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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