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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Detalles Bibliográficos
Autor: Pena Sapena, Arnau
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
Descripción
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.