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:
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"MessageHead" Automatic symbol for messages - Setting the option from NDSolve and related functions is explained in NDSolve Finite Element Options.
Examples
open allclose allBasic Examples (7)
Create a numerical region of a disk:
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:
The boundary mesh is now populated:
Define a NumericalRegion based on the mesh:
Retrieve the predicate and the symbolic region of the NumericalRegion:
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:
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