Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs
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ISBN-13:
9783031383830
Veröffentl:
2023
Einband:
Paperback
Erscheinungsdatum:
14.10.2023
Seiten:
224
Autor:
Dinh D¿ng
Gewicht:
347 g
Format:
235x155x13 mm
Serie:
2334, Lecture Notes in Mathematics
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.
There is no similar text, at present, where sparsity forward and inverse UQ for these PDEs can be currently found
- 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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