Line data    Source code

       1             : // The libMesh Finite Element Library.
       2             : // Copyright (C) 2002-2025 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
       3             : 
       4             : // This library is free software; you can redistribute it and/or
       5             : // modify it under the terms of the GNU Lesser General Public
       6             : // License as published by the Free Software Foundation; either
       7             : // version 2.1 of the License, or (at your option) any later version.
       8             : 
       9             : // This library is distributed in the hope that it will be useful,
      10             : // but WITHOUT ANY WARRANTY; without even the implied warranty of
      11             : // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      12             : // Lesser General Public License for more details.
      13             : 
      14             : // You should have received a copy of the GNU Lesser General Public
      15             : // License along with this library; if not, write to the Free Software
      16             : // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
      17             : 
      18             : 
      19             : 
      20             : #ifndef LIBMESH_EIGEN_TIME_SOLVER_H
      21             : #define LIBMESH_EIGEN_TIME_SOLVER_H
      22             : 
      23             : #include "libmesh/libmesh_config.h"
      24             : #ifdef LIBMESH_HAVE_SLEPC
      25             : 
      26             : // Local includes
      27             : #include "libmesh/time_solver.h"
      28             : 
      29             : // C++ includes
      30             : 
      31             : namespace libMesh
      32             : {
      33             : 
      34             : // Forward declarations
      35             : template <typename T> class EigenSolver;
      36             : 
      37             : 
      38             : /**
      39             :  * The name of this class is confusing...it's meant to refer to the
      40             :  * base class (TimeSolver) while still telling one that it's for solving
      41             :  * (generalized) EigenValue problems that arise from finite element
      42             :  * discretizations.  For a time-dependent problem du/dt=F(u), with a
      43             :  * steady solution 0=F(u_0), we look at the time evolution of a small
      44             :  * perturbation, p=u-u_0, for which the (linearized) governing equation is
      45             :  *
      46             :  * dp/dt = F'(u_0)p
      47             :  *
      48             :  * where F'(u_0) is the Jacobian.  The generalized eigenvalue problem arises
      49             :  * by considering perturbations of the general form p = exp(lambda*t)x, which
      50             :  * leads to
      51             :  *
      52             :  *  Ax = lambda*Bx
      53             :  *
      54             :  * where A is the (discretized by FEM) Jacobian matrix and B is the
      55             :  * (discretized by FEM) mass matrix.
      56             :  *
      57             :  * The EigenSystem class (by Steffen Petersen) is related but does not
      58             :  * fall under the FEMSystem paradigm invented by Roy Stogner.  The EigenSolver
      59             :  * class (also by Steffen) is meant to provide a generic "linear solver"
      60             :  * interface for EigenValue software.  The only current concrete implementation
      61             :  * is a SLEPc-based eigensolver class, which we make use of here as well.
      62             :  *
      63             :  * \author John W. Peterson
      64             :  * \date 2007
      65             :  */
      66           0 : class EigenTimeSolver : public TimeSolver
      67             : {
      68             : public:
      69             :   /**
      70             :    * The type of system
      71             :    */
      72             :   typedef DifferentiableSystem sys_type;
      73             : 
      74             :   /**
      75             :    * The parent class
      76             :    */
      77             :   typedef TimeSolver Parent;
      78             : 
      79             :   /**
      80             :    * Constructor. Requires a reference to the system
      81             :    * to be solved.
      82             :    */
      83             :   explicit
      84             :   EigenTimeSolver (sys_type & s);
      85             : 
      86             :   /**
      87             :    * Destructor.
      88             :    */
      89             :   virtual ~EigenTimeSolver ();
      90             : 
      91             :   /**
      92             :    * The initialization function.  This method is used to
      93             :    * initialize internal data structures before a simulation begins.
      94             :    */
      95             :   virtual void init () override;
      96             : 
      97             :   /**
      98             :    * The reinitialization function.  This method is used after
      99             :    * changes in the mesh
     100             :    */
     101             :   virtual void reinit () override;
     102             : 
     103             :   /**
     104             :    * Implements the assembly of both matrices A and B, and calls
     105             :    * the EigenSolver to compute the eigenvalues.
     106             :    */
     107             :   virtual void solve () override;
     108             : 
     109             :   /**
     110             :    * It doesn't make sense to advance the timestep, so we shouldn't call this.
