fdaPDE (version 1.1-21)

eval.FEM.time: Evaluate a FEM.time object at a set of point locations

Description

It evaluates a FEM.time object at the specified set of locations or regions. If space.time.locations is provided locations, incidence_matrix and time.instants must be NULL. Otherwise time.instants and one of locations and incidence_matrix must be given. In this case the evaluation is perform on the tensor grid time.instants-by-locations (or time.instants-by-areal domains).

Usage

eval.FEM.time(FEM.time, locations = NULL, time.instants = NULL, 
                     space.time.locations = NULL, incidence_matrix = NULL, lambdaS = 1, 
                     lambdaT = 1, search = "tree", bary.locations = NULL)

Value

A matrix of numeric evaluations of the FEM.time object. Each row indicates the location where the evaluation has been taken, the column indicates the function evaluated.

Arguments

FEM.time

A FEM.time object to be evaluated.

locations

A 2-columns (in case of planar mesh) or 3-columns(in case of 2D manifold in a 3D space or a 3D volume) matrix with the spatial locations where the FEM.time object should be evaluated.

time.instants

A vector with the time instants where the FEM.time object should be evaluated.

space.time.locations

A 3-columns (in case of planar mesh) or 4-columns(in case of 2D manifold in a 3D space or a 3D volume) matrix with the time instants and spatial locations where the FEM.time object should be evaluated. The first column is for the time instants. If given, locations, incidence_matrix and time.instants must be NULL.

incidence_matrix

In case of areal data, the #regions x #elements incidence matrix defining the regions.

lambdaS

The index of the lambdaS choosen for the evaluation.

lambdaT

The index of the lambdaT choosen for the evaluation.

search

a flag to decide the search algorithm type (tree or naive or walking search algorithm).

bary.locations

A list with three vectors: locations, location points which are same as the given locations options. (checks whether both locations are the same); element ids, a vector of element id of the points from the mesh where they are located; barycenters, a vector of barycenter of points from the located element.

References

Devillers, O. et al. 2001. Walking in a Triangulation, Proceedings of the Seventeenth Annual Symposium on Computational Geometry

Examples

library(fdaPDE)
## Upload the horseshoe2D data
data(horseshoe2D)
boundary_nodes = horseshoe2D$boundary_nodes
boundary_segments = horseshoe2D$boundary_segments
locations = horseshoe2D$locations

## Create the 2D mesh
mesh = create.mesh.2D(nodes = rbind(boundary_nodes, locations), segments = boundary_segments)
## Create the FEM basis
FEMbasis = create.FEM.basis(mesh)
## Compute the coeff vector evaluating the desired function at the mesh nodes
## In this case we consider the fs.test() function introduced by Wood et al. 2008
time = 1:5
coeff = rep(fs.test(mesh$nodes[,1], mesh$nodes[,2]),5)*time
## Create the FEM.time object
FEM_time_function = FEM.time(coeff=coeff, time_mesh=1:5, FEMbasis=FEMbasis, FLAG_PARABOLIC=TRUE)

evaluations = eval.FEM.time(FEM_time_function, locations = matrix(c(-0.92,0), ncol=2), 
                            time.instants = time)