Nothing
## ----include = FALSE----------------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
dev = "png",
dev.args = list(type = "cairo-png"),
fig.width = 7,
fig.height = 5
# out.width = 250,
# out.height = 250
)
options("bitmapType" = "cairo")
## ----setup--------------------------------------------------------------------
suppressPackageStartupMessages(library(fmesher))
set.seed(1234L)
## ----basic2-------------------------------------------------------------------
domain <- cbind(rnorm(4, sd = 3), rnorm(4))
(mesh2 <- fm_mesh_2d(
boundary = fm_extensions(domain, c(2.5, 5)),
max.edge = c(0.5, 2)
))
plot(mesh2, axes = TRUE)
## ----basic1-------------------------------------------------------------------
(mesh1 <- fm_mesh_1d(
c(0, 2, 4, 7, 10),
boundary = "free", # c("neumann", "dirichlet"),
degree = 2
))
## ----lookup2------------------------------------------------------------------
pts <- cbind(rnorm(400, sd = 3), rnorm(400))
# Find what triangle each point is in, and it's triangular Barycentric coordinates
bary <- fm_bary(mesh2, loc = pts)
# How many points are outside the mesh?
sum(is.na(bary$t))
head(bary$bary)
# Construct an evaluator object
evaluator <- fm_evaluator(mesh2, loc = pts)
sum(!evaluator$proj$ok)
# Values for the basis function weights; for ordinary 2d meshes this coincides
# with the resulting values at the vertices, but this is not true for e.g.
# 2nd order B-splines on 1d meshes.
field <- mesh2$loc[, 1]
value <- fm_evaluate(evaluator, field = field)
sum(abs(pts[, 1] - value), na.rm = TRUE)
## ----lookup1------------------------------------------------------------------
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$t))
head(bary1$bary)
# Construct an evaluator object.
evaluator1 <- fm_evaluator(mesh1, loc = pts1)
# mesh_1d basis functions are defined everywhere
sum(!evaluator1$proj$ok)
# 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")
## -----------------------------------------------------------------------------
plot(mesh2)
## -----------------------------------------------------------------------------
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))
## -----------------------------------------------------------------------------
fem1 <- fm_fem(mesh1, order = 2)
names(fem1)
fem2 <- fm_fem(mesh2, order = 2)
names(fem2)
## -----------------------------------------------------------------------------
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)
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