scholarly journals Survey of appropriate matching algorithms for large scale systems of differential algebraic equations

Author(s):  
Jens Frenkel ◽  
Günter Kunze ◽  
Peter Fritzson
Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2057
Author(s):  
Juan Tang ◽  
Yongsheng Rao

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications has emerged and became widely accepted; they generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAE systems with large dimensions, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on the Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameters has been presented. It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples, and preliminary numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.


Author(s):  
Juan Tang ◽  
Yongsheng Rao

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter has been presented.It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.


Author(s):  
Jason Mayes ◽  
Mihir Sen

Dynamic analysis of large-scale flow networks is made difficult by the large system of differential-algebraic equations resulting from its modelling. To simplify analysis, the mathematical model must be sufficiently reduced in complexity. For self-similar tree networks, this reduction can be made using the network’s structure in way that can allow simple, analytical solutions. For very large, but finite, networks, analytical solutions are more difficult to obtain. In the infinite limit, however, analysis is sometimes greatly simplified. It is shown that approximating large finite networks as infinite not only simplifies the analysis, but also provides an excellent approximate solution.


1994 ◽  
Vol 116 (2) ◽  
pp. 429-436 ◽  
Author(s):  
J. D. Trom ◽  
M. J. Vanderploeg

This paper presents a new approach for linearization of large multibody dynamic systems. The approach uses an analytical differentiation of terms evaluated in a numerical equation formulation. This technique is more efficient than finite difference and eliminates the need to determine finite difference pertubation values. Because the method is based on a relative coordinate formalism, linearizations can be obtained for equilibrium configurations with non-zero Cartesian accelerations. Examples illustrate the accuracy and efficiency of the algorithm, and its ability to compute linearizations for large-scale systems that were previously impossible.


Author(s):  
Martin J. Vanderploeg ◽  
Jeff D. Trom

Abstract This paper presents a new approach for linearization of large multi-body dynamic systems. The approach uses an analytical differentiation of terms evaluated in a numerical equation formulation. This technique is more efficient than finite difference and eliminates the need to determine finite difference pertubation values. Because the method is based on a relative coordinate formalism, linearizations can be obtained for equilibrium configurations with non-zero Cartesian accelerations. Examples illustrate the accuracy and efficiency of the algorithm, and its ability to compute linearizations for large-scale systems that were previously impossible.


2013 ◽  
Vol 4 (1) ◽  
pp. 243-250
Author(s):  
H. Yoshimura

Abstract. In this paper, we propose an efficient numerical scheme to compute sparse matrix inversions for Implicit Differential Algebraic Equations of large-scale nonlinear mechanical systems. We first formulate mechanical systems with constraints by Dirac structures and associated Lagrangian systems. Second, we show how to allocate input-output relations to the variables in kinematical and dynamical relations appearing in DAEs by introducing an oriented bipartite graph. Then, we also show that the matrix inversion of Jacobian matrix associated to the kinematical and dynamical relations can be carried out by using the input-output relations and we explain solvability of the sparse Jacobian matrix inversion by using the bipartite graph. Finally, we propose an efficient symbolic generation algorithm to compute the sparse matrix inversion of the Jacobian matrix, and we demonstrate the validity in numerical efficiency by an example of the stanford manipulator.


2016 ◽  
Vol 13 (10) ◽  
pp. 7705-7711 ◽  
Author(s):  
Juan Tang ◽  
Wenyuan Wu ◽  
Xiaolin Qin ◽  
Yong Feng

Motivated by Pryce’s structural analysis method for differential algebraic equations (DAEs), we show the complexity of the fixed-point iteration algorithm (FPIA) and propose a fixed-point iteration method with parameters. It leads to a block fixed-point iteration method (BFPIM) which can be applied to immediately calculate the crucial canonical offsets for large-scale (coupled) DAE systems with block-triangular structure, and its complexity analysis is also given in this paper. Moreover, preliminary numerical experiments show that the time complexity of BFPIM can be reduced by at least O(l) compared to the FPIA.


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