A new algorithm for index determination in DAEs using algorithmic differentiation

作者：Lamour Rene^*; Monett Dagmar

来源：Numerical Algorithms, 2011, 58(2): 261-292.

DOI：10.1007/s11075-011-9455-8

• DAE
• Index determination
• Tractability index
• AD
• Algorithmic differentiation
• Automatic differentiation

We present an approach for determining the tractability index using truncated polynomial arithmetic. In particular, computing the index this way generates a sequence of matrices that contains itself derivatives. We implement the time differentiations using algorithmic differentiation techniques, specially using the standard ADOL-C package, with which calculating the derivatives becomes a simple shift and scaling of coefficients. We present the theory supporting the procedure we propose, as well as the implementation issues behind it to provide a convenient interface to the standard ADOL-C functionality. We give also examples of academic and practical problems and report several experimental results we have obtained with them.

• 出版日期2011-10