The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.

Basic fmesher use

Finn Lindgren

suppressPackageStartupMessages(library(fmesher))
set.seed(1234L)

Mesh construction

domain <- cbind(rnorm(4, sd = 3), rnorm(4))
(mesh2 <- fm_mesh_2d(
  boundary = fm_extensions(domain, c(2.5, 5)),
  max.edge = c(0.5, 2)
))
#> fm_mesh_2d object:
#>   Manifold:  R2
#>   V / E / T: 880 / 2598 / 1719
#>   Euler char.:   1
#>   Constraints:   39 boundary edges (1 group: 1), 111 interior edges (1 group: 1)
#>   Bounding box: (-11.963110,  8.246925) x (-5.522181, 5.499657) x (0,0)
#>   Basis d.o.f.:  880
plot(mesh2, axes = TRUE)

(mesh1 <- fm_mesh_1d(
  c(0, 2, 4, 7, 10),
  boundary = "free", # c("neumann", "dirichlet"),
  degree = 2
))
#> fm_mesh_1d object:
#>   Manifold:  R1
#>   #{knots}:  5
#>   Interval:  ( 0, 10)
#>   Boundary:  (free, free)
#>   B-spline degree:   2
#>   Basis d.o.f.:  6

Point lookup and evaluation

pts <- cbind(rnorm(400, sd = 3), rnorm(400))

# Find what triangle each point is in, and it's triangular Barycentric coordinates
bary <- fm_bary(mesh2, loc = pts)
# How many points are outside the mesh?
sum(is.na(bary$t))
#> [1] 2
head(bary$bary)
#>            [,1]      [,2]      [,3]
#> [1,] 0.04720217 0.5813611 0.3714367
#> [2,] 0.13930150 0.7219260 0.1387725
#> [3,] 0.43189448 0.1384910 0.4296145
#> [4,] 0.20127814 0.3716721 0.4270498
#> [5,] 0.21259133 0.3686084 0.4188003
#> [6,] 0.44390951 0.1739205 0.3821700

# Construct an evaluator object
evaluator <- fm_evaluator(mesh2, loc = pts)
sum(!evaluator$proj$ok)
#> [1] 2

# Values for the basis function weights; for ordinary 2d meshes this coincides
# with the resulting values at the vertices, but this is not true for e.g.
# 2nd order B-splines on 1d meshes.
field <- mesh2$loc[, 1]
value <- fm_evaluate(evaluator, field = field)
sum(abs(pts[, 1] - value), na.rm = TRUE)
#> [1] 5.438358e-14
pts1 <- seq(-2, 12, length.out = 1000)

# Find what segment, and its interval Barycentric coordinates
bary1 <- fm_bary(mesh1, loc = pts1)
# Points outside the interval are treated differently depending on the
# boundary conditions:
sum(is.na(bary1$t))
#> [1] 0
head(bary1$bary)
#>          [,1]      [,2]
#> [1,] 2.000000 -1.000000
#> [2,] 1.992993 -0.992993
#> [3,] 1.985986 -0.985986
#> [4,] 1.978979 -0.978979
#> [5,] 1.971972 -0.971972
#> [6,] 1.964965 -0.964965

# Construct an evaluator object.
evaluator1 <- fm_evaluator(mesh1, loc = pts1)
# mesh_1d basis functions are defined everywhere
sum(!evaluator1$proj$ok)
#> [1] 0

# Values for the basis function weights; for ordinary 2d meshes this coincides
# with the resulting values at the vertices, but this is not true for e.g.
# 2nd order B-splines on 1d meshes.
field1 <- rnorm(fm_dof(mesh1))
value1 <- fm_evaluate(evaluator1, field = field1)
plot(pts1, value1, type = "l")

Plotting

Base graphics

plot(mesh2)

ggplot graphics

suppressPackageStartupMessages(library(ggplot2))
ggplot() +
  geom_fm(data = mesh2)


ggplot() +
  geom_fm(data = mesh1, weights = field1 + 2, xlim = c(-2, 12)) +
  geom_fm(data = mesh1, linetype = 2, alpha = 0.5, xlim = c(-2, 12))

Finite element calculations

fem1 <- fm_fem(mesh1, order = 2)
names(fem1)
#> [1] "c0"  "c1"  "g1"  "g2"  "g01" "g02" "g12"
fem2 <- fm_fem(mesh2, order = 2)
names(fem2)
#> [1] "b1" "c0" "c1" "g1" "g2" "k1" "k2" "ta" "va"

Stochastic process simulation

samp <- fm_matern_sample(mesh2, alpha = 2, rho = 4, sigma = 1)[, 1]
evaluator <- fm_evaluator(mesh2, lattice = fm_evaluator_lattice(mesh2, dims = c(150, 50)))
image(evaluator$x, evaluator$y, fm_evaluate(evaluator, field = samp), asp = 1)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.