NDSolve`FEM`
NDSolve`FEM`

NumericalRegion

NumericalRegion[…]

represents data that is used for describing a numerical region.

Details and Options

  • NumericalRegion[…] is generated by ToNumericalRegion.
  • In standard output format, the bounding box and a symbolic representation of the region, if any, are shown.
  • NumericalRegion objects are used as input for InitializePDECoefficients, InitializeBoundaryConditions, and ToElementMesh.
  • NumericalRegion contains at least one region representation. NumericalRegion may contain both a symbolic representation of the region and ElementMesh representations of the region.
  • NumericalRegion has the following properties:
  • "BoundaryFunction"gives boundary function of symbolic region
    "BoundaryMesh"gives the boundary mesh if present
    "Bounds"gives the bounds
    "ClearCache"clears the cached meshes
    "Constraints"gives constraints
    "ElementMesh"gives the full mesh if present
    "EmbeddingDimension"gives the embedding dimensions
    "Predicates"gives the predicates of the region
    "PredicateVariables"gives the predicate variables of the region
    "Properties"gives the properties
    "SymbolicRegion"gives the symbolic region representation if any

Examples

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Basic Examples  (6)

Load the package:

Create a numerical region of a full region in two dimensions:

Extract the bounding box:

Extract the predicates:

Extract the embedding dimension:

Create a numerical region of a disk and extract the predicates and the predicate variables:

Extract the symbolic region:

Extract the boundary function:

The boundary function returns a value for which the zero contour is the region boundary, negative inside and positive outside.

Plot the boundary function:

Create a numerical region from an implicit region:

Extract properties from the numerical region:

Create a numerical region of a full region in two dimensions:

Extract the ElementMesh:

Create an ElementMesh with ToElementMesh:

The ElementMesh field is now populated:

The boundary ElementMesh is now also populated:

Clear the meshes and constraints:

Create a numerical region of a full region in two dimensions:

Initially, boundary and element meshes are not populated:

Create a boundary mesh:

The boundary mesh is now populated:

Create a mesh:

Define a NumericalRegion based on the mesh:

Retrieve the predicate and the symbolic region of the NumericalRegion:

Retrieve the bounding box and variables:

The meshes are the same:

There is no boundary mesh associated:

Possible Issues  (1)

Not all string properties are available for all input:

A way around that is to use exact numbers as input:

Wolfram Research (2014), NumericalRegion, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/NumericalRegion.html.

Text

Wolfram Research (2014), NumericalRegion, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/NumericalRegion.html.

CMS

Wolfram Language. 2014. "NumericalRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/FEMDocumentation/ref/NumericalRegion.html.

APA

Wolfram Language. (2014). NumericalRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/FEMDocumentation/ref/NumericalRegion.html

BibTeX

@misc{reference.wolfram_2024_numericalregion, author="Wolfram Research", title="{NumericalRegion}", year="2014", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/NumericalRegion.html}", note=[Accessed: 23-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_numericalregion, organization={Wolfram Research}, title={NumericalRegion}, year={2014}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/NumericalRegion.html}, note=[Accessed: 23-April-2024 ]}