Infinite Element Domain
An Infinite Element Domain node () applies a real-valued coordinate scaling to a layer of virtual domains surrounding the physical region of interest. When the dependent variables vary slowly with radial distance from the center of the physical domain, the finite elements can be stretched in the radial direction such that boundary conditions on the outside of the infinite element layer are effectively applied at a very large distance from any region of interest.
To add an Infinite Element Domain to any Component, click Infinite Element Domain in the Definitions toolbar, or right-click the Definitions node under the Component and choose Infinite Element Domain. If the nodes under the Component node are grouped by type, you can instead right-click Artificial Domains under Definitions.
Settings
The Label is the default infinite element domain name.
The default Name (for the first infinite element domain in the model) is ie. The Name provides a namespace for variables created by the Infinite Element Domain node. For example, the scaled x coordinate can typically be accessed in equations and postprocessing as ie1.x. See the Equation View subnode for a complete list of available variables.
To display the Equation View node under all nodes creating variables, click the Show More Options button () and select Equation View in the Show More Options dialog box. See also Equation View.
Domain Selection
Select a set of domains conforming to the selected geometry type. See Standard Geometry Configurations.
Geometry
Select a Type: Cartesian (the default), Spherical, Cylindrical, or User defined.
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If Spherical is selected, enter the position of the center of the spherical geometry in the Center coordinate table. For axisymmetric models, only the z coordinate is required since the geometry must be centered on the axis.
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If Cylindrical is selected, enter the position of a point on the cylinder axis in the Center coordinate table. For 3D models, also enter a Center axis direction vector.
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If User defined is selected, first choose the Number of stretching directions appropriate for the geometrical configuration. Then for each stretching direction specify a Distance function, evaluating to the distance from the inner boundary of the infinite element domain measured in the stretching direction, and the Thickness of the domain in the same direction.
Each of these types (except the user-defined type) requires certain geometrical configurations and not all of them are available for all space dimensions.
Scaling
Select a Coordinate stretching type: Rational (the default) or User defined. See Infinite Element Implementation for a detailed explanation of the options.
For the default Rational stretching type, enter expressions for the Physical width (SI unit: m) and the Pole distance (SI unit: m). The default values, 1e3*dGeomChar and dGeomChar, respectively, lead to an infinite element domain that is very large compared to the geometry dimensions and with a nearly singular 1/r stretching.
For the User defined stretching type, select a Stretching function from functions defined under Global>Definitions or under Definitions in a component, or leave the default value None, which is interpreted as f(ξ) = ξ. Any function node defining a single function of one arguments is eligible for use as a stretching function. The argument is interpreted as a dimensionless distance, ξ, in the range 0 to 1.
If you have the AC/DC Module, see this example:
Modeling of a 3D Inductor: Application Library path ACDC_Module/Inductive_Devices_and_Coils/inductor_3d
If you have the Batteries & Fuel Cells Module, Corrosion Module, Electrochemistry Module, or Electrodeposition Module see this example:
Voltammetry at a Microdisk Electrode: Application Library path Batteries_and_Fuel_Cells_Module/General_Electrochemistry/microdisk_voltammetry, Corrosion_Module/General_Electrochemistry/microdisk_voltammetry, Electrochemistry_Module/Electroanalysis/microdisk_voltammetry, Electrodeposition_Module/Tutorials/microdisk_voltammetry