Summary for: ElementBase < handle

Class summary

Elements ElementBase class for finite element implementation

Properties

.edge_definitions Edge definitions

Definition of edges in terms of nodes. Array of size number_of_edges x nodes_per_edge.

Each row defines the nodes (of reference element) nodes that define a single edge, in order

.is_isoparametric Boolean

True if element is isoparametric

.reference_element Definition for reference element.

Number of nodes x number of dimensions array, defining the coordinates of nodes in the reference element.

.reference_element_center Center of reference element.

Coordinates.

.type Type string

Identifier string

.unroll_order Ordering of nodes

Order for reference element nodes such that a meaningful (counter-clockwise?) polygon is formed of them

Methods

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

.Elements **ElementBase** class for finite element implementation

Documentation for ElementBase/ElementBase doc ElementBase

.get_mapping_matrix Vectorized mapping from reference element to global.

For non-isoparametric (non-curved) elements, the mapping is constant over each element volume, so the method returns [F, F0] = get_mapping_matrix(this, msh, elements, x_local) where F is the mapping matrix array, each column corresponding to the mapping matrix in column-major format, and F0 is the linear part of the mapping operation.

For isoparametric / curved elements, the mapping depends on the local coordinate x_local, the the method returns [dFdx, Fx] = get_mapping_matrix(this, msh, elements, x_local) where dFdx is the Jacobian matrix of the mapping, and Fx is the value of the mapping aka the global coordinate corresponding to x_local.

** WARNING For non-curved elements, the implementation here assumes a simplex element type, i.e. triangle or tetrahedron. Implementation for rectangular quads or octs, prisms, etc. must be subclassed.

.get_quadrature_points Quadrature points and weights.

[xq, wq] = get_quadrature_points(this, integrand_order) return the quadrature points xq and weights to integrate an integrand of the given order over the reference element volume.

.TRIPLOT Plots a 2D triangulation

TRIPLOT(TRI,X,Y) displays the triangles defined in the M-by-3 matrix TRI. A row of TRI contains indices into X,Y that define a single triangle. The default line color is blue.

TRIPLOT(TR) displays the triangles in the triangulation TR.

TRIPLOT(…,COLOR) uses the string COLOR as the line color.

H = TRIPLOT(…) returns a line handle representing the displayed triangles edges.

TRIPLOT(…,’param’,’value’,’param’,’value’…) allows additional line param/value pairs to be used when creating the plot.

Example 1: X = rand(10,2); dt = delaunayTriangulation(X); triplot(dt)

Example 2: % Plotting a Delaunay triangulation in face-vertex format X = rand(10,2); dt = delaunayTriangulation(X); tri = dt(:,:); triplot(tri, X(:,1), X(:,2));

See also TRISURF, TRIMESH, DELAUNAY, triangulation, delaunayTriangulation.