A Spectral Stochastic Collocation Method for Capacitance Extraction of Interconnects with Process Variations

2006 ◽  
Author(s):  
Hengliang Zhu ◽  
Xuan Zeng ◽  
Wei Cai ◽  
Dian Zhou
Keyword(s):  
Collocation Method ◽  
Process Variations ◽  
Stochastic Collocation ◽  
Stochastic Collocation Method ◽  
Capacitance Extraction

scholarly journals Uncertainty Quantification in Small-Timescale Model-Based Fatigue Crack Growth Analysis Using a Stochastic Collocation Method

Metals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 646
Author(s):  
Hesheng Tang ◽  
Xueyuan Guo ◽  
Songtao Xue
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Uncertainty Quantification ◽  
Crack Growth ◽  
Collocation Method ◽  
Life Prediction ◽  
Remaining Useful Life ◽  
Stochastic Collocation ◽  
Stochastic Collocation Method ◽  
Model Based

Due to the uncertainties originating from the underlying physical model, material properties and the measurement data in fatigue crack growth (FCG) processing, the prediction of fatigue crack growth lifetime is still challenging. The objective of this paper was to investigate a methodology for uncertainty quantification in FCG analysis and probabilistic remaining useful life prediction. A small-timescale growth model for the fracture mechanics-based analysis and predicting crack-growth lifetime is studied. A stochastic collocation method is used to alleviate the computational difficulties in the uncertainty quantification in the small-timescale model-based FCG analysis, which is derived from tensor products based on the solution of deterministic FCG problems on sparse grids of collocation point sets in random space. The proposed method is applied to the prediction of fatigue crack growth lifetime of Al7075-T6 alloy plates and verified by fatigue crack-growth experiments. The results show that the proposed method has the advantage of computational efficiency in uncertainty quantification of remaining life prediction of FCG.

A Stochastic Finite Element Heterogeneous Multiscale Method for Seepage Field in Heterogeneous Ground

2012 ◽  
Vol 594-597 ◽  
pp. 2545-2551
Author(s):  
Yan Hua Xia
Keyword(s):  
Finite Element ◽  
Collocation Method ◽  
Multiscale Method ◽  
Computational Techniques ◽  
Stochastic Collocation ◽  
Fine Scale ◽  
Stochastic Finite Element ◽  
Seepage Field ◽  
Stochastic Collocation Method ◽  
Heterogeneous Multiscale

The finite element heterogeneous multiscale method (FEHM) combined with stochastic collocation method (SCM) called SHMFE is applied to studying the seepage field of naturally heterogeneous multiscale subsurface formations. Kinds of stochastic finite element (SFEM) are mainly computational techniques for the class of problems. But those methods do not report the multiscale nature of the properties of subsurface formations. When the random permeability field is heterogeneous in fine scale comparing to study domain, the simulation by the classic SFEM is not a trivial task. The SHMFE can efficiently solve the problems. In the method, Karhunen-Loµeve (KL) decomposition is used to represent the log hydraulic conductivity Y = lnKεin fine scale. The SCM which couples the generalized polynomial chaos is used to make the problem determined, and then the FEHM method is used to solve it. Sparse grid stochastic collocation method is used when KL expansion has many random variables. The numerical examples demonstrate that the SHMFE approach can efficiently simulate the flow in naturally multiscale heterogeneous subsurface formations with relatively lower computational cost comparing with the SFEM methods.

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