| makenodes {SpatialfdaR} | R Documentation |
Compute the matrix nodes containing all the nodes in the mesh.
Description
Each basis function is associated with a node. If the order of the finite elements is 1, the nodes are the vertices of the triangles. If the order is 2, the nodes are also at the midpoints of the edges.
Usage
makenodes(pts, tri, order=2)
Arguments
pts |
A two-column matrix of the locations of the vertices of the mesh. |
tri |
A three-column matrix of the indices in |
order |
The order of the finite element, which is either 1 or 2. |
Details
Computes a matrix nodes containing coordinates for all of the nodes to be used, a matrix nodeindex defining which nodes correspond to each element. If norder is 1, nodes corresponds to vertices and nodeindex is identical to triangles. If norder is 2, the midpoint of each edge is computed and added to points to obtain matrix nodes. The row index of that midpoint is then added to the rows of triangles containing that edge to define nodeindex.
Value
A list object containing these members:
order The order of the finite elements, which is either 1 or 2.
nodes A numnodes*2 matrix whose i'th row contains the coordinates of the i'th nodal variable. Nodes for the second order element consist of vertices and midpoints of edges, that is, 6 per triangle. Points are listed first followed by midpoints. Nodes for the first order element consist of only vertices.
nodeindex If norder == 1, nodeindex is triangles. If norder == 2, an nele*6 matrix whose i'th row contains the row numbers (in nodes) of the nodal variables defining the i'th finite element. If the i'th row of FMESH is [V1 V2 V3] then the i'th row of nodeindex is [V1 V(12) V2 V(23) V3 V(31)], where Vi is the row number of the i'th point and V(ij) is the row number of the midpoint of the edge defined by the i'th and j'th points. If norder == 1, nodeindex is triangles
jvec Jacobian, which is the area of triangle.
metric Metric matrix.