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From: David Andrs <David.Andrs@in...>  20110915 18:52:28

/* $Id: ex4.C 2501 20071120 02:33:29Z benkirk $ */ /* The Next Great Finite Element Library. */ /* Copyright (C) 2003 Benjamin S. Kirk */ /* This library is free software; you can redistribute it and/or */ /* modify it under the terms of the GNU Lesser General Public */ /* License as published by the Free Software Foundation; either */ /* version 2.1 of the License, or (at your option) any later version. */ /* This library is distributed in the hope that it will be useful, */ /* but WITHOUT ANY WARRANTY; without even the implied warranty of */ /* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU */ /* Lesser General Public License for more details. */ /* You should have received a copy of the GNU Lesser General Public */ /* License along with this library; if not, write to the Free Software */ /* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 021111307 USA */ // <h1>Example 19  Solving the 2D Young Laplace Problem using nonlinear solvers</h1> // // This example shows how to use the NonlinearImplicitSystem class // to efficiently solve nonlinear problems in parallel. // // In nonlinear systems, we aim at finding x that satisfy R(x) = 0. // In nonlinear finite element analysis, the residual is typically // of the form R(x) = K(x)*x  f, with K(x) the system matrix and f // the "righthandside". The NonlinearImplicitSystem class expects // two callback functions to compute the residual R and its Jacobian // for the Newton iterations. Here, we just approximate // the true Jacobian by K(x). // // You can turn on preconditining of the matrix free system using the // jacobian by passing "pre" on the command line. Currently this only // work with Petsc so this isn't used by using "make run" // // This example also runs with the experimental Trilinos NOX solvers by specifying // the usetrilinos command line argument. // C++ include files that we need #include <iostream> #include <algorithm> #include <cmath> // Various include files needed for the mesh & solver functionality. #include "libmesh.h" #include "mesh.h" #include "mesh_refinement.h" #include "exodusII_io.h" #include "equation_systems.h" #include "fe.h" #include "quadrature_gauss.h" #include "dof_map.h" #include "sparse_matrix.h" #include "numeric_vector.h" #include "dense_matrix.h" #include "dense_vector.h" #include "elem.h" #include "string_to_enum.h" #include "getpot.h" // The nonlinear solver and system we will be using #include "nonlinear_solver.h" #include "nonlinear_implicit_system.h" #include "trilinos_preconditioner.h" // Necessary for programmatically setting petsc options #ifdef LIBMESH_HAVE_PETSC #include <petsc.h> #endif #ifdef LIBMESH_HAVE_ML #include "ml_MultiLevelPreconditioner.h" #endif // Bring in everything from the libMesh namespace using namespace libMesh; // A reference to our equation system EquationSystems *_equation_system = NULL; // Lets define the physical parameters of the equation const Real kappa = 1.; const Real sigma = 0.2; // This function computes the Jacobian K(x) void compute_jacobian (const NumericVector<Number>& soln, SparseMatrix<Number>& jacobian, NonlinearImplicitSystem& sys) { // Get a reference to the equation system. EquationSystems &es = *_equation_system; // Get a constant reference to the mesh object. const MeshBase& mesh = es.get_mesh(); // The dimension that we are running const unsigned int dim = mesh.mesh_dimension(); // Get a reference to the NonlinearImplicitSystem we are solving NonlinearImplicitSystem& system = es.get_system<NonlinearImplicitSystem>("LaplaceYoung"); // A reference to the \p DofMap object for this system. The \p DofMap // object handles the index translation from node and element numbers // to degree of freedom numbers. We will talk more about the \p DofMap // in future examples. const DofMap& dof_map = system.get_dof_map(); // Get a constant reference to the Finite Element type // for the first (and only) variable in the system. FEType fe_type = dof_map.variable_type(0); // Build a Finite Element object of the specified type. Since the // \p FEBase::build() member dynamically creates memory we will // store the object as an \p AutoPtr<FEBase>. This can be thought // of as a pointer that will clean up after itself. AutoPtr<FEBase> fe (FEBase::build(dim, fe_type)); // A 5th order Gauss quadrature rule for numerical integration. QGauss qrule (dim, FIFTH); // Tell the finite element object to use our quadrature rule. fe>attach_quadrature_rule (&qrule); // Here we define some references to cellspecific data that // will be