FATODE: A LIBRARY FOR FORWARD, ADJOINT, AND TANGENT LINEAR INTEGRATION OF ODES
FATODE: A LIBRARY FOR FORWARD, ADJOINT, AND TANGENT LINEAR INTEGRATION OF ODES
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DOI：
10.1137/130912335
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发表时间：
2014-01-01
影响因子：
3.1
通讯作者：
Sandu, Adrian
中科院分区：
文献类型：
--
作者：
Zhang, Hong;Sandu, Adrian
FATODE是一个Fortran库，用于集成具有直接和伴随灵敏度分析功能的常微分方程。本文介绍了该软件包的功能、实现、代码组织和使用方法。FATODE实现了四种方法：非刚性问题的显式Runge-Kutta，全隐式Runge-Kutta，单对角隐式Runge-Kutta和刚性问题的Rosenbrock。每个系列包含几种具有不同精度的方法;用户可以通过简单地提供其系数来添加新方法。对于每个家庭的前向，伴随和切线线性模型的实施。通用求解器的密集和稀疏线性代数使用;用户可以很容易地将问题定制的线性代数例程。在几个测试问题上证明了该软件包的性能。据我们所知，FATODE是第一个公开可用的通用软件包，提供了前向和伴随的敏感性分析功能的情况下，龙格库塔法。广泛的应用，预计将受益于它的使用，例子包括参数估计，数据同化，最优控制和不确定性量化。
FATODE is a Fortran library for the integration of ordinary differential equations with direct and adjoint sensitivity analysis capabilities. The paper describes the capabilities, implementation, code organization, and usage of this package. FATODE implements four families of methods: explicit Runge-Kutta for nonstiff problems, fully implicit Runge-Kutta, singly diagonally implicit Runge-Kutta, and Rosenbrock for stiff problems. Each family contains several methods with different orders of accuracy; users can add new methods by simply providing their coefficients. For each family the forward, adjoint, and tangent linear models are implemented. General purpose solvers for dense and sparse linear algebra are used; users can easily incorporate problem-tailored linear algebra routines. The performance of the package is demonstrated on several test problems. To the best of our knowledge FATODE is the first publicly available general purpose package that offers forward and adjoint sensitivity analysis capabilities in the context of Runge-Kutta methods. A wide range of applications is expected to benefit from its use; examples include parameter estimation, data assimilation, optimal control, and uncertainty quantification.