Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | Dr. Yue Zhao，Space Engineering University of PLA
| | Inviter: | | Title:
| A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition | Time & Venue:
| 2021.11.27 11:00-12:00 南楼702教室 | Abstract:
| We consider a stochastic fractional diffusion-reaction equation and combine a Galerkin spectral method based on poly-fractonomials with the modal decomposition of the stochastic fields to formulate effective numerical methods for stochastic fractional partial differential equations. Specifically, we employ a generalized KL expansion and proper dynamically-orthogonal/bi-orthogonal (DO/BO) constraints to derive new Galerkin formulations for the mean solution, the time-dependent spatial basis, and the stochastic time-dependent coefficients. Both the DO and BO methods converge fast with respect to the number of modes, and they are especially effective for nonlinear problems and long-time integration for a modest number of stochastic dimensions.
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