used to assemble the linear system. // We begin with the element Jacobian * quadrature weight at each // integration point. const std::vector<Real>& JxW = fe>get_JxW(); // The element shape functions evaluated at the quadrature points. const std::vector<std::vector<Real> >& phi = fe>get_phi(); // The element shape function gradients evaluated at the quadrature // points. const std::vector<std::vector<RealGradient> >& dphi = fe>get_dphi(); // Define data structures to contain the Jacobian element matrix. // Following basic finite element terminology we will denote these // "Ke". More detail is in example 3. DenseMatrix<Number> Ke; // This vector will hold the degree of freedom indices for // the element. These define where in the global system // the element degrees of freedom get mapped. std::vector<unsigned int> dof_indices; // Now we will loop over all the active elements in the mesh which // are local to this processor. // We will compute the element Jacobian contribution. MeshBase::const_element_iterator el = mesh.active_local_elements_begin(); const MeshBase::const_element_iterator end_el = mesh.active_local_elements_end(); for ( ; el != end_el; ++el) { // Store a pointer to the element we are currently // working on. This allows for nicer syntax later. const Elem* elem = *el; // Get the degree of freedom indices for the // current element. These define where in the global // matrix and righthandside this element will // contribute to. dof_map.dof_indices (elem, dof_indices); // Compute the elementspecific data for the current // element. This involves computing the location of the // quadrature points (q_point) and the shape functions // (phi, dphi) for the current element. fe>reinit (elem); // Zero the element Jacobian before // summing them. We use the resize member here because // the number of degrees of freedom might have changed from // the last element. Note that this will be the case if the // element type is different (i.e. the last element was a // triangle, now we are on a quadrilateral). Ke.resize (dof_indices.size(), dof_indices.size()); // Now we will build the element Jacobian. This involves // a double loop to integrate the test funcions (i) against // the trial functions (j). Note that the Jacobian depends // on the current solution x, which we access using the soln // vector. // for (unsigned int qp=0; qp<qrule.n_points(); qp++) { Gradient grad_u; for (unsigned int i=0; i<phi.size(); i++) grad_u += dphi[i][qp]*soln(dof_indices[i]); const Number K = 1./std::sqrt(1. + grad_u*grad_u); for (unsigned int i=0; i<phi.size(); i++) for (unsigned int j=0; j<phi.size(); j++) Ke(i,j) += JxW[qp]*( K*(dphi[i][qp]*dphi[j][qp]) + kappa*phi[i][qp]*phi[j][qp] ); } dof_map.constrain_element_matrix (Ke, dof_indices); // Add the element matrix to the system Jacobian. jacobian.add_matrix (Ke, dof_indices); } // That's it. } // Here we compute the residual R(x) = K(x)*x  f. The current solution // x is passed in the soln vector void compute_residual (const NumericVector<Number>& soln, NumericVector<Number>& residual, NonlinearImplicitSystem& sys) { EquationSystems &es = *_equation_system; // Get a constant reference to the mesh object. const MeshBase& mesh = es.get_mesh(); // The dimension that we are running const unsigned int dim = mesh.mesh_dimension(); libmesh_assert (dim == 2); // Get a reference to the NonlinearImplicitSystem we are solving NonlinearImplicitSystem& system = es.get_system<NonlinearImplicitSystem>("LaplaceYoung"); // A reference to the \p DofMap object for this system. The \p DofMap // object handles the index translation from node and element numbers // to degree of freedom numbers. We will talk more about the \p DofMap // in future examples. const DofMap& dof_map = system.get_dof_map(); // Get a constant reference to the Finite Element type // for the first (and only) variable in the system. FEType fe_type = dof_map.variable_type(0); // Build a Finite Element object of the specified type. Since the // \p FEBase::build() member dynamically creates memory we will // store the object as an \p AutoPtr<FEBase>. This can be thought // of as a pointer that will clean up after itself. AutoPtr<FEBase> fe (FEBase::build(dim, fe_type)); // A 5th order Gauss quadrature rule for numerical integration. QGauss qrule (dim, FIFTH); // Tell the finite element object to use our quadrature rule. fe>attach_quadrature_rule (&qrule); // Declare a special finite element object for // boundary integration. AutoPtr<FEBase> fe_face (FEBase::build(dim, fe_type)); // Boundary integration requires one quadraure rule, // with dimensionality one less than the