Computation of consistent initial values for properly stated index 3 DAEs

Lamour, René; Mazzia, Francesca

doi:10.1007/s10543-009-0212-5

Cited by 14 publications

(6 citation statements)

References 18 publications

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“…The latter provides a more completed view of the whole project because almost all global variables, functions, and classes are there documented. 3 The work in progress includes the extension of our method for computing consistent initial values from time-invariant linear problems to general smooth DAEs [18].…”

Section: Discussionmentioning

confidence: 99%

A new algorithm for index determination in DAEs using algorithmic differentiation

Lamour

Monett

2011

Numer Algor

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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.

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Section: Discussionmentioning

confidence: 99%

A new algorithm for index determination in DAEs using algorithmic differentiation

Lamour

Monett

2011

Numer Algor

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“…For an extensive overview, we refer to [1]. The recent algorithm for index-3 DAEs from [2] is discussed in Remark 4. Let us focus on the papers related to the method presented below. The approach described in [3] for index-2 systems and its modification presented in [4] compute a consistent initialization solving a nonlinear system of appropriate equations involving the projectors of the tractability-index.…”

Section: Definitionmentioning

confidence: 99%

“…In contrast to the above approach, the algorithm presented in [2] is not restricted to DAEs in Hessenberg Form. In order to cope with general nonlinear DAEs, two major approaches are combined.…”

Section: Remarkmentioning

confidence: 99%

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Consistent initialization for DAEs in Hessenberg form

Schwarz

2009

Numer Algor

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For nonlinear DAEs, we can hardly make a reasonable statement unless structural assumptions are given. Many results are restricted to explicit DAEs, often in Hessenberg form of order up to three. For the DAEs resulting from circuit simulation, different beneficial structures have been found and exploited for the computation of consistent initial values. In this paper, a class of DAEs in nonlinear Hessenberg form of arbitrary high order is defined and analyzed with regard to consistent initialization. For this class of DAEs, the hidden constraints can be systematically described and the consistent initialization can be determined step-by-step solving linear subproblems, an approach hitherto used for the DAEs resulting from circuit simulation. Finally, it is shown that the DAEs resulting from mechanical systems fulfill the defined structural assumptions. The algorithm is illustrated by several examples.

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“…Berzins et al (1989) combined both methods and expanded the Euler steps to try to provide a more flexible method. Lamour and Mazzia (2009) outlined a method that approximates the system's derivatives and can be used for systems of DAEs up to index-3. However, the method has some restrictions caused by the inner differentiations required for higher indexed systems.…”

Section: Introductionmentioning

confidence: 99%

Extending explicit and linearly implicit ODE solvers for index-1 DAEs

Lawder

Ramadesigan

Suthar

et al. 2015

Computers & Chemical Engineering

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a b s t r a c tNonlinear differential-algebraic equations (DAE) are typically solved using implicit stiff solvers based on backward difference formula or RADAU formula, requiring a Newton-Raphson approach for the nonlinear equations or using Rosenbrock methods specifically designed for DAEs. Consistent initial conditions are essential for determining numeric solutions for systems of DAEs. Very few systems of DAEs can be solved using explicit ODE solvers. This paper applies a single-step approach to system initialization and simulation allowing for systems of DAEs to be solved using explicit (and linearly implicit) ODE solvers without a priori knowledge of the exact initial conditions for the algebraic variables. Along with using a combined process for initialization and simulation, many physical systems represented through large systems of DAEs can be solved in a more robust and efficient manner without the need for nonlinear solvers. The proposed approach extends the usability of explicit and linearly implicit ODE solvers and removes the requirement of Newton-Raphson type iteration.Published by Elsevier Ltd.

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Computation of consistent initial values for properly stated index 3 DAEs

Cited by 14 publications

References 18 publications

A new algorithm for index determination in DAEs using algorithmic differentiation

A new algorithm for index determination in DAEs using algorithmic differentiation

Consistent initialization for DAEs in Hessenberg form

Extending explicit and linearly implicit ODE solvers for index-1 DAEs

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