FEMDocumentation`
FEMDocumentation`

TetrahedronElement

TetrahedronElement[{{i11,i12,i13,i14},,{in1,in2,in3,in4}}]

represents n linear tetrahedron elements ek with incidents {ik1,ik2,ik3,ik4}.

TetrahedronElement[{{i11,,i110},,{in1,,in10}}]

represents n quadratic tetrahedron elements ek with incidents {ik1,,ik10}.

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

represents n tetrahedron elements ek and n integer markers mk.

Details and OptionsDetails
  • TetrahedronElement is used to represent tetrahedron mesh elements in ElementMesh.
  • TetrahedronElement can be used as an input to ToElementMesh or ToBoundaryMesh.
  • Incidents ikj are integers that index an array of spatial coordinates. The coordinates referenced by ek={ik1,} are the nodes of the k^(th) tetrahedron.
  • The first four incidents ik1, ik2, ik3, and ik4 are always vertices.
  • For quadratic tetrahedron elements, the next six incidents are mid-side nodes of possibly curved edges.
  • Linear elements are order 1 elements and quadratic elements are order 2 elements.
  • In TetrahedronElement[{e1,,en}], all elements ek need to be of the same order.
  • The tetrahedra in TetrahedronElement[{e1,,en}] will share common nodes, edges, and faces but cannot intersect with each other, or for second-order tetrahedra, with themselves.
  • The nodes for a linear and a quadratic tetrahedra are shown:
  • For a TetrahedronElement, the face incidents opposite a vertex ij must be counterclockwise. An element {i1,i2,i3,i4} has the face incidents {i4,i3,i2}, {i4,i1,i3}, {i4,i2,i1}, and {i1,i2,i3} for the four faces.
  • The tetrahedron element is knnown in the finite element method as a Lagrange element.
  • Examples

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    Basic Examples  (1)

    Load the package:

    In[1]:=
    Click for copyable input

    Create a mesh with one quad element:

    In[2]:=
    Click for copyable input
    Out[2]=

    Generalizations & Extensions  (4)

    Applications  (1)

    Possible Issues  (6)

    See Also

    ToElementMesh  ToBoundaryMesh  ElementMesh  PointElement  LineElement  TriangleElement  QuadElement  TetrahedronElement  HexahedronElement

    Tutorials