     111             :    */
     112           0 :   virtual void advance_timestep () override {}
     113             : 
     114             :   /**
     115             :    * error convergence order against deltat is
     116             :    * not applicable to an eigenvalue problem.
     117             :    */
     118             :   Real error_order() const { return 0.; }
     119             : 
     120             :   /**
     121             :    * Forms either the spatial (Jacobian) or mass matrix part of the
     122             :    * operator, depending on which is requested.
     123             :    */
     124             :   virtual bool element_residual (bool get_jacobian,
     125             :                                  DiffContext &) override;
     126             : 
     127             :   /**
     128             :    * Forms the jacobian of the boundary terms.
     129             :    */
     130             :   virtual bool side_residual (bool get_jacobian,
     131             :                               DiffContext &) override;
     132             : 
     133             :   /**
     134             :    * Forms the jacobian of the nonlocal terms.
     135             :    */
     136             :   virtual bool nonlocal_residual (bool get_jacobian,
     137             :                                   DiffContext &) override;
     138             : 
     139             :   /**
     140             :    * \returns 0, but derived classes should override this function to
     141             :    * compute the size of the difference between successive solution
     142             :    * iterates ||u^{n+1} - u^{n}|| in some norm.
     143             :    */
     144           0 :   virtual Real du (const SystemNorm &) const override { return 0.; }
     145             : 
     146             :   /**
     147             :    * This is effectively a steady-state solver.
     148             :    */
     149           0 :   virtual bool is_steady() const override { return true; }
     150             : 
     151             :   /**
     152             :    * The EigenSolver object.  This is what actually
     153             :    * makes the calls to SLEPc.
     154             :    */
     155             :   std::unique_ptr<EigenSolver<Number>> eigen_solver;
     156             : 
     157             :   /**
     158             :    * The linear solver tolerance to be used when solving the
     159             :    * eigenvalue problem. FIXME: need more info...
     160             :    */
     161             :   double tol;
     162             : 
     163             :   /**
     164             :    * The maximum number of iterations allowed to solve the problem.
     165             :    */
     166             :   unsigned int maxits;
     167             : 
     168             :   /**
     169             :    * The number of eigenvectors/values to be computed.
     170             :    */
     171             :   unsigned int n_eigenpairs_to_compute;
     172             : 
     173             :   /**
     174             :    * The number of basis vectors to use in the computation.  According
     175             :    * to ex16, the number of basis vectors must be >= the number of
     176             :    * eigenpairs requested, and ncv >= 2*nev is recommended.
     177             :    * Increasing this number, even by a little bit, can _greatly_
     178             :    * reduce the number of (EigenSolver) iterations required to compute
     179             :    * the desired number of eigenpairs, but the _cost per iteration_
     180             :    * goes up drastically as well.
     181             :    */
     182             :   unsigned int n_basis_vectors_to_use;
     183             : 
     184             :   /**
     185             :    * After a solve, holds the number of eigenpairs successfully
     186             :    * converged.
     187             :    */
     188             :   unsigned int n_converged_eigenpairs;
     189             : 
     190             :   /**
     191             :    * After a solve, holds the number of iterations required to converge
     192             :    * the requested number of eigenpairs.
     193             :    */
     194             :   unsigned int n_iterations_reqd;
     195             : 
     196             : private:
     197             : 
     198             :   enum NowAssembling {
     199             :     /**
     200             :      * The matrix associated with the spatial part of the operator.
     201             :      */
     202             :     Matrix_A,
     203             : 
     204             :     /**
     205             :      * The matrix associated with the time derivative (mass matrix).
     206             :      */
     207             :     Matrix_B,
     208             : 
     209             :     /**
     210             :      * The enum is in an invalid state.
     211             :      */
     212             :     Invalid_Matrix
     213             :   };
     214             : 
     215             :   /**
     216             :    * Flag which controls the internals of element_residual() and side_residual().
     217             :    */
     218             :   NowAssembling now_assembling;
     219             : };
     220             : 
     221             : } // namespace libMesh
     222             : 
     223             : 
     224             : #endif // LIBMESH_HAVE_SLEPC
     225             : #endif // LIBMESH_EIGEN_TIME_SOLVER_H