[libROM tutorial] Projection-based reduced order model for nonlinear system | скачать в хорошем качестве

[libROM tutorial] Projection-based reduced order model for nonlinear system |

The nonlinear systems introduce difficulties when applying projection-based reduced order model because the nonlinear complexity scales with the full order model size. To resolve this issue, various hyper-reduction techniques are available. In this tutorial, we introduce a general concept of hyper-reduction and two different approaches, i.e., collocation method and discrete empirical interpolation method (DEIM). A numerical example of time dependent nonlinear structure problem illustrates that the DEIM achieves a relative error less than 1% and a speed-up of 8. If you seek research papers about hyper-reduction methods, we recommend the following two papers: Nonlinear Model Reduction via Discrete Empirical Interpolation ( https://epubs.siam.org/doi/abs/10.113... ) SNS: A Solution-based Nonlinear Subspace Method for Time-Dependent Model Order Reduction ( https://epubs.siam.org/doi/abs/10.113... ) You can run an example of hyper-reduced order model on a time-dependent nonlinear structure problem with libROM. Please check out the following libROM webpage: https://www.librom.net/examples.html and look for the example, "Nonlinear elasticity, PROM." For example, you can follow the following sequence of command line options to run local reduced order model examples: offline phase: ./nonlinear_elasticity_global_rom --mesh "../../../dependencies/mfem/data/beam-hex-nurbs.mesh" --offline -dt 0.01 -tf 5.0 -s 14 -vs 10 -sc 3.9 -id 0 offline phase: ./nonlinear_elasticity_global_rom --mesh "../../../dependencies/mfem/data/beam-hex-nurbs.mesh" --offline -dt 0.01 -tf 5.0 -s 14 -vs 10 -sc 4.1 -id 1 merge phase: ./nonlinear_elasticity_global_rom --mesh "../../../dependencies/mfem/data/beam-hex-nurbs.mesh" --merge -ns 2 -dt 0.01 -tf 5.0 fom phase: ./nonlinear_elasticity_global_rom --mesh "../../../dependencies/mfem/data/beam-hex-nurbs.mesh" --offline -dt 0.01 -tf 5.0 -s 14 -vs 5 -sc XXX -id 2 online phase: ./nonlinear_elasticity_global_rom --mesh "../../../dependencies/mfem/data/beam-hex-nurbs.mesh" --online -dt 0.01 -tf 5.0 -s 14 -vs 5 -hyp -rvdim 40 -rxdim 10 -hdim 71 -nsr 200 -sc XXX You can replace XXX in the fom and online phase above to take any value between 3.9 and 4.1 libROM can be downloaded from the following GitHub page: https://github.com/LLNL/libROM A list of libROM tutorials: 1. Poisson equation & its finite element discretization (    • [libROM tutorial] Poisson equation & its f...   ) 2. Projection-based reduced order model for Poisson equation (    • [libROM tutorial] Projection-based reduced...   ) 3. Physics-informed sampling method for reduced order models (    • [libROM tutorial] Physics-informed samplin...   ) 4. Local reduced order models and interpolation-based parameterization (    • [libROM tutorial] Local reduced order mode...   ) 5. Projection-based reduced order model for nonlinear system (    • [libROM tutorial] Projection-based reduced...   ) 6. A complete derivation of dynamic mode decomposition (    • [libROM tutorial] A complete derivation of...   ) If you have any questions, please leave any comments down below.