Description
- Abstract:
- The lack of an efficient and stable numerical method remains a serious bottleneck for long-time simulations. Time parallel integration methods can break the bottleneck by decomposing the time domain and solving these subdomains parallel-in-time. I propose a Supervised Parallel-in-time Algorithm for Stochastic Dynamics (SPASD), which aims to significantly accelerate stochastic Lagrangian solvers for long-time simulations. Based on the bottom-up coarse-graining philosophy, stochastic particle models such as dissipative particle dynamics converge to continuum macroscopic models in the scale limit. The macroscopic system can then serve as a predictor to supervise the high-dimensional stochastic Lagrangian simulation. Even though the governing equations of the macroscopic model, generally in the form of partial differential equations, are different from those of the microscopic model, the macroscopic model can capture the correct mean-field behavior of the microscopic system in the continuum limit. In particular, an inexpensive continuum solver solves the macroscopic model in serial, and an expensive but parallelizable solver resolves the molecular details by performing stochastic microscopic simulations. In my thesis, I tested the accuracy and convergence of SPASD and showed that the transient and final solutions match the analytical/reference solutions even when our estimation to the systemâs mean-field behavior is far from the true behavior. More importantly, the SPASD algorithm is able to preserve the stochastic fluctuations of the microscopic model. I demonstrated that SPASD provides better parallel efficiency and thus better scalability than the conventional domain decomposition method for long-time simulations. For a practical demonstration, I applied SPASD, in conjunction to domain decomposition, to accelerate massive Lagrangian simulations of blood flow in a zebrafish hindbrain. In this example, the complex vascular network is a digital reconstruction of a real zebrafish and is comprised with 95 branches and 57 bifurcations. To show the accuracy of SPASD, I simulated the same problem with and without the parallel-in-time scheme. I found that the maximum normalized l2 error is only on the order of one percent in our complex fluid example, and it does not grow over iterations.
- Notes:
- Thesis (Ph. D.)--Brown University, 2020
Access Conditions
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Citation
Blumers, Ansel Lou,
"Spatial and Temporal Acceleration of Mesoscopic Blood-flow Simulations"
(2020).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:1129461/
