dolfin team mailing list archive

[Johan Hake <johan.hake@xxxxxxxxx>]

On Thursday May 26 2011 07:25:55 Douglas Brinkerhoff wrote:
> Question #159021 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/159021
> 
> Douglas Brinkerhoff posted a new comment:
> How would one create an expression out of some already known data?  It
> seems as though the Expression class is very good for building a
> spatially dependent combination of parameters and elementary functions,
> but I'm not sure how I could turn some list or array of data into an
> expression.  

Try this:

from dolfin import *

mesh = UnitCube(10,10,10)
V = FunctionSpace(mesh,"Lagrange",1)
W = MixedFunctionSpace([V,V])

u0 = Function(V)
v0 = Function(V)

# Fill u0, v0
u0.vector()[:] = 1.0
v0.vector()[:] = 2.0

class InitConditions(Expression):
    def __init__(self, u0, v0):
        self.u0 = u0
        self.v0 = v0

    def eval(self, value, x):
        value[0] = self.u0(x)
        value[1] = self.v0(x)

    def value_shape(self):
        return (2,)

init_cond = InitConditions(u0, v0)

U0 = project(init_cond, W)

############
This can be done as a compiled expression for better speed up. But I guess a 
Python Expression is enough for this case.

Johan








> Stated another way:
> 
> In my particular application, I'm solving for vertically averaged
> velocities within glacial ice (Basically shallow water equations, with
> some extra stuff).  There is a 0-order solution which is solely a
> function of local geometry, e.g. Surface slope and ice thickness, which
> are currently parameterized as coefficients.  This is just a simple
> calculation, not a PDE, and it is also stored as coefficients, called u0
> and v0.  I want to use this zero order solution as an initial guess for
> a non-linear system of equations which yields a first order solution.
> Is there a way to package u0 and v0 as an expression, or something like
> it, such that it is available to be projected, assigned, or
> interpolated?