The Electrostatics, Boundary Elements Interface
The Electrostatics, Boundary Elements (esbe) interface (), found under the AC/DC>Electric Fields and Currents branch when adding a physics interface, is used for computing the potential distribution in dielectrics under conditions where the electric potential distribution on the boundaries is explicitly prescribed. The formulation is based on the boundary element method and the interface is available in 2D and 3D.
The physics interface solves Laplace’s equation for the electric potential using the scalar electric potential as the dependent variable
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For a discussion about the boundary element method, see Theory for the Boundary Elements PDE in the COMSOL Multiphysics Reference Manual.
When this physics interface is added, these default nodes are also added to the Model Builder — Charge Conservation, Zero Charge (on exterior boundaries and in 3D also on interior edges) and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, electric potential and surface charge density conditions. You can also right-click Electrostatics, Boundary Elements to select physics features from the context menu.
If both The Electrostatics Interface and The Electrostatics, Boundary Elements Interface are available, the Electric Scalar-Scalar Potential Coupling node is available from the Multiphysics menu in the Physics toolbar or by right-clicking the Multiphysics Couplings node in Model Builder.
The Electrostatics Interface and The Electrostatics, Boundary Elements Interface can also be coupled by using the same name for the dependent variable for both interfaces. Then Electric Scalar-Scalar Potential Coupling is not needed. How to set the name for the dependent variable is described in the Dependent Variables section.
Physics-Controlled Mesh
The physics-controlled mesh is controlled from the Mesh node’s Settings window (if the Sequence type is Physics-controlled mesh). There, in the table in the Physics-Controlled Mesh section, find the physics interface in the Contributor column and select or clear the check box in the Use column on the same table row for enabling (the default) or disabling contributions from the physics interface to the physics-controlled mesh.
Information from the physics will be used to automatically set up an appropriate mesh sequence.
In the COMSOL Multiphysics Reference Manual see the Physics-Controlled Mesh section for more information about how to define the physics-controlled mesh.
Domain selection
From the Selection list, select any of the options — Manual, All domains, All voids, or All domains and voids (the default). The geometric entity list displays the selected domain entity numbers. Edit the list of selected domain entity numbers using the selection toolbar buttons to the right of the list or by selecting the geometric entities in the Graphics window. Entity numbers for voids can be entered by clicking the Paste () button in the selection toolbar and supplying the entity numbers in the dialog box. The entity number for the infinite void is 0, and finite voids have negative entity numbers.
Selections can also be entered using the Selection List window, available from the Windows menu in the Home toolbar.
For more information about making selections, see Working with Geometric Entities in the COMSOL Multiphysics Reference Manual.
Physics Symbols
Select the Enable physics symbols check box to display symmetry planes (in 3D) and lines (in 2D) in the Graphics window, as specified in the Symmetry settings.
Thickness (2D components)
For 2D components, enter a default value for the Out-of-plane thickness d (SI unit: m). The default value of 1 is typically not representative for a thin dielectric medium. Instead it describes a unit thickness that makes the 2D equation identical to the equation used for 3D components.
Manual Terminal Sweep Settings
Select the Use manual terminal sweep check box to invoke a parametric sweep over terminals. Enter a Sweep parameter name to assign a specific name to the variable that controls the terminal number solved for during the sweep. The Sweep parameter name must also be declared as a model parameter. The default is PortName.
For most applications it is simpler to sweep over terminals using the Stationary Source Sweep study step. See Stationary Source Sweep in the COMSOL Multiphysics Reference Manual and (for more details) Stationary Source Sweep in the Modeling with the AC/DC Module chapter of this manual.
To correctly calculate the terminal charge and the corresponding capacitances, if voltage Terminal is used on boundaries between The Electrostatics Interface and The Electrostatics, Boundary Elements Interface, let the dependent variable for The Electrostatics, Boundary Elements Interface be the same as the dependent variable for The Electrostatics Interface and disable Electric Scalar-Scalar Potential Coupling. How to set the name for the dependent variable is described in the Dependent Variables section. Since the Electric Scalar-Scalar Potential Coupling is disabled, add manually a Fully Coupled node to the Stationary Solver below the Solution node in the Solver Configurations.
Symmetry
For 3D components, from the Condition for the x = x0 plane, Condition for the y = y0 plane, and Condition for the z = z0 plane lists, choose Off (the default), Symmetric, or Antisymmetric. Then enter the value for the plane location x0, y0, or z0 (SI unit: m) as required.
For 2D components, from the Condition for the x = x0 plane and Condition for the y = y0 plane lists, choose Off (the default), Symmetric, or Antisymmetric. Then enter the value for the plane location x0 or z0 (SI unit: m) as required.
Far-Field Approximation
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
For more information about the Far Field Approximation settings, see Far-Field Approximation Settings in the COMSOL Multiphysics Reference Manual.
Infinity Condition
For 3D components, select the Infinity condition — Total charge (the default) or Asymptotic value at infinity. Specify the Total charge Qtot (SI unit: C; the default value is 0 C) or Electric potential at infinity V∞ (SI unit: V; the default value is 0 V). If there is an antisymmetric symmetry in the potential field, it acts as an added infinite ground plane with a fixed value of the electric potential. The value at infinity is fixed to 0 by the presence of the infinite ground plane, so for this case there is a fixed Zero potential at infinity condition.
For 2D components, select the Infinity condition — Total charge (the default) or Value at reference distance. Specify the Total charge Qtot (SI unit: C; the default value is 0 C) or Electric potential at reference distance Vref (SI unit: V; the default value is 0 V). If there is an antisymmetric symmetry in the potential field, it acts as an added ground line with a fixed value of the electric potential. The value at a reference distance is fixed to 0 by the presence of the ground line, so for this case there is a fixed Zero potential at reference distance condition.
Quadrature
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
For more information about the Quadrature settings, see Quadrature in the COMSOL Multiphysics Reference Manual.
Discretization
From the Electric potential/Surface charge density list, choose from predefined options for the boundary element discretization order for the electric potential variable and the surface charge density variable, respectively. The predefined options represent the suitable combinations of element orders such as Quadratic/Linear (the default).
For 3D components, the Line charge variable will have the same discretization order as the Electric potential variable.
The settings under Value types when using splitting of complex variables are important for sensitivity and optimization computations. See the description of the built-in operators fsens and fsensimag.
Dependent Variables
The dependent variable (field variable) is for the Electric potential V. The name can be changed but the names of fields and dependent variables must be unique within a model.