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Shape Holomorphy of the Calderón Projector for the Laplacean in R2
(2019)SAM Research ReportReport -
Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems
(2019)SAM Research ReportReport -
Exponential ReLU DNN expression of holomorphic maps in high dimension
(2019)SAM Research ReportReport -
Multilevel approximation of Gaussian random fields: fast simulation
(2019)SAM Research ReportReport -
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Analysis of multilevel MCMC-FEM for Bayesian inversion of log-normal diffusions
(2019)SAM Research ReportWe develop the Multilevel Markov Chain Monte Carlo Finite Element Method (MLMCMC-FEM for short) to sample from the posterior density of the Bayesian inverse problems. The unknown is the diffusion coefficient of a linear, second order divergence form elliptic equation in a bounded, polytopal subdomain of $ \mathbb{R}^d$ . We provide a convergence analysis with absolute mean convergence rate estimates for the proposed modified MLMCMC method, ...Report -
Multilevel quasi-Monte Carlo uncertainty quantification for advection-diffusion-reaction
(2019)SAM Research ReportWe survey the numerical analysis of a class of deterministic, higher-order QMC integration methods in forward and inverse uncertainty quantification algorithms for advection-reaction-diffusion (ARD) equations in polygonal domains $D \subset \mathbb{R}^2$ with distributed uncertain inputs. We admit spatially heterogeneous material properties. For the parametrization of the uncertainty, we assume at hand systems of functions which are ...Report -
Domain Uncertainty Quantification in Computational Electromagnetics
(2019)SAM Research ReportReport -