Multi-domain integration

Construct integration points on tensor product spaces

Usage

fm_int(domain, samplers = NULL, ...)

# S3 method for class 'list'
fm_int(domain, samplers = NULL, ...)

# S3 method for class 'numeric'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'character'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'factor'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'SpatRaster'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'fm_lattice_2d'
fm_int(domain, samplers = NULL, name = "x", ...)

# S3 method for class 'fm_mesh_1d'
fm_int(
  domain,
  samplers = NULL,
  name = "x",
  int.args = NULL,
  format = NULL,
  ...
)

# S3 method for class 'fm_mesh_2d'
fm_int(
  domain,
  samplers = NULL,
  name = NULL,
  int.args = NULL,
  format = NULL,
  ...
)

Arguments

domain

Functional space specification; single domain or a named list of domains

samplers

For single domain fm_int methods, an object specifying one or more subsets of the domain, and optional weighting in a weight variable. For fm_int.list, a list of sampling definitions, where data frame elements may contain information for multiple domains, in which case each row represent a separate tensor product integration subspace.

...

Additional arguments passed on to other methods

name

For single-domain methods, the variable name to use for the integration points. Default 'x'

int.args

List of arguments passed to line and integration methods.

• method: "stable" (to aggregate integration weights onto mesh nodes) or "direct" (to construct a within triangle/segment integration scheme without aggregating onto mesh nodes)

• nsub1, nsub2: integers controlling the number of internal integration points before aggregation. Points per triangle: (nsub2+1)^2. Points per knot segment: nsub1

format

character; determines the output format, as either "sf" (default for fm_mesh_2d when the sampler is NULL), "numeric" (default for fm_mesh_1d), "bary", or "sp". When NULL, determined by the domain and sampler types.

Value

A tibble, sf, or SpatialPointsDataFrame of 1D and 2D integration points, including a weight column and .block column.

Methods (by class)

• fm_int(list): Multi-domain integration

• fm_int(numeric): Discrete double or integer space integration

• fm_int(character): Discrete character space integration

• fm_int(factor): Discrete factor space integration

• fm_int(SpatRaster): SpatRaster integration. Not yet implemented.

• fm_int(fm_lattice_2d): fm_lattice_2d integration. Not yet implemented.

• fm_int(fm_mesh_1d): fm_mesh_1d integration. Supported samplers:

  • NULL for integration over the entire domain;

  • A length 2 vector defining an interval;

  • A 2-column matrix with a single interval in each row;

  • A tibble with a named column containing a matrix, and optionally a weight column.

• fm_int(fm_mesh_2d): fm_mesh_2d integration. Any sampler class with an associated fm_int_mesh_2d() method is supported.

Examples

# Integration on the interval (2, 3.5) with Simpson's rule
ips <- fm_int(fm_mesh_1d(0:4), samplers = cbind(2, 3.5))
plot(ips$x, ips$weight)


# Create integration points for the two intervals [0,3] and [5,10]
ips <- fm_int(
  fm_mesh_1d(0:10),
  matrix(c(0, 3, 5, 10), nrow = 2, byrow = TRUE)
)
plot(ips$x, ips$weight)


# Convert a 1D mesh into integration points
mesh <- fm_mesh_1d(seq(0, 10, by = 1))
ips <- fm_int(mesh, name = "time")
plot(ips$time, ips$weight)


if (require("ggplot2", quietly = TRUE)) {
  #' Integrate on a 2D mesh with polygon boundary subset
  ips <- fm_int(fmexample$mesh, fmexample$boundary_sf[[1]])
  ggplot() +
    geom_sf(data = fm_as_sfc(fmexample$mesh, multi = TRUE), alpha = 0.5) +
    geom_sf(data = fmexample$boundary_sf[[1]], fill = "red", alpha = 0.5) +
    geom_sf(data = ips, aes(size = weight)) +
    scale_size_area()
}


ips <- fm_int(
  fm_mesh_1d(0:10, boundary = "cyclic"),
  rbind(c(0, 3), c(5, 10))
)
plot(ips$x, ips$weight)