A Numerical framework to address the inverse problem of estimating Lamé parameters using HDG Runge-Kutta methods

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dc.catalogadoraba
dc.contributor.advisorSánchez Uribe, Manuel
dc.contributor.authorCortés Castillo, Pablo
dc.contributor.otherPontificia Universidad Católica de Chile. Escuela de Ingeniería
dc.date.accessioned2025-01-31T14:48:50Z
dc.date.available2025-01-31T14:48:50Z
dc.date.issued2024
dc.descriptionTesis (Master of Science in Engineering)--Pontificia Universidad Católica de Chile, 2024.
dc.description.abstractIn engineering, the problem of characterizing the immediate subsoil of the earth’s crust is a subject of extensive research. A common approach for solving this problem is to induce elastic waves from the surface to the underground. So, when the propagating media is not homogeneous, we expect collisions of these waves with inclusions, represented by changes in the Lame parameters ´ (λ, µ) that uniquely determine the composition of the isotropic solid. An inverse problem arises from measuring the elastic waves that propagate back to the surface and compare with some direct model predictions. To address this problem, we rst deliver an accurate numerical characterization of the time-dependent elastic waves by solving the elastodynamics PDE using an HDG nite elements spatial discretization with weak symmetry. We also present several time-marching schemes with different orders of convergence and properties and prove optimal error estimates for every scheme, generating a wide variety of fully-discrete direct solvers. Furthermore, we provide suitable treatment for numerical artifacts, such as the locking phenomenon, and review relevant techniques to perform computational domain truncation, such as PMLs, including a damping term. Finally, we consider the inverse problem of minimizing a mis-t L2 loss between boundary measurements of the ground truth and the forward model numerical solution. We propose a rst-order algorithm that iteratively delivers descent directions by characterizing Frechet derivatives of the loss function in a discrete fashion. ´Moreover, we present a full adjoint analysis of the continuous PDE-restricted optimization problem; this provides a continuous characterization of the second-order information of the Loss function when L2 regularization is included.
dc.fechaingreso.objetodigital2025-01-31
dc.format.extentxiii, 89 páginas
dc.fuente.origenSRIA
dc.identifier.doi10.7764/tesisUC/ING/102130
dc.identifier.urihttps://doi.org/10.7764/tesisUC/ING/102130
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/102130
dc.information.autorucEscuela de Ingeniería; Sánchez Uribe, Manuel; S/I; 1057448
dc.information.autorucEscuela de Ingeniería; Cortés Castillo, Pablo; S/I; 1045406
dc.language.isoen
dc.nota.accesocontenido completo
dc.rightsacceso abierto
dc.subjectIInverse problems
dc.subjectLinear elasticity
dc.subjectHDG-FEM
dc.subjectRunge-Kutta
dc.subjectMultistep
dc.subjectFirst-order methods
dc.subjectProblemas inversos
dc.subjectElasticidad lineal
dc.subjectHDG-FEM
dc.subjectRunge-Kutta
dc.subjectMétodos multi-paso
dc.subjectMétodos de primer orden
dc.subject.ddc620
dc.subject.deweyIngenieríaes_ES
dc.titleA Numerical framework to address the inverse problem of estimating Lamé parameters using HDG Runge-Kutta methods
dc.typetesis de maestría
sipa.codpersvinculados1057448
sipa.codpersvinculados1045406
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