Efficient Numerical Integration of Dynamical Systems based on Structural-Algebraic Regularization avoiding State Selection
Efficient Numerical Integration of Dynamical Systems based on Structural-Algebraic Regularization avoiding State Selection
复制标题
基于结构代数正则化避免状态选择的动力系统的高效数值积分
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Steinbrecher
中科院分区：
文献类型：
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作者：
L. Scholz;A. Steinbrecher
微分代数方程自然出现在动态过程的建模中，特别是使用MODELICA作为建模语言。通常，模型方程可以具有更高的指标，即它们可能包含导致数值积分不稳定和阶数降低的隐藏约束。因此，需要对模型方程进行正则化或重构。获取隐藏约束所需信息的一种方法是基于系统的稀疏性模式进行结构分析。对于确定一个规则的指数缩减系统公式，通常一个关键的步骤是所谓的状态选择。在本文中，我们将提出一种新的动态系统重构方法，即利用从结构分析中获得的信息来构造正则化的过定系统公式。这个超定的系统可以使用特别适应的数值积分器来解决，这样在模拟运行期间，状态选择可以在数值积分器内执行。
Differential-algebraic equations naturally arise in the modeling of dynamical processes, in particular using MODELICA as modeling language. In general, the model equations can be of higher index, i.e., they can contain hidden constraints which lead to instabilities and order reductions in the numerical integration. Therefore, a regularization or remodeling of the model equations is required. One way to obtain the required information on the hidden constraints is a structural analysis based on the sparsity pattern of the system. For the determination of a regular index-reduced system formulation then, usually, a crucial step is the so-called state selection. In this paper, we will present a new approach for the remodeling of dynamical systems that uses the information obtained from the structural analysis to construct a regularized overdetermined system formulation. This overdetermined system can then be solved using specially adapted numerical integrators, in such a way that the state selection can be performed within the numerical integrator during runtime of the simulation.