NDSolve`FEM`
NDSolve`FEM`

# ElementMeshRegionProduct

ElementMeshRegionProduct[mesh1,mesh2]

represents the Cartesian product of the ElementMesh mesh1 and mesh2.

# Details and Options

• ElementMeshRegionProduct is also known as outer product region or region extrusion.
• ElementMeshRegionProduct[mesh1,mesh2] represents the region .
• The embedding dimension of the product region is the sum of embedding dimensions, and the geometric dimension is the sum of geometric dimensions.
• The highest product dimension supported is 3.
• ElementMeshRegionProduct has the same options as ToElementMesh, with the following additions and changes:
•  "RegionMarkerFunction" None specify region markers

# Examples

open allclose all

## Basic Examples(2)

Create an ElementMesh:

Compute the ElementMesh region product:

Visualize the region product mesh:

Create three ElementMesh instances:

Compute the ElementMesh region product:

Visualize the region product mesh:

## Scope(1)

Create two ElementMesh instances:

Extrude the first ElementMesh with the second by forming a region product:

Visualize the region product mesh:

## Options(2)

### "RegionMarkerFunction"(2)

Create a marker association and a region member function:

Define a region marker function:

Create ElementMesh that is used in each direction:

Compute the ElementMesh region product:

Inspect the "MeshElementMarkerUnion" of the generated mesh:

Visualize the region product mesh with the region markers:

Create a marker association and a region member function:

Define a region marker function:

Create ElementMesh that is used in each direction:

Compute the ElementMesh region product:

Inspect the "MeshElementMarkerUnion" of the generated mesh:

Visualize the region product mesh with the region markers:

## Applications(2)

Create a 2D graded mesh from a product of two 1D graded meshes:

Create a 1D graded mesh with a "Central" point distribution:

Create a second 1D graded mesh with a "Central" point distribution and 50 elements:

Construct a region product:

Visualize the region product of the anisotropic mesh:

Create a third 1D graded mesh with a "BothEnds" point distribution, 50 elements and an endpoint distance of 1/200:

Create the region product:

Wolfram Research (2021), ElementMeshRegionProduct, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/ElementMeshRegionProduct.html (updated 2023).

#### Text

Wolfram Research (2021), ElementMeshRegionProduct, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/ElementMeshRegionProduct.html (updated 2023).

#### CMS

Wolfram Language. 2021. "ElementMeshRegionProduct." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/FEMDocumentation/ref/ElementMeshRegionProduct.html.

#### APA

Wolfram Language. (2021). ElementMeshRegionProduct. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/FEMDocumentation/ref/ElementMeshRegionProduct.html

#### BibTeX

@misc{reference.wolfram_2024_elementmeshregionproduct, author="Wolfram Research", title="{ElementMeshRegionProduct}", year="2023", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/ElementMeshRegionProduct.html}", note=[Accessed: 10-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_elementmeshregionproduct, organization={Wolfram Research}, title={ElementMeshRegionProduct}, year={2023}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/ElementMeshRegionProduct.html}, note=[Accessed: 10-September-2024 ]}