Intrusive and Non-intrusive Polynomial Chaos Methods for Uncertainty Quantification
Author | : Kechen Qian |
Publisher | : |
Total Pages | : |
Release | : 2021 |
ISBN-10 | : OCLC:1257336353 |
ISBN-13 | : |
Rating | : 4/5 (53 Downloads) |
Book excerpt: "With the remarkable development of very-large-scale integration(VLSI) technology, the variability of electronic devices' physical and geometrical parameters will play a more important role on the performance of electronic systems. The phenomenon asks us to focus on the impact of these uncertainties in electronic circuits. In mathematical literature, predicting these effect of the variability is known as uncertainty quantification. In nowadays industry, Monte Carlo analysis is the most popular and easy-implemented method. However, on the other hand, it is also time-consuming due to its large number of simulation times. To address these defects of Monte Carlo, this thesis introduces two different Stochastic analysis methods based on Hermite Polynomial Chaos, which are Stochastic Collocation Method(SCM) and Stochastic Galerkin Method(SGM), to realise uncertainty quantification. SCM is a non-intrusive method and depends on good sampling points. SGM is an intrusive method and leads to very large decoupled systems. Both methods are more efficient than Monte Carlo, but they also have their limitations. Additionally, a decoupling method based on original Stochastic Galerkin Method is introduced by deriving an alternative closed-form model for augmented matrices. Then the augmented system can be factorized into blocks by applying eigen-decomposition and solved in parallel. The relationship between all these methods above are also demonstrated.In the end, several examples are presented to illustrate the accuracy and efficiency of methods above, as well as their equivalence"--