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首页> 外文期刊>Journal of Computational Physics >An improved algorithm and its parallel implementation for solving a general blood-tissue transport and metabolism model
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An improved algorithm and its parallel implementation for solving a general blood-tissue transport and metabolism model

机译：一种解决一般血液运输代谢模型的改进算法及其并行实现

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摘要

Fast algorithms for simulating mathematical models of coupled blood-tissue transport and metabolism are critical for the analysis of data on transport and reaction in tissues. Here, by combining the method of characteristics with the standard grid discretization technique, a novel algorithm is introduced for solving a general blood-tissue transport and metabolism model governed by a large system of one-dimensional semilinear first order partial differential equations. The key part of the algorithm is to approximate the model as a group of independent ordinary differential equation (ODE) systems such that each ODE system has the same size as the model and can be integrated independently. Thus the method can be easily implemented in parallel on a large-scale multiprocessor computer. The accuracy of the algorithm is demonstrated for solving a simple blood-tissue exchange model introduced by Sangren and Sheppard [W.C. Sangren, C.W. Sheppard, A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment, Bull. Math. Biophys. 15 (1953) 387-394], which has an analytical solution. Numerical experiments made on a distributed-memory parallel computer (an HP Linux cluster) and a shared-memory parallel computer (a SGI Origin 2000) demonstrate the parallel efficiency of the algorithm.
机译：模拟耦合的组织运输和代谢的数学模型的快速算法对于分析组织中的运输和反应数据至关重要。在此，通过将特征方法与标准网格离散技术相结合，提出了一种新颖的算法，用于求解由一维半线性一阶偏微分方程的大系统控制的一般组织运输和代谢模型。该算法的关键部分是将模型近似为一组独立的常微分方程（ODE）系统，以使每个ODE系统具有与模型相同的大小并且可以独立集成。因此，该方法可以容易地在大型多处理器计算机上并行实现。证明了该算法的正确性，可以解决Sangren和Sheppard [W.C. Sangren，C.W. Sheppard，《标记物质在容器中流动的液体与外部隔室之间的交换》的数学推导，Bull。数学。生物物理学。 15（1953）387-394]，其具有分析解决方案。在分布式内存并行计算机（HP Linux群集）和共享​​内存并行计算机（SGI Origin 2000）上进行的数值实验证明了该算法的并行效率。

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