dimensionality // of the element. QGauss qface(dim1, FIFTH); // Tell the finte element object to use our // quadrature rule. fe_face>attach_quadrature_rule (&qface); // Here we define some references to cellspecific data that // will be used to assemble the linear system. // We begin with the element Jacobian * quadrature weight at each // integration point. const std::vector<Real>& JxW = fe>get_JxW(); // The element shape functions evaluated at the quadrature points. const std::vector<std::vector<Real> >& phi = fe>get_phi(); // The element shape function gradients evaluated at the quadrature // points. const std::vector<std::vector<RealGradient> >& dphi = fe>get_dphi(); // Define data structures to contain the resdual contributions DenseVector<Number> Re; // This vector will hold the degree of freedom indices for // the element. These define where in the global system // the element degrees of freedom get mapped. std::vector<unsigned int> dof_indices; // Now we will loop over all the active elements in the mesh which // are local to this processor. // We will compute the element residual. residual.zero(); MeshBase::const_element_iterator el = mesh.active_local_elements_begin(); const MeshBase::const_element_iterator end_el = mesh.active_local_elements_end(); for ( ; el != end_el; ++el) { // Store a pointer to the element we are currently // working on. This allows for nicer syntax later. const Elem* elem = *el; // Get the degree of freedom indices for the // current element. These define where in the global // matrix and righthandside this element will // contribute to. dof_map.dof_indices (elem, dof_indices); // Compute the elementspecific data for the current // element. This involves computing the location of the // quadrature points (q_point) and the shape functions // (phi, dphi) for the current element. fe>reinit (elem); // We use the resize member here because // the number of degrees of freedom might have changed from // the last element. Note that this will be the case if the // element type is different (i.e. the last element was a // triangle, now we are on a quadrilateral). Re.resize (dof_indices.size()); // Now we will build the residual. This involves // the construction of the matrix K and multiplication of it // with the current solution x. We rearrange this into two loops: // In the first, we calculate only the contribution of // K_ij*x_j which is independent of the row i. In the second loops, // we multiply with the rowdependent part and add it to the element // residual. for (unsigned int qp=0; qp<qrule.n_points(); qp++) { Number u = 0; Gradient grad_u; for (unsigned int j=0; j<phi.size(); j++) { u += phi[j][qp]*soln(dof_indices[j]); grad_u += dphi[j][qp]*soln(dof_indices[j]); } const Number K = 1./std::sqrt(1. + grad_u*grad_u); for (unsigned int i=0; i<phi.size(); i++) Re(i) += JxW[qp]*( K*(dphi[i][qp]*grad_u) + kappa*phi[i][qp]*u ); } // At this point the interior element integration has // been completed. However, we have not yet addressed // boundary conditions. // The following loops over the sides of the element. // If the element has no neighbor on a side then that // side MUST live on a boundary of the domain. for (unsigned int side=0; side<elem>n_sides(); side++) if (elem>neighbor(side) == NULL) { // The value of the shape functions at the quadrature // points. const std::vector<std::vector<Real> >& phi_face = fe_face>get_phi(); // The Jacobian * Quadrature Weight at the quadrature // points on the face. const std::vector<Real>& JxW_face = fe_face>get_JxW(); // Compute the shape function values on the element face. fe_face>reinit(elem, side); // Loop over the face quadrature points for integration. for (unsigned int qp=0; qp<qface.n_points(); qp++) { // This is the righthandside contribution (f), // which has to be subtracted from the current residual for (unsigned int i=0; i<phi_face.size(); i++) Re(i) = JxW_face[qp]*sigma*phi_face[i][qp]; } } dof_map.constrain_element_vector (Re, dof_indices); residual.add_vector (Re, dof_indices); } // That's it. } // Begin the main program. int main (int argc, char** argv) { // Initialize libMesh and any dependent libaries, like in example 2. LibMeshInit init (argc, argv); #if !defined(LIBMESH_HAVE_PETSC) && !defined(LIBMESH_HAVE_TRILINOS) if (libMesh::processor_id() == 0) std::cerr << "ERROR: This example requires libMesh to be\n" << "compiled with nonlinear solver support from\n" << "PETSc or Trilinos!" << std::endl; return 0; #endif #ifndef LIBMESH_ENABLE_AMR if (libMesh::processor_id() == 0) std::cerr << "ERROR: This example requires libMesh to be\n" << "compiled with AMR support!" << std::endl; return 