Researchers from the University of California, Irvine, and the University of Science and Technology of China have developed a novel numerical framework for simulating complex biological and chemical processes. The team, consisting of Jingyuan Hu, Zhongjian Wang, Jack Xin, and Zhiwen Zhang, has introduced the stochastic interacting particle-field method with particle-in-cell acceleration (SIPF-PIC) to efficiently model three-dimensional (3D) parabolic-parabolic Keller-Segel (KS) systems. Their research was published in the Journal of Computational Physics.
The SIPF-PIC method combines Lagrangian particle dynamics with spectral field solvers, utilizing localized particle-grid interpolations and fast Fourier transform (FFT) techniques. This integration allows for a significant reduction in computational complexity compared to the original SIPF method. While the original method had a complexity of O(PH^3), the new SIPF-PIC method achieves a complexity of O(P + H^3 log H) per time step, where P represents the number of particles and H represents the number of Fourier modes per spatial dimension. This improvement in computational efficiency does not compromise numerical accuracy.
The researchers have also conducted a rigorous error analysis, demonstrating that the discretization errors of the SIPF-PIC method are of order O(H^(-16/13) + P^(-1/2)H^(4/13)). To validate their theoretical findings, the team presented numerical experiments that confirmed the convergence rates and showcased the method’s computational efficiency. Notably, the experiments revealed that the SIPF-PIC method can capture intricate blowup dynamics, including ring-type singularities where mass concentrates into evolving annular structures.
The practical applications of this research for the energy sector are primarily indirect but significant. The ability to efficiently simulate complex biological and chemical processes can aid in the development of biofuels and other renewable energy sources. Understanding chemotaxis, the movement of organisms in response to chemical stimuli, can also inform the design of microbial fuel cells and other bioenergy technologies. Furthermore, the computational efficiency of the SIPF-PIC method can be leveraged in various energy-related simulations, such as fluid dynamics and reactor modeling, to optimize processes and improve overall energy systems.
This article is based on research available at arXiv.