Accelerating the Finite-Element Method for Reaction-Diffusion Simulations on GPUs with CUDA

Area of Science:

• Biochemistry
• Nanotechnology
• Computational Science

Background:

• DNA nanotechnology enables precise control over biochemical reactions.
• Reaction-diffusion systems in microfluidics exhibit complex spatio-temporal dynamics.
• Simulating these systems, especially in complex geometries, requires significant computational resources.

Purpose of the Study:

• To investigate the acceleration of reaction-diffusion simulations in DNA nanotechnology using Graphics Processing Units (GPUs).
• To solve complex reaction-diffusion equations in a tortuous geometry (maze) representative of experimental DNA-based microsystems.
• To evaluate the computational speedup achieved by GPU acceleration compared to traditional CPU-based methods.

Main Methods:

• Solving partial differential equations governing a DNA-based predator-prey reaction-diffusion system.
• Implementing the Finite Element Method (FEM) for simulation on a GPU.
• Utilizing a tortuous geometry (maze) to capture subtle geometric effects.

Main Results:

• Demonstrated a significant speedup of approximately 100x for GPU-accelerated simulations compared to a 20-core CPU at the same resolution.
• Successfully simulated reaction-diffusion dynamics in a complex, maze-like geometry.
• Validated the feasibility of applying GPU computing to accelerate complex simulations in DNA nanotechnology.

Conclusions:

• GPU acceleration offers a substantial performance improvement for reaction-diffusion simulations in DNA nanotechnology.
• This computational approach can facilitate the study of complex systems and geometries, advancing the field.
• The findings pave the way for more efficient design and analysis of DNA-based microfluidic devices.