Back
2024INF012
Doctoral thesis

Isogeometric analysis of partial differential equations on random domains

  • 2024

PhD: Università della Svizzera italiana

BEM
Diffusion
Helmholtz
IGA
MC
Morse-Smale
P-MLMC
PDE
UQ
English We examine the numerical solution of partial differential equations on random domains using isogeometric analysis, wherein the primary focus is on uncertainty quantification; specifically, quantities of interest, i.e., expectation and correlation, are considered for two types of partial differential equations on complex geometries. To handle such complex geometries, we use the Morse-Smale complex to convert triangulated surfaces into conforming quad NURBS surfaces. As an application of the NURBS surface reconstruction method, we develop a shape optimisation approach that utilises the Morse-Smale complex at each iteration to minimise geometric singularities. Further, we propose the efficient computation of the space-time correlation using an online singular value decomposition in case of the diffusion equation and employ the p-multilevel Monte Carlo method to compute quantities of interest for the Helmholtz equation.
Collections
Language
  • English
Classification
Computer science and technology
License
License undefined
Open access status
green
Identifiers
Persistent URL
https://n2t.net/ark:/12658/srd1329457
Statistics
Document views: 114 File downloads:
  • 2024INF012: 36