Study of acceleration algorithms in large scale topology optimization
Topology Optimization is a well stablished computational technique tailored to optimize material distribution for a given domain by minimizing a cost function and fulfilling a set of constraints. However it is a very demanding technique where, specially for large scale optimization, the computationa...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/421740 |
| Acceso en línea: | https://hdl.handle.net/2117/421740 |
| Access Level: | acceso abierto |
| Palabra clave: | Topology Conjugate gradient methods Computer algorithms Topology optimization Nesterov acceleration Polyak acceleration Conjugate gradient Topologia Gradient conjugat, Mètode del Algorismes computacionals Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia |
| Sumario: | Topology Optimization is a well stablished computational technique tailored to optimize material distribution for a given domain by minimizing a cost function and fulfilling a set of constraints. However it is a very demanding technique where, specially for large scale optimization, the computational time becomes prohibitive. Thus, in this thesis different acceleration methodologies are presented in order to improve the current convergence velocities. First, we will deal with accelerating the resolution of the linear system of equations of the elastic problem by introducing the Conjugate Gradient iterative solver with adaptative tolerance. Second, we will also accelerate the optimization process by introducing the momentum term, widely used in machine learning gradient descent algorithms. Additionally, we will also introduce the matrix-free notation of the elastic problem in order to also address the memory limitations of assembling large stiffness matrix. Finally, a mixed acceleration of both elastic problem and optimization will be analysed to determine the best tuning parameters combinations. |
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