Typically, If you want to solve the continuous equation L u = f where L is a Laplacian or any PDE operator and f is some forcing function of (x,y,z) using FEM, then you form your algebraic system using weak formulation by multiplying with test functions and integrating (and applying Green's formula or integration by parts) so Phi_j appears on both sides. So typically for your algebraic system A U = F
F will be integral f(x,y,z) Phi_j and A will be integral L phi_j and then you do integration by parts etc. Since you want to express f(x,y,z) = f_i Phi_i F = integral f_i Phi_i Phi_j 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
