Simple computation of reaction–diffusion processes on point clouds
Simple computation of reaction–diffusion processes on point clouds
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DOI：
10.1073/pnas.1221408110
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
C. Macdonald;B. Merriman;Steven J. Ruuth
中科院分区：
文献类型：
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作者：
C. Macdonald;B. Merriman;Steven J. Ruuth
一般曲面上反应扩散过程的研究要比在标准笛卡尔坐标空间上复杂得多。在这里，我们展示了如何以一种极其简单的方式在表面上表述和求解反应-扩散方程组，仅使用标准笛卡尔形式的微分算子和一个离散的无组织点集来表示表面。我们的方法将曲面几何与底层微分算子解耦。因此，在一般表面上表述和求解相当一般的反应-扩散方程成为可能，而不必考虑微分几何的复杂性或复杂的数值分析。为了说明该方法的通用性，对各种复杂点云表面进行了表面扩散、模式形成、可激发介质和体-表面耦合的计算。
The study of reaction–diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction–diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction–diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.