NDSolve`FEM`
NDSolve`FEM`

# PrismElement

PrismElement[{{i11,i12,i13,i14,i15,i16},,{in1,in2,in3,in4,in5,in6}}]

represents n linear prism elements ek with incidents {ik1,ik2,ik3,ik4,ik5,ik6}.

PrismElement[{{i11,,i115},,{in1,,in15}}]

represents n quadratic prism elements ek with incidents {ik1,,ik15}.

PrismElement[{e1,,en},{m1,,mn}]

represents n prism elements ek and n integer markers mk.

# Details and Options

• PrismElement is used to represent prism mesh elements in ElementMesh.
• PrismElement can be used as an input to ToElementMesh.
• Incidents ik,j are integers that index an array of spatial coordinates. The coordinates referenced by ek={ik1,} are the nodes of the k prism.
• The first six incidents ik1, ik2, ik3, ik4, ik5 and ik6 are always vertices.
• For quadratic prism elements, the next nine incidents are mid-side nodes of possibly curved edges.
• Linear elements are order-1 elements and quadratic elements are order-2 elements.
• In PrismElement[{e1,,en}], all elements ek need to be of the same order.
• The prism in PrismElement[{e1,,en}] will share common nodes, edges and faces, but these cannot intersect with each other, or for second-order prisms, with themselves.
• The nodes for a linear and a quadratic prism are shown:
• For a PrismElement, the face incidents must be counterclockwise. An element {i1,i2,i3,i4,i5,i6} has the face incidents {i1,i2,i3,0}, {i4,i5,i6,0}, {i2,i5,i6,i3}, {i3,i6,i4,i1} and {i1,i4,i5,i2} for the five faces.
• The prism element is known in the finite element method as a serendipity element.
• Prism elements can be used to extrude 2D triangle meshes into 3D.
• Prism elements can connect tetrahedron and hexahedron elements in the same mesh.

# Examples

open allclose all

## Basic Examples(1)

Create a mesh with one prism element:

## Generalizations & Extensions(4)

The base coordinates of the linear element:

The base incidents of the linear element:

A mesh with a linear unit element:

Visualization of the linear unit element:

The base coordinates of the quadratic element:

The base incidents of the quadratic element:

The base face incidents of the linear element:

The base face incidents of the quadratic element:

## Applications(2)

Prism elements can be used to extrude a two-dimensional triangle mesh to three dimensions. Create and visualize a 2D first-order mesh:

Extract the coordinates of the 2D mesh, add a third dimension in the -direction and extrude the coordinates in the -direction:

Create and visualize the 3D prism element mesh:

Combine a prism and a tetrahedron element with markers:

Visualize the mesh with the elements' markers:

## Possible Issues(6)

The incidents must be of the appropriate length:

The incident order cannot be mixed:

The incidents must be lists of integers:

The number of markers must match the number of incidents:

Markers must be a vector of integers:

When possible, noninteger markers will be converted to integers:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_prismelement, author="Wolfram Research", title="{PrismElement}", year="2021", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/PrismElement.html}", note=[Accessed: 03-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_prismelement, organization={Wolfram Research}, title={PrismElement}, year={2021}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/PrismElement.html}, note=[Accessed: 03-August-2024 ]}