Field functions¶
A field function where and is defined by:
(1)¶
with and . A field function transforms a multivariate stochastic process:
where is discretized according to the into the multivariate stochastic process:
such that:
where the mesh is discretized according to the .
A field function also acts on fields and produces fields of possibly different dimension () and mesh ( or ).
Value function¶
A value function is a particular field function that leaves the mesh of a field invariant and can be defined using a function such that:
(2)¶
Let us note that the input dimension of is still , the dimension of . Its output dimension is equal to . The creation of a value function requires the function and the integer : the dimension of the vertices of the mesh . These data are required to test the compatibility of the dimensions when a composite process is created using the value function.
Vertex value function¶
A vertex-value function is a particular field function that leaves the mesh of a field invariant and is defined by a function such that:
(3)¶
Let us note that the input dimension of is still , the dimension of . Its output dimension is equal to .