create.mesh.1.5D {fdaPDE}

Create a 1.5D linear network mesh

Description

Create a 1.5D linear network mesh

Usage

create.mesh.1.5D(nodes, edges = NULL, order = 1, nodesattributes = NULL)

Arguments

nodes

A #nodes-by-2 matrix containing the x and y coordinates of the mesh nodes.

edges

A #edges-by-2 (when order = 1) or #triangles-by-3 (when order = 2) matrix. This option is used when a triangulation is already available. It specifies the edges giving the row's indices in nodes of the edges' vertices and (when nodes = 2) also if the triangles' edges midpoints. The triangles' vertices and midpoints are ordered as 1—3—2 In this case the function create.mesh.1.5D is used to produce a complete mesh.1.5D object.

order

Either '1' or '2'. It specifies wether each mesh should be represented by 2 nodes (the edges vertices) or by 3 nodes (the edges's vertices and midpoint). These are respectively used for linear (order = 1) and quadratic (order = 2) Finite Elements. Default is order = 1.

nodesattributes

A matrix with #nodes rows containing nodes' attributes. These are passed unchanged to the output. If a node is added during the triangulation process or mesh refinement, its attributes are computed by linear interpolation using the attributes of neighboring nodes. This functionality is for instance used to compute the value of a Dirichlet boundary condition at boundary nodes added during the triangulation process.

Value

An object of the class mesh.1.5D with the following output:

nodes

A #nodes-by-2 matrix containing the x and y coordinates of the mesh nodes.

nodesmarkers

A vector of length #nodes, with entries either '1' or '0'. An entry '1' indicates that the corresponding node is a boundary node; an entry '0' indicates that the corresponding node is not a boundary node.

nodesattributes

A matrix with #nodes rows containing nodes' attributes. These are passed unchanged from the input.

edges

A #edges-by-2 matrix containing all the edges of the triangles in the output triangulation. Each row contains the row's indices in nodes, indicating the nodes where the edge starts from and ends to.

neighbors

A #edges-by-2 matrix of list. Each row contains the indices of the neighbouring edges. An empty entry indicates that one node of the edge is a boundary node.

order

Either '1' or '2'. It specifies wether each mesh triangle should be represented by 3 nodes (the triangle' vertices) or by 6 nodes (the triangle's vertices and midpoints). These are respectively used for linear (order = 1) and quadratic (order = 2) Finite Elements.