NDSolve`FEM`
NDSolve`FEM`

# ToNumericalRegion

ToNumericalRegion[r]

generates a NumericalRegion object from a region r.

ToNumericalRegion[r,{{xmin,xmax},}]

generates a NumericalRegion object from a region r restricted to the bounding box .

ToNumericalRegion[emesh]

generates a NumericalRegion object from an ElementMesh object.

# Details and Options

• ToNumericalRegion[r] generates a NumericalRegion object that keeps the original representation of the region r together with ElementMesh approximations that may be computed later.
• The specification for region r is similar to the one given for ToElementMesh.
• The region r should be a constant region for which ConstantRegionQ gives True.
• ToNumericalRegion has the following options:
•  "MessageHead" Automatic symbol for messages
• Setting the option from NDSolve and related functions is explained in NDSolve Finite Element Options.

# Examples

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## Basic Examples(7)

Create a numerical region of a disk:

Extract the bounding box:

Create a numerical region of a full region in two dimensions with a bounding box:

Create a numerical region of an empty region in two dimensions:

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

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:

## Generalizations & Extensions(1)

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

Set up variable and solution data:

Initialize the coefficients and boundary conditions that have a discontinuity:

Inspect the constraints introduced by the PDE coefficients and boundary conditions:

Visualize the boundary mesh with the autogenerated internal boundary along the discontinuity:

Visualize the full mesh:

Wolfram Research (2014), ToNumericalRegion, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/ToNumericalRegion.html (updated 2020).

#### Text

Wolfram Research (2014), ToNumericalRegion, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/ToNumericalRegion.html (updated 2020).

#### CMS

Wolfram Language. 2014. "ToNumericalRegion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/FEMDocumentation/ref/ToNumericalRegion.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_tonumericalregion, author="Wolfram Research", title="{ToNumericalRegion}", year="2020", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/ToNumericalRegion.html}", note=[Accessed: 24-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_tonumericalregion, organization={Wolfram Research}, title={ToNumericalRegion}, year={2020}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/ToNumericalRegion.html}, note=[Accessed: 24-July-2024 ]}