Isogeometric analysis of partial differential equations on random domains
- Huang, Wei
- Multerer, Michael (Degree supervisor)
- 2024
PhD: Università della Svizzera italiana
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
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- English
- Classification
- Computer science and technology
- License
- License undefined
- Open access status
- green
- Identifiers
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- NDP-USI 2024INF012
- ARK ark:/12658/srd1329457
- URN urn:nbn:ch:rero-006-122383
- Persistent URL
- https://n2t.net/ark:/12658/srd1329457
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