0; #else // Create a GetPot object to parse the command line GetPot command_line (argc, argv); // Check for proper calling arguments. if (argc < 3) { if (libMesh::processor_id() == 0) std::cerr << "Usage:\n" <<"\t " << argv[0] << " r 2" << std::endl; // This handy function will print the file name, line number, // and then abort. libmesh_error(); } // Brief message to the user regarding the program name // and command line arguments. else { std::cout << "Running " << argv[0]; for (int i=1; i<argc; i++) std::cout << " " << argv[i]; std::cout << std::endl << std::endl; } // Read number of refinements int nr = 2; if ( command_line.search(1, "r") ) nr = command_line.next(nr); // Read FE order from command line std::string order = "FIRST"; if ( command_line.search(2, "Order", "o") ) order = command_line.next(order); // Read FE Family from command line std::string family = "LAGRANGE"; if ( command_line.search(2, "FEFamily", "f") ) family = command_line.next(family); // Cannot use dicontinuous basis. if ((family == "MONOMIAL")  (family == "XYZ")) { std::cout << "ex19 currently requires a C^0 (or higher) FE basis." << std::endl; libmesh_error(); } if ( command_line.search(1, "pre") ) { #ifdef LIBMESH_HAVE_PETSC //Use the jacobian for preconditioning. PetscOptionsSetValue("snes_mf_operator",PETSC_NULL); #else std::cerr<<"Must be using PetsC to use jacobian based preconditioning"<<std::endl; //returning zero so that "make run" won't fail if we ever enable this capability there. return 0; #endif //LIBMESH_HAVE_PETSC } // Skip this 2D example if libMesh was compiled as 1Donly. libmesh_example_assert(2 <= LIBMESH_DIM, "2D support"); // Create a mesh from file. Mesh mesh; mesh.read ("lshaped.xda"); if (order != "FIRST") mesh.all_second_order(); MeshRefinement(mesh).uniformly_refine(nr); // Print information about the mesh to the screen. mesh.print_info(); // Create an equation systems object. EquationSystems equation_systems (mesh); _equation_system = &equation_systems; // Declare the system and its variables. // Creates a system named "LaplaceYoung" NonlinearImplicitSystem& system = equation_systems.add_system<NonlinearImplicitSystem> ("LaplaceYoung"); // Here we specify the tolerance for the nonlinear solver and // the maximum of nonlinear iterations. equation_systems.parameters.set<Real> ("nonlinear solver tolerance") = 1.e12; equation_systems.parameters.set<unsigned int> ("nonlinear solver maximum iterations") = 50; // Adds the variable "u" to "LaplaceYoung". "u" // will be approximated using secondorder approximation. system.add_variable("u", Utility::string_to_enum<Order> (order), Utility::string_to_enum<FEFamily>(family)); // Give the system a pointer to the functions that update // the residual and Jacobian. system.nonlinear_solver>residual = compute_residual; system.nonlinear_solver>jacobian = compute_jacobian; // Uncomment this for matrixfree assembling // system.nonlinear_solver>jacobian = NULL; // Initialize the data structures for the equation system. equation_systems.init(); // Preconditioning TrilinosPreconditioner<Number> pc; pc.set_matrix(*system.matrix); // pc.set_type(SOR_PRECOND); // pc.set_type(ILU_PRECOND); // Teuchos::ParameterList list; // list.set("fact: leveloffill", 5); // use ILU(5) // pc.set_params(list); pc.set_type(AMG_PRECOND); Teuchos::ParameterList list; // ML_Epetra::SetDefaults("DD", list); // list.set("max levels",6); // list.set("increasing or decreasing","increasing"); // list.set("aggregation: type", "METIS"); // list.set("aggregation: nodes per aggregate", 16); // list.set("smoother: pre or post", "both"); // list.set("coarse: type","AmesosKLU"); // list.set("smoother: type", "Aztec"); ML_Epetra::SetDefaults("SA", list); list.set("max levels",2); list.set("increasing or decreasing","decreasing"); list.set("aggregation: type", "MIS"); list.set("coarse: type","AmesosKLU"); pc.set_params(list); pc.init(); system.nonlinear_solver>attach_preconditioner(&pc); // Prints information about the system to the screen. equation_systems.print_info(); // Solve the system "LaplaceYoung", print the number of iterations // and final residual equation_systems.get_system("LaplaceYoung").solve(); // Print out final convergence information. This duplicates some // output from during the solve itself, but demonstrates another way // to get this information after the solve is complete. std::cout << "LaplaceYoung system solved at nonlinear iteration " << system.n_nonlinear_iterations() << " , final nonlinear residual norm: " << system.final_nonlinear_residual() << std::endl; #ifdef LIBMESH_HAVE_EXODUS_API // After solving the system write the solution ExodusII_IO (mesh).write_equation_systems ("out.e", equation_systems); #endif // #ifdef LIBMESH_HAVE_EXODUS_API #endif // #ifndef LIBMESH_ENABLE_AMR // All done. return 0; } 
