Colloquium
I: Highdimensionality, Uncertainty Quantification and Scientific Computing, II: Model Reduction for Stochastic Partial Differe
작성자Author
sugarless
작성일Date
20170403 16:23
조회Views
991
분야Field  2017 Math Colloquium  

날짜Date  20170602  시간Time  15:50 ~ 18:00 
장소Place  Math Sci Bldg 404  초청자Host   
연사Speaker  Minseok Choi  소속Affiliation  POSTECH 
TOPIC  I: Highdimensionality, Uncertainty Quantification and Scientific Computing, II: Model Reduction for Stochastic Partial Differe  
소개 및 안내사항Content  part I: Highdimensionality, Uncertainty Quantification and Scientific Computing Abstract: Uncertainty quantification (UQ) has recently gained an increasing amount of attention in scientific computing community and is a fundamental challenge in numerical simulations of many physical/engineering problems. We introduce uncertainty quantification and discuss some of the recently developed UQ methods such as generalized polynomial chaos (gPC) and how to deal with highdimensional problem inherent in complex problems. part II: Model Reduction for Stochastic Partial Differential Equations Abstract: We present a hybrid methodology for stochastic PDEs based on the dynamically orthogonal (DO) and biorthogonal (BO) expansions that provide a low dimensional representation for square integrable random processes. The solution to SPDEs follows the characteristics of KL expansion onthefly at any given time. We prove the equivalence of two approaches and provide a unified hybrid framework of those methods by utilizing an invertible and linear transformation between them. We present numerical examples to illustrate the proposed methods, which exhibit exponential convergence comparable with the polynomial chaos (PC) method but with substantially smaller computational cost. 
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