POLYNOMIAL CHAOS FOR SEMIEXPLICIT DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX 1
POLYNOMIAL CHAOS FOR SEMIEXPLICIT DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX 1
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指数1的半显微分代数方程的多项式混沌
DOI：
10.1615/int.j.uncertaintyquantification.2011003306
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发表时间：
2013
影响因子：
1.7
通讯作者：
R. Pulch
中科院分区：
文献类型：
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作者：
R. Pulch
技术应用的数学建模通常会产生微分代数方程组。通过引入随机变量，可以考虑物理参数的不确定性。一个相应的不确定性量化需要解决的随机模型。我们专注于半显式系统的非线性微分代数方程指数为1。随机模型的求解使用广义多项式混沌的扩展。我们研究了随机配置技术和随机Galerkin方法来确定未知系数函数。特别地，我们分析了由随机Galerkin方法得到的较大耦合系统的指数。数值模拟测试的例子，这两种方法进行了比较，其效率。
Mathematical modeling of technical applications often yields systems of differential algebraic equations. Uncertainties of physical parameters can be considered by the introduction of random variables. A corresponding uncertainty quantification requires one to solve the stochastic model. We focus on semiexplicit systems of nonlinear differential algebraic equations with index 1. The stochastic model is solved using the expansion of the generalised polynomial chaos. We investigate both the stochastic collocation technique and the stochastic Galerkin method to determine the unknown coefficient functions. In particular, we analyze the index of the larger coupled systems, which result from the stochastic Galerkin method. Numerical simulations of test examples are presented, where the two approaches are compared with respect to their efficiency.