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Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation

https://doi.org/10.1137/23M1565449

Klibanov, Michael V.; Li, Jingzhi; Nguyen, Loc H.; Romanov, Vladimir; Yang, Zhipeng (September 2023, SIAM Journal on Imaging Sciences)

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Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation

https://doi.org/10.1137/22M1509837

Klibanov, Michael V.; Li, Jingzhi; Nguyen, Loc H.; Yang, Zhipeng (March 2023, SIAM Journal on Imaging Sciences)

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A Multigrid Multilevel Monte Carlo Method for Stokes–Darcy Model with Random Hydraulic Conductivity and Beavers–Joseph Condition

https://doi.org/10.1007/s10915-021-01742-2

Yang, Zhipeng; Ming, Ju; Qiu, Changxin; Li, Maojun; He, Xiaoming (February 2022, Journal of Scientific Computing)

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A stochastic collocation method based on sparse grids for a stochastic Stokes-Darcy model

https://doi.org/10.3934/dcdss.2021104

Yang, Zhipeng; Li, Xuejian; He, Xiaoming; Ming, Ju (January 2021, Discrete and Continuous Dynamical Systems - Series S)

In this paper, we develop a sparse grid stochastic collocation method to improve the computational efficiency in handling the steady Stokes-Darcy model with random hydraulic conductivity. To represent the random hydraulic conductivity, the truncated Karhunen-Loève expansion is used. For the discrete form in probability space, we adopt the stochastic collocation method and then use the Smolyak sparse grid method to improve the efficiency. For the uncoupled deterministic subproblems at collocation nodes, we apply the general coupled finite element method. Numerical experiment results are presented to illustrate the features of this method, such as the sample size, convergence, and randomness transmission through the interface.
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