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EMDtool

Summary

Nodal2D Lagrange (nodal) shape function in 2D.

Class for representing and evaluating shape functions and their partial derivatives. Objects of the class can be instantiated with

  • N = Nodal2D( Operators.I ) or Nodal2D() for evaluating the function itself.

  • N = Nodal2D( Operators.grad ) for evaluating function gradients.

  • N = Nodal2D( Operators.curl ) for evaluating curls.

The actual evaluation is performed with N.eval(args) by specifying

  • the mesh used

  • elements of the mesh to evaluate on

  • LOCAL coordinates to evaluate on. The local coordinates must fall within the so-called reference element (unit-triangle ((0,0), (1,0), (0,1)) for triangular elements) associated with the mesh element types. The actual evaluation then takes place on the GLOBAL coordinates, i.e. a point within each of the listed elements corresponding to the given local coordinate. For instance, the local point [0.25;0.25] is mapped (more or less) to the global element center.

  • Index of shape function. As nodal shape functions are each associated with a mesh node, there are 3 shape functions that are non-zero over a first-order element. Example: for the element e , the shape function k is associated the node mesh.t(k, e).

    PROPERTIES

  • op - operator

Methods

Class methods are listed below. Inherited methods are not included.

* Nodal2D Constructor

this = Nodal()

For evaluating raw nodal shape function N.

this = Nodal( Operators.grad )

this = Nodal( Operators.curl )

For evaluating grad N or curl N, respectively.

* eval Global evaluation.

vals = eval(this, k, x_local, mesh, elements)

Evaluates (this.op x N_k), where N_k is the k:th node of the elementType of the given mesh. The expression is evaluated at the global coordinates corresponding to the given local coordinates, on the specified elements of the given mesh .

Input arguments:

  • k : index of shape function to evaluate. 1…3 for first-order triangular elements.

  • x_local : local coordinates to evaluate at.

  • mesh : the mesh to evaluate on.

  • elements : indices of elements (mesh.t(:, elements)) to evaluate on.

vals = eval(this, k, x_local, mapping, mapping_determinant)

The same as above, but specify the local-to-global mapping and its determinant instead of the element indices. Mainly used for speed purposes.

Input arguments:

  • mapping : see SimpleMesh.getMappingMatrix

  • mapping_determinant : see MatrixDeterminant

* evaluates the reference shape function (either identity or

gradient)

Nref = eval(ref, this, k, x_local, mesh)

* getData Data for matrix assembly.

* Nodal2D/getIndices is a function.

inds = getIndices(~, k, msh, varargin)