Hi Karen: Take a look at any Nonlinear example problem. Whenever you want to use any solution vector in your residual computation, you will need to interpolate the nodal values using the FEM shape functions for this element and then do the integration. It is very similar to what you want to do. That is why I suggested the Mass matrix trick. It is very simple to implement and fast too especially if you want to change f often. You can use the same Mass matrix with differen f. The catch is that you are using your FE shape functions for your interpolation. As long as you are happy with linear interpolation for f this should do. If you want to interpolate f with a higher order polynomial than your FE shape function then this wont work.
Btw, if I was not clear earlier: You have to form a global Mass matrix by integrating phi_i phi_j over all elements and doing a typically FEM assembly. Then you can simply multiply this global Mass matrix with you global nodal vector for f. On Fri, Mar 26, 2010 at 12:51 AM, Karen Lee <[email protected]> wrote: > 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 >> >>> >> >>> >> >>> ------------------------------------------------------------------------------ >> >>> Download Intel® Parallel Studio Eval >> >>> Try the new software tools for yourself. Speed compiling, find bugs >> >>> proactively, and fine-tune applications for parallel performance. >> >>> See why Intel Parallel Studio got high marks during beta. >> >>> http://p.sf.net/sfu/intel-sw-dev >> >>> _______________________________________________ >> >>> Libmesh-users mailing list >> >>> [email protected] >> >>> https://lists.sourceforge.net/lists/listinfo/libmesh-users >> >>> >> >>> >> >>> >> >> 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 >> >> >> > >> > ------------------------------------------------------------------------------ >> > Download Intel® Parallel Studio Eval >> > Try the new software tools for yourself. Speed compiling, find bugs >> > proactively, and fine-tune applications for parallel performance. >> > See why Intel Parallel Studio got high marks during beta. >> > http://p.sf.net/sfu/intel-sw-dev >> > _______________________________________________ >> > Libmesh-users mailing list >> > [email protected] >> > https://lists.sourceforge.net/lists/listinfo/libmesh-users >> > > > ------------------------------------------------------------------------------ Download Intel® Parallel Studio Eval Try the new software tools for yourself. Speed compiling, find bugs proactively, and fine-tune applications for parallel performance. See why Intel Parallel Studio got high marks during beta. http://p.sf.net/sfu/intel-sw-dev _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
