Re: [Libmesh-users] Euler Beam Equation Using Reduced Basis

[David K. <dav...@ak...>]

I suggest you first get an example working using a standard finite element
implementation (e.g. based on one of the "systems_of_equations" examples).
Once you have that working you can then try to convert it into a reduced
basis implementation. But note that normally reduced basis is not used for
1D models since those models are generally fast enough to solve without any
model reduction. A better case to consider might be 3D elasticity.

David

On Tue, Dec 12, 2017 at 8:10 PM, 강신성 <ss...@pu...> wrote:

>
>
>
>   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&gt;&amp;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 &lt;= 3.8
>       Average Off-Processor Bandwidth &lt;= 0
>       Maximum  On-Processor Bandwidth &lt;= 5
>       Maximum Off-Processor Bandwidth &lt;= 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&amp;)
> 1: libMesh::MacroFunctions::report_error(char const*, int, char const*,
> char const*)
> 2: libMesh::RBConstruction::check_convergence(libMesh::
> LinearSolver&lt;double&gt;&amp;)
> 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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