Hi Rahul, I'm not completely sure what you mean.
I would like to form my RHS by integrating f_i Phi_i (I guess there's no
need to multiply Phi_j? But you can correct me) for each element.
In order to do so, I need values of f at various quadrature points. I have f
at various nodal values. The question is, how do I get this linear
interpolation...
Do you mean that, for each element, I form the mass matrix by the xyz values
of the nodes (and a constant 1) and solve for the coefficient by saying
\sum_j A_ij y_j= f_i, where:
A = [1 x1 y1 z1;
1 x2 y2 z2;
1 x3 y3 z3;
1 x4 y4 z4] and y_j would be my unknown (where j = 1 corresponds to
the constant value, and 2, 3, 4 corresponds to the gradient in the x, y, z
directions respectively)?
Thanks,
Karen
On Thu, Mar 25, 2010 at 11:44 PM, Rahul Sampath <[email protected]>wrote:
> If you want to form a RHS by integrating f_i Phi_i Phi_j, You could
> form a Mass matrix and then multiply with your vector of nodal values.
>
> Rahul
>
> On Thu, Mar 25, 2010 at 11:40 PM, Karen Lee <[email protected]> wrote:
> > I'm afraid you misunderstood. I don't have the function that when given
> x,
> > y, z values gives me the function value. What I do have is just the
> values
> > at the nodes of the mesh, which need to be linearly interpolated such
> that I
> > will have something like exact_function. which gives me the value when
> > supplied with any x, y, z.
> >
> >
> >
> > On Thu, Mar 25, 2010 at 10:54 PM, Liang <[email protected]> wrote:
> >
> >> Karen Lee wrote:
> >>
> >>> I guess I'm not clear how to do this: Load data as a solution into
> that,
> >>> and
> >>> query
> >>> it when you're integrating your real system.
> >>>
> >>> I have:
> >>> Mesh mesh(3);
> >>> MeshData mesh_data(mesh);
> >>> mesh_data.activate();
> >>> mesh.read (mesh_file, &mesh_data);
> >>> mesh_data.read(mesh_file);
> >>> EquationSystems equation_systems (mesh);
> >>>
> >>>
> >>> equation_systems.add_system<ExplicitSystem> ("RHS");
> >>> equation_systems.get_system("RHS").add_variable("R", FIRST);
> >>>
> >>> After that, I'm not clear how exactly to load data as a solution in the
> >>> code. My goal is to get a linearly interpolated function of my data on
> the
> >>> nodes (in the form of exact_solution, such that I get the function
> value
> >>> out
> >>> when supplying x, y and z).
> >>>
> >>> Hope that clarifies things, and sorry for the multiple emails...
> >>>
> >>> Karen
> >>>
> >>>
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> >>>
> >>>
> >> so you already have the function, which is obtained from your discreted
> >> data?
> >> then just put the function as the exact_function.
> >> I think you are trying the 3D case, start from a 2d will be easier.
> >>
> >> Liang
> >>
> >
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