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Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs
ISBN-13:
9783031383847
Veröffentl:
2023
Seiten:
207
Autor:
Dinh Dung
Serie:
2334, Lecture Notes in Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
The present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered.
- 1. Introduction. - 2. Preliminaries. - 3. Elliptic Divergence-Form PDEs with Log-Gaussian Coefficient. - 4. Sparsity for Holomorphic Functions. - 5. Parametric Posterior Analyticity and Sparsity in BIPs. - 6. Smolyak Sparse-Grid Interpolation and Quadrature. - 8. Multilevel Smolyak Sparse-Grid Interpolation and Quadrature. - 8. Conclusions.
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