scholarly journals Local sensitivity analysis and spectral convergence of the stochastic Galerkin method for discrete-velocity Boltzmann equations with multi-scales and random inputs

2019 ◽  
Vol 12 (5) ◽  
pp. 969-993
Author(s):  
Shi Jin ◽  
◽  
Yingda Li ◽  
Keyword(s):  
Sensitivity Analysis ◽  
Galerkin Method ◽  
Boltzmann Equations ◽  
Local Sensitivity ◽  
Random Inputs ◽  
Local Sensitivity Analysis ◽  
Stochastic Galerkin Method ◽  
Spectral Convergence ◽  
Stochastic Galerkin ◽  
Multi Scales

scholarly journals A local sensitivity analysis for the hydrodynamic Cucker-Smale model with random inputs

2020 ◽  
Vol 268 (2) ◽  
pp. 636-679
Author(s):  
Seung-Yeal Ha ◽  
Shi Jin ◽  
Jinwook Jung ◽  
Woojoo Shim
Keyword(s):  
Sensitivity Analysis ◽  
Local Sensitivity ◽  
Random Inputs ◽  
Local Sensitivity Analysis

scholarly journals A local sensitivity analysis for the kinetic Kuramoto equation with random inputs

2019 ◽  
Vol 14 (2) ◽  
pp. 317-340
Author(s):  
Seung-Yeal Ha ◽  
◽  
Shi Jin ◽  
Jinwook Jung ◽  
◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Local Sensitivity ◽  
Random Inputs ◽  
Local Sensitivity Analysis

A Stochastic Galerkin Method for the Boltzmann Equation with Multi-Dimensional Random Inputs Using Sparse Wavelet Bases

2017 ◽  
Vol 10 (2) ◽  
pp. 465-488 ◽  
Author(s):  
Ruiwen Shu ◽  
Jingwei Hu ◽  
Shi Jin
Keyword(s):  
Boltzmann Equation ◽  
Galerkin Method ◽  
Collision Operator ◽  
Collision Kernel ◽  
Wavelet Bases ◽  
Random Inputs ◽  
Stochastic Galerkin Method ◽  
The Boltzmann Equation ◽  
Accuracy Result ◽  
Stochastic Galerkin

AbstractWe propose a stochastic Galerkin method using sparse wavelet bases for the Boltzmann equation with multi-dimensional random inputs. Themethod uses locally supported piecewise polynomials as an orthonormal basis of the random space. By a sparse approach, only a moderate number of basis functions is required to achieve good accuracy in multi-dimensional random spaces. We discover a sparse structure of a set of basis-related coefficients, which allows us to accelerate the computation of the collision operator. Regularity of the solution of the Boltzmann equation in the random space and an accuracy result of the stochastic Galerkin method are proved in multi-dimensional cases. The efficiency of the method is illustrated by numerical examples with uncertainties from the initial data, boundary data and collision kernel.

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