Hello everyone,
 
  
 
  I want to solve the Euler cantilever beam equation using reduced basis to 
understand the RB method.
 
  However, I don't know how to deal with a 2nd derivative term of a weak form 
of the Euler beam equation.
 
  
 
  First, I created a 1D mesh. Then, refferring to the RB examples, I made a 
basic RB code. 
 
  After that, I tried to use "SECOND" variable and "d2phi" in the RB code, but 
I can't solve it. The error message is as follows. 
  
=================================================================================
 
  ***************************************************************
* Running App  run_Beam_Euler-opt
***************************************************************
 
./run_Beam_Euler-opt  2>&1 | tee output.txt
 Mesh Information:
  elem_dimensions()={1}
  spatial_dimension()=2
  n_nodes()=15
    n_local_nodes()=15
  n_elem()=7
    n_local_elem()=7
    n_active_elem()=7
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=1
   System #0, "RBElasticity"
    Type "RBConstruction"
    Variables="u" 
    Finite Element Types="LAGRANGE" 
    Approximation Orders="SECOND" 
    n_dofs()=15
    n_local_dofs()=15
    n_constrained_dofs()=1
    n_local_constrained_dofs()=1
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 3.8
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 5
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 1
      Average DoF Constraint Length= 0

Initializing training parameters with random training set...
Parameter length: log scaling = 0
Parameter load: log scaling = 0
Parameter point_load: log scaling = 0

RBConstruction parameters:
system name: RBElasticity
Nmax: 20
Greedy relative error tolerance: 0.001
Greedy absolute error tolerance: 1e-12
Do we normalize RB error bound in greedy? 0
Aq operators attached: 1
Fq functions attached: 1
n_outputs: 0
Number of parameters: 3
Parameter length: Min = 1, Max = 20
Parameter load: Min = -5, Max = 5
Parameter point_load: Min = -5, Max = 5
n_training_samples: 1000
quiet mode? 1

Assembling inner product matrix
*** Warning, This code is untested, experimental, or likely to see future API 
changes: src/systems/dg_fem_context.C, line 35, compiled Aug 25 2017 at 
02:20:14 ***
Assembling affine operator 1 of 1
Assembling affine vector 1 of 1
Convergence error. Error id: -11
Stack frames: 8
0: libMesh::print_trace(std::ostream&)
1: libMesh::MacroFunctions::report_error(char const*, int, char const*, char 
const*)
2: 
libMesh::RBConstruction::check_convergence(libMesh::LinearSolver<double>&)
3: libMesh::RBConstruction::compute_Fq_representor_innerprods(bool)
4: libMesh::RBConstruction::train_reduced_basis(bool)
5: ./run_Beam_Euler-opt() [0x416482]
6: __libc_start_main
7: ./run_Beam_Euler-opt() [0x416ed9]
[0] src/reduced_basis/rb_construction.C, line 2124, compiled Aug 25 2017 at 
02:17:58
application called MPI_Abort(MPI_COMM_WORLD, 1) - process 0
[unset]: aborting job:
application called MPI_Abort(MPI_COMM_WORLD, 1) - process 0
=================================================================================
 
  
 
  I wonder if this is right way. If not, I want to know another way to solve 
the Euler cantilever beam equation.
 
  
 
  Best regards,
 
  S. Kang.
 
 
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