtech.com/content/emferma More about EM.Ferma.]'''