Modeling of the mixed form of wave problems with correcting terms based on training artificial neural networks: application to acoustic black holes
(English) This thesis presents novel approaches and computational methods for solving wave propagation problems in acoustics and linear elasticity. Stabilized finite element methods in the context of the variational multi-scale method are developed to model the mixed form of the wave equation in tim...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/692200 |
| Acceso en línea: | http://hdl.handle.net/10803/692200 https://dx.doi.org/10.5821/dissertation-2117-414772 |
| Access Level: | acceso abierto |
| Palabra clave: | Àrees temàtiques de la UPC::Enginyeria civil Àrees temàtiques de la UPC::Enginyeria mecànica Àrees temàtiques de la UPC::Informàtica 004 621 624 |
| Sumario: | (English) This thesis presents novel approaches and computational methods for solving wave propagation problems in acoustics and linear elasticity. Stabilized finite element methods in the context of the variational multi-scale method are developed to model the mixed form of the wave equation in time and frequency domains. Additionally, the thesis explores the incorporation of correcting terms based on artificial neural networks to enhance the accuracy and efficiency of the solutions of the numerical simulations. The first part of the thesis focuses on the field of acoustics. The wave equation in its irreducible and mixed form is computed including the contributions from both element interiors and interelement boundaries, which are often overlooked in traditional stabilization methods. Moreover, non-reflecting boundary conditions are employed to reduce spurious reflections. The stability, convergence and performance of the proposed methods are demonstrated through different numerical examples. A really important point of this work is the presentation of a general approach to refine coarse models by introducing a correcting term based on fine solutions. This term is computed and trained making use of learning algorithms, such as the least squares model or a model constructed from an artificial neural network (ANN). This technique is applied to both the time and the frequency domains of the wave equation in the context of acoustics. Its effectiveness is evaluated through multiple numerical examples, where fine solutions with finer discretization in either time or space are used. In the second part of the thesis, the wave equation in the field of elastodynamics is explored. Concretely, stabilized finite element methods are developed for the mixed velocity-stress elasticity equations and their irreducible form, where just the velocity is computed. Both time and frequency domains are considered, with the latter assuming harmonic behavior in time, the study of the mixed form in frequency domain is one of the novelties of this thesis. One of the advantages of using this new mixed form is the flexibility to switch between the primal and dual functional frameworks by appropriately selecting algorithmic parameters, moreover, using the mixed formulation the locking problem is avoided. The proposed formulations are validated through various numerical examples, including a convergence study. Finally, as a case study we consider acoustic black holes (ABHs) on beams and plates. These structural configurations are designed to trap flexural elastic waves by gradually reducing the structural thickness according to a power-law profile at the end of a beam or within a two-dimensional circular indentation in a plate. When a propagating wave encounters an ABH, it undergoes a decrease in wavelength and an increase in amplitude, resulting in a reduction in wave propagation speed as it approaches the termination point in the case of beams or the center point in the case of plates. To ensure the optimal functionality of the ABH, it is imperative that the thickness at the termination or center of the structure be exceedingly small, which demands very fine computational meshes. At this point, the previously presented correcting technique based on training ANN is employed to mitigate computational expenses by allowing the use of coarse meshes maintaining the precision of fine meshes. The effectiveness of this approach is demonstrated through different simulations of ABHs on coarse meshes for values of ABH order and residual thickness outside the training test, as well as for different excitation frequencies. |
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