From: Roy Stogner <roystgnr@ic...>  20110920 19:02:28

On Thu, 15 Sep 2011, David Andrs wrote: > 1) Improving AztecOO solver: >  using more of its builtin preconditioners >  using more solver types  like CG, BISTABCG > > 2) Improving NOX >  can do preconditioned JFNK (IFPACK must be enabled AFAIK) >  can do jacobian There's a bug here: you forgot to change PetscNonlinearSolver to NoxNonlinearSolver in a couple START_LOG lines. > 3) Adding supprt for ML package The configure part of the patch didn't apply for me here, presumably because I ran a bootstrap or someone else checked in a bootstrap using a different autoconf. Applying the rest of the patch and rebootstrapping worked. > Attached is also modified ex19, where I played and tested those > patches. There are commented lines with a few preconditioners to try > out (ILU, AMG). No time to play much with them myself, but I don't see any other obvious problems, if you're ready to commit the main patches. Trilinos support still isn't in great shape (anyone know why I'm seeing AMR convergence stall on ex14?) but you're at least uniformly improving it. :) > Notes on preconditioners: I'm not an expert here, but there are only > two preconds implemented: ILU (thru IFPACK) and AMG (thru ML). > IFPACK supports a lot more than just ILU, however there are no > PRECOND_ enum entries for those and I'm not quite sure if there > should be one. What would be a good thing to do? Add new ENUM > entries and support those? I think so. Derek ought to have the last word there, though; he's more on top of the Preconditioner classes than I am. The only problem is: > There is a possibility there is an overlap, but the names are just > slightly different: like (ICC in PETSc) and ICT in Trilinos. I do > not know. If someone knows, let me know or just build on top of my > patches. It would be nice to get that straightened out before adding new enums; otherwise any fix to consolidate the enums later would require a backwardsincompatible API change or a collection of "deprecated" enums in every test.  Roy 
From: Derek Gaston <friedmud@gm...>  20110920 19:22:33
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On Sep 20, 2011, at 1:02 PM, Roy Stogner wrote: > >> Notes on preconditioners: I'm not an expert here, but there are only >> two preconds implemented: ILU (thru IFPACK) and AMG (thru ML). >> IFPACK supports a lot more than just ILU, however there are no >> PRECOND_ enum entries for those and I'm not quite sure if there >> should be one. What would be a good thing to do? Add new ENUM >> entries and support those? > > I think so. Derek ought to have the last word there, though; he's > more on top of the Preconditioner classes than I am. The only problem > is: We can add enums if possible… but I'd really rather try to match things in Trilinos to our current enums. There has to be an ASM for example… and an LU, etc… Derek 
From: Roy Stogner <roystgnr@ic...>  20110923 19:54:07

On Tue, 20 Sep 2011, Roy Stogner wrote: > There's a bug here: you forgot to change PetscNonlinearSolver to > NoxNonlinearSolver in a couple START_LOG lines. One more serious bug, too: there's a use of libmesh_cast_ref which breaks for me in optimized modes. Apparently (at least in Trilinos 9.0.3) the Epetra_Operator is a virtual base class of Epetra_FECrsMatrix, so we're not allowed to optimize that into a static_cast. Replacing libmesh_cast_ref with dynamic_cast fixes compilation for me.  Roy 
From: David Andrs <David.Andrs@in...>  20110928 15:37:58
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Roy Stogner <roystgnr@...> wrote on 09/23/2011 01:53:58 PM: > > > On Tue, 20 Sep 2011, Roy Stogner wrote: > > > There's a bug here: you forgot to change PetscNonlinearSolver to > > NoxNonlinearSolver in a couple START_LOG lines. > > One more serious bug, too: there's a use of libmesh_cast_ref which > breaks for me in optimized modes. Apparently (at least in Trilinos > 9.0.3) the Epetra_Operator is a virtual base class of > Epetra_FECrsMatrix, so we're not allowed to optimize that into a > static_cast. Replacing libmesh_cast_ref with dynamic_cast fixes > compilation for me. Fixed both issues. Also found another one: returning total number of _lin._ iterations instead of _nonlinear_ ones. While doing that, I implemented get_total_linear_iterations for Nox solver as mentioned in another thread here. All is checked in.  David 
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