DNA nanotechnology offers a fine control over biochemistry by programming chemical reactions in DNA templates. Coupled to microfluidics, it has enabled DNA-based reaction-diffusion microsystems with advanced spatio-temporal dynamics such as traveling waves. The Finite Element Method (FEM) is a standard tool to simulate the physics of such systems where boundary conditions play a crucial role. However, a fine discretization in time and space is required for complex geometries (like sharp corners) and highly nonlinear chemistry. Graphical Processing Units (GPUs) are increasingly used to speed up scientific computing, but their application to accelerate simulations of reaction-diffusion in DNA nanotechnology has been little investigated. Here we study reaction-diffusion equations (a DNA-based predator-prey system) in a tortuous geometry (a maze), which was shown experimentally to generate subtle geometric effects. We solve the partial differential equations on a GPU, demonstrating a speedup of ∼100 over the same resolution on a 20 cores CPU.

中文翻译：

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使用CUDA加速GPU上反应扩散仿真的有限元方法

DNA纳米技术通过对DNA模板中的化学反应进行编程，可以很好地控制生物化学。结合微流体技术，它使基于DNA的反应扩散微系统成为可能，并具有先进的时空动力学，例如行波。有限元方法（FEM）是一种标准工​​具，可以模拟边界条件起关键作用的此类系统的物理特性。但是，对于复杂的几何形状（例如尖角）和高度非线性的化学过程，需要在时间和空间上进行精细离散。图形处理单元（GPU）越来越多地用于加快科学计算的速度，但是很少用于研究DNA纳米技术中反应扩散模拟的应用。在这里，我们研究曲折几何形状（迷宫）中的反应扩散方程（基于DNA的捕食者－被捕食系统），实验证明可以产生微妙的几何效果。我们在GPU上求解偏微分方程，证明在20核CPU上以相同的分辨率可实现约100的加速。