RMdivfree: Divfree Covariance Model

In RandomFields: Simulation and Analysis of Random Fields

Description

RMdivfree is a multivariate covariance model which depends on a univariate stationary covariance model where the covariance function phi(h) is twice differentiable.

The corresponding matrix-valued covariance function C of the model only depends on the difference h between two points and it is given by the following components:

• the potential

• the vector field given by

  C(h)=( - Δ E + \nabla \nabla^T ) C_0(h)

• the curl field

Usage

RMdivfree(phi, which, var, scale, Aniso, proj)

Arguments

phi	a univariate stationary covariance model (in 2 or 3 dimensions).
which	vector of integers. If not given all components are returned; otherwise the selected components are returned.
var,scale,Aniso,proj	optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Details

The model returns the potential field in the first component, the corresponding divfree field and the field of curl strength in the last component.

See also the models RMcurlfree and RMvector.

Value

RMdivfree returns an object of class RMmodel.

References

• Scheuerer, M. and Schlather, M. (2012) Covariance Models for Divergence-Free and Curl-Free Random Vector Fields. Stochastic Models 28:3.

See Also

RMcurlfree, RMderiv, RMvector, RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RMdivfree(RMgauss(), scale=4)
plot(model, dim=2)

x.seq <- y.seq <- seq(-10, 10, 0.2)
simulated <- RFsimulate(model=model, x=x.seq, y=y.seq)

plot(simulated)
plot(simulated, select.variables=1)
plot(simulated, select.variables=2:3)
plot(simulated, select.variables=list(2:3))
plot(simulated, select.variables=list(1, 2:3, 4))
plot(simulated, select.variables=list(1, c(1, 2:3), 4))

RandomFields documentation built on Jan. 19, 2022, 1:06 a.m.