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 lets invariant the mesh of a
field and defined by a function
such that:
(2)¶
Let’s note that the input dimension of
still designs
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
. This data is
required for tests on the compatibility of dimension when a composite
process is created using the value function.
Vertex value function
A vertex-value function
is
a particular field function that lets invariant the mesh of a
field and defined by a function
such that:
(3)¶
Let’s note that the input dimension of
still design
the dimension of
:
. Its output dimension is
equal to
.