Transformation of Differential Algebraic Array Equations to Index One Form
Transformation of Differential Algebraic Array Equations to Index One Form
复制标题
微分代数数组方程向索引一种形式的变换
DOI：
10.3384/ecp17132565
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
H. Elmqvist
中科院分区：
文献类型：
--
作者：
M. Otter;H. Elmqvist
提出了几种新算法，实际上将 DAE（微分代数方程）转换为可以用标准 DAE 积分器模拟的特殊索引形式。在不求解线性和/或非线性方程组的情况下执行到这种形式的变换，保持方程的稀疏性，并且阵列方程仍然是阵列方程或其微分版本。此外，某些 DAE 可以在结构指数约简方法失败的情况下得到处理。预计这些新算法将有助于以目前可能的更好方式处理任何索引的大型 Modelica 模型。该算法已在使用 Julia 编程语言实现的实验模拟环境 Modia 中进行了评估和测试。
Several new algorithms are proposed that in effect transform DAEs (Differential Algebraic Equations) to a special index one form that can be simulated with standard DAE integrators. The transformation to this form is performed without solving linear and/or nonlinear equation systems, the sparsity of the equations is kept, and array equations remain array equations or differentiated versions of them. Furthermore, certain DAEs can be handled where structural index reduction methods fail. It is expected that these new algorithms will help to treat large Modelica models of any index in a better way as it is currently possible. The algorithms have been evaluated and tested in the experimental simulation environment Modia that is implemented with the Julia programming language.