Yeah, this makes perfect sense to me. I'm having difficulty with step 2 though. In main, I define a MeshData that I read in from an input file with the Mesh itself and the associated data. Basically, F_nodal IS mesh_data.get_data(el.get_node(i))[0], but I don't see a get_mesh_data function or something similar in the class doc for System... Nor can I find a way to access the MeshData object associated with the mesh once I have the mesh object pointer...
On Fri, Mar 26, 2010 at 5:38 PM, Rahul Sampath <[email protected]>wrote: > Here are the steps to solve Laplacian u(x,y,z) = f(x,y,z): > > 1. Form A = Assembly( A_elem ) where A_elem = integral(dPhi_i*dPhi_j) > 2. Form F_nodal = f(x_i,y_i,z_i) at all mesh nodes > 3. Form MassMatrix = Assembly( M_elem ) where M_elem = integral(Phi_k, > Phi_j) > 4. Form RHS = MassMatrix*F_nodal > 5. Solve A U_nodal = RHS for U_nodal > > > > On Fri, Mar 26, 2010 at 5:26 PM, Karen Lee <[email protected]> wrote: > > This would be for the interpolation only right? > > > > So if I use this GlobalRHS, and construct my LHS based on the actual > problem > > I want to solve (just a Poisson, so I would be using dphi), it would be > > equivalent to solving the problem with the RHS being interpolated? > > > > Karen > > > > > > On Fri, Mar 26, 2010 at 5:23 PM, Rahul Sampath <[email protected]> > > wrote: > >> > >> To be more precise: > >> > >> GlobalMassMatrix = Sum_over_elements{ > >> integral_over_current_element_using_quadrature(phi_i*phi_j) } > >> > >> GlobalRHS = GlobalMassMatrix*Nodal_F_Vector > >> > >> On Fri, Mar 26, 2010 at 5:22 PM, Rahul Sampath <[email protected] > > > >> wrote: > >> > This is what I meant: > >> > > >> > MassMatrix = integral(phi_i*phi_j) > >> > > >> > RHS = MassMatrix*Nodal_F_Vector > >> > > >> > > >> > On Fri, Mar 26, 2010 at 5:11 PM, Karen Lee <[email protected]> > wrote: > >> >> Sorry, I think I was probably confused. I guess you just meant that I > >> >> can > >> >> simply use integral of f_i phi_i phi_j as my RHS, and my original LHS > >> >> as my > >> >> LHS, and that would already be effectively an interpolation? Please > let > >> >> me > >> >> know if this is the correct way to think about it instead of the long > >> >> message I sent with lots of code... > >> >> > >> >> My 2 questions regarding access to data would still remain: > >> >> > >> >> 1) I am still having problems accessing MeshData from the assemble > >> >> function. I would like to do something like > >> >> mesh_data.get_data(el.get_node(i))[0] to get the first data variable > >> >> for > >> >> node i with an element, i from 0 to 3, but I'm not sure how to access > >> >> mesh_data from my System. (I should use Linear Implicit System so I > can > >> >> have > >> >> the matrix on the lhs right?) > >> >> > >> >> 2) The other question is, for Fe, do I integrate over all the > >> >> quadrature > >> >> points of phi_i and phi_j with f_i being a constant? > >> >> > >> >> Thank you so much!!! > >> >> Karen > >> >> > >> >> > >> >> On Fri, Mar 26, 2010 at 4:57 PM, Karen Lee <[email protected]> > wrote: > >> >>> > >> >>> Thanks Rahul. Your responses have clarified things for me. > >> >>> > >> >>> I am still having problems accessing MeshData from the assemble > >> >>> function > >> >>> (which is only supposed to have 2 arguments right?) > >> >>> > >> >>> I can do: > >> >>> > >> >>> void assemble_load(EquationSystems& es, > >> >>> const std::string& system_name) > >> >>> { > >> >>> > >> >>> libmesh_assert (system_name == "load"); > >> >>> > >> >>> > >> >>> const MeshBase& mesh = es.get_mesh(); > >> >>> printf("mesh_data obtained"); > >> >>> > >> >>> ...... > >> >>> > >> >>> But I'm not sure how I can get the MeshData object that I created in > >> >>> main > >> >>> that's attached to the mesh I created. In the look iterating over > the > >> >>> elements el, I know that I have to use something like > >> >>> mesh_data.get_data(el.get_node(i))[0] to get the first data variable > >> >>> for > >> >>> node i with an element, i from 0 to 3, but I'm not sure how to > access > >> >>> mesh_data from my System. (I should use Linear Implicit System so I > >> >>> can have > >> >>> the matrix on the lhs right?) > >> >>> > >> >>> My code is based on example 3, and the relevant part is this (not > sure > >> >>> if > >> >>> it's correct): > >> >>> > >> >>> for ( ; el != end_el ; ++el) > >> >>> { > >> >>> const Elem* elem = *el; > >> >>> > >> >>> dof_map.dof_indices (elem, dof_indices); > >> >>> > >> >>> fe->reinit (elem); > >> >>> > >> >>> Ke.resize (dof_indices.size(), > >> >>> dof_indices.size()); > >> >>> > >> >>> Fe.resize (dof_indices.size()); > >> >>> > >> >>> for (unsigned int qp=0; qp<qrule.n_points(); qp++) > >> >>> { > >> >>> > >> >>> for (unsigned int i=0; i<phi.size(); i++) > >> >>> for (unsigned int j=0; j<phi.size(); j++) > >> >>> { > >> >>> Ke(i,j) += JxW[qp]*(phi[i][qp]*phi[j][qp]); > >> >>> } > >> >>> > >> >>> { > >> >>> for (unsigned int i=0; i<phi.size(); i++) > >> >>> { > >> >>> for (unsigned int k=0; k<phi.size(); k++) > >> >>> { > >> >>> Fe(i) += > >> >>> JxW[qp]*mesh_data.get_data(el.get_node(k))[0]*phi[i][qp]phi[k][qp]; > >> >>> > >> >>> } > >> >>> } > >> >>> } > >> >>> .... > >> >>> > >> >>> The other question is, for Fe, do I integrate over all the > quadrature > >> >>> points of phi_i and phi_j with f_i being a constant? > >> >>> > >> >>> Then once I get this solution (the variable name is "R", let's say), > I > >> >>> hope to use it in place of mesh_data.get_data(el.get_node(k))[0] > and > >> >>> do > >> >>> something like this (of course this is another system that I'm > adding > >> >>> to > >> >>> EquationSystems): > >> >>> > >> >>> for (unsigned int qp=0; qp<qrule.n_points(); qp++) > >> >>> { > >> >>> > >> >>> for (unsigned int i=0; i<phi.size(); i++) > >> >>> > >> >>> > >> >>> for (unsigned int j=0; j<phi.size(); j++) > >> >>> { > >> >>> Ke2(i,j) += JxW[qp]*(dphi[i][qp]*dphi[j][qp]); > >> >>> > >> >>> > >> >>> } > >> >>> > >> >>> { > >> >>> const Real x = q_point[qp](0); > >> >>> const Real y = q_point[qp](1); > >> >>> const Real z = q_point[qp](2); > >> >>> > >> >>> > >> >>> > >> >>> > >> >>> const Real fxy = R(x,y,z); > >> >>> > >> >>> for (unsigned int i=0; i<phi.size(); i++) > >> >>> > >> >>> > >> >>> Fe2(i) += JxW[qp]*fxy*phi[i][qp]; > >> >>> } > >> >>> } > >> >>> > >> >>> I'm not sure how to access anything in a Variable object though... > >> >>> Let's > >> >>> say "R" being a a variable I add to the first system to get the RHS > >> >>> interpolation, and "u" is the variable I add to the second equation > >> >>> system, > >> >>> which is the actual solution I'm after... I just know that I can > >> >>> output the > >> >>> values of the solution at various nodal points in a file, but am not > >> >>> sure > >> >>> what to do with the data structure and how I can extract values at > >> >>> different > >> >>> arbitrary locations. > >> >>> > >> >>> Apologies for the lengthy email... > >> >>> > >> >>> Thanks, > >> >>> Karen > >> >>> > >> >>> > >> >>> On Fri, Mar 26, 2010 at 9:15 AM, Rahul Sampath > >> >>> <[email protected]> > >> >>> wrote: > >> >>>> > >> >>>> 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. 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