Multerer, Michael Huang, Wei 2024 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. application/pdf https://localhost:5000/ark:/12658/srd1329457 https://susi.usi.ch/global/documents/329457 https://susi.usi.ch/documents/329457/files/2024INF012.pdf eng info:eu-repo/semantics/altIdentifier/ark/12658/srd1329457 info:eu-repo/semantics/altIdentifier/urn/urn:nbn:ch:rero-006-122383 info:eu-repo/semantics/openAccess License undefined BEM Diffusion Helmholtz IGA MC Morse-Smale P-MLMC PDE UQ info:eu-repo/classification/udc/004 Isogeometric analysis of partial differential equations on random domains http://purl.org/coar/resource_type/c_db06