Efficient index reduction algorithm for large scale systems of differential algebraic equations

Qin, Xiaolin; Tang, Juan; Feng, Yong; Bachmann, Bernhard; Fritzson, Peter

doi:10.1016/j.amc.2015.11.091

Cited by 5 publications

(5 citation statements)

References 32 publications

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“…The index reduction algorithm with dummy-states, described in Söderlind and Mattsson (1993), reduces the system to index one, so that it can be simulated with common solvers. Alternative methods to handle index reduction have been proposed in Qin et al (2016Qin et al ( , 2018. Simulation without index reduction is also possible, but less reliable.…”

Section: Index Reductionmentioning

confidence: 99%

The OpenModelica Integrated Environment for Modeling, Simulation, and Model-Based Development

Fritzson¹,

Pop²,

Abdelhak³

et al. 2020

MIC

Self Cite

112

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OpenModelica is a unique large-scale integrated open-source Modelica-and FMI-based modeling, simulation, optimization, model-based analysis and development environment. Moreover, the OpenModelica environment provides a number of facilities such as debugging; optimization; visualization and 3D animation; web-based model editing and simulation; scripting from Modelica, Python, Julia, and Matlab; efficient simulation and co-simulation of FMI-based models; compilation for embedded systems; Modelica-UML integration; requirement verification; and generation of parallel code for multi-core architectures. The environment is based on the equation-based object-oriented Modelica language and currently uses the MetaModelica extended version of Modelica for its model compiler implementation. This overview paper gives an up-to-date description of the capabilities of the system, short overviews of used open source symbolic and numeric algorithms with pointers to published literature, tool integration aspects, some lessons learned, and the main vision behind its development.

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Section: Index Reductionmentioning

confidence: 99%

The OpenModelica Integrated Environment for Modeling, Simulation, and Model-Based Development

Fritzson¹,

Pop²,

Abdelhak³

et al. 2020

MIC

Self Cite

112

View full text Add to dashboard Cite

show abstract

“…All codes are written in Matlab 2016a under Windows 10 system and run on a personal computer with Intel(R) Core(TM) i5-3570 CPU @ 3.40 GHz, 4.00 GB RAM and 64-bit operating system. We do corresponding random trials for FPIA, extended signature matrix method (ESMM [14]), MPA and BPA with r = {10, 20, 40} and n = 800 : 200 : 2400, and calculate their constants in µ • n ν using the standard least-square method. The running times of these algorithms are shown in Figure 1, respectively; some ratios of the running times are given in Figure 2.…”

Section: Numerical Experimentationmentioning

confidence: 99%

“…They compute the fine BTF for system's numerical scheme via valid global offset vectors or the local offsets of each separated coarse block. Qin and Tang et al in [14] generalized the Σ method for large-scale DAE systems. In addition, there are other index reduction methods for different DAEs [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

Tang

Rao

2020

Mathematics

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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.

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“…They compute the fine BTF for system's numerical scheme via valid global offset vectors or the local offsets of each separated coarse block. Qin and Tang et al in [13] generalized the Σ method for large-scale DAE systems. In addition, there are other index reduction methods for different DAEs [14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

A New Block Structural Index Reduction Approach for Large-scale Differential Algebraic Equations

Tang¹,

Rao²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Efficient index reduