This book explores four guiding themes reduced order modelling, high dimensional problems, efficient algorithms, and applications by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs. Highlighting the most promising approaches for (near-) future improvements in the way uncertainty quantification problems in the partial differential equation setting are solved, and gathering contributions by leading international experts, the books content will impact the scientific, engineering, financial, economic, environmental, social, and commercial sectors.
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2. Brugiapaglia S., A compressive
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3. DElia, M. et al., Surrogate-based Ensemble Grouping
Strategies for Embedded Sampling-based Uncertainty Quantification.-
4.
Afkham, B.M. et al., Conservative Model Order Reduction for Fluid Flow.-
5.
Clark C.L. and Winter C.L., A Semi-Markov Model of Mass Transport through
Highly Heterogeneous Conductivity Fields.-
6. Matthies, H.G., Analysis of
Probabilistic and Parametric Reduced Order Models.-
7. Carraturo, M. et al.,
Reduced Order Isogeometric Analysis Approach for PDEs in Parametrized
Domains.-
8. Boccadifuoco, A. et al., Uncertainty quantification applied to
hemodynamic simulations of thoracic aorta aneurysms: sensitivity to inlet
conditions.-
9. Anderlini, A.et al., Cavitation model parameter calibration
for simulations of three-phase injector flows.-
10. Hijazi, S. et al.,
Non-Intrusive Polynomial Chaos Method Applied to Full-Order and Reduced
Problems in Computational Fluid Dynamics: a Comparison and Perspectives.-
11.
Bulté, M. et al., A practical example for the non-linear Bayesian filtering
of model parameters.
Dr. Marta D'Elia is a staff member at Sandia National Laboratories. She graduated with honors in Mathematical Engineering at Politecnico di Milano, 2007, and she has a Phd in Applied Mathematics from Emory University, 2011. She was a postdoctoral fellow at Florida State University from 2012 to 2014. Her research deals with computational science and engineering, and it is mainly focused on modeling and simulation of nonlocal problems. She authored more than 30 research papers, she is the principal investigator of a Laboratory Directed R&D grant, associate editor of the SIAM Journal on Scientific Computing and organizer of several international conferences.
Max Gunzburger, a Distinguished Professor at Florida State University, has advised 46 PhD students and 36 postdocs, published over 300 journal articles, conducted research funded by several US agencies, consulted for government and private labs, and served as EIC of two SIAM journals. His research interests include numerical analysis, finite elements, control, grid generation, and differential and integral equations with applications in mechanics, diffusion, climate, superconductivity, subsurface flows, etc.
Gianluigi Rozza is a Professor of Numerical Analysis and Scientific Computing at SISSA, the International School for Advanced Studies, in Trieste, Italy, where he is a lecturer and coordinator of the SISSA doctoral program in Mathematical Analysis, Modelling and Applications, and director delegate for innovation, valorisation of research and technology transfer. His research chiefly focuses on developing reduced order methods. The author of more than 120 scientific publications, Principal Investigator of the European Research Council AROMA-CFD project. Winner of the 2004 Bill Morton CFD Prize (Oxford University); ECCOMAS Phd Award 2006; Springer CSE prize in 2009; and ECCOMAS Jacques Louis Lions Award in 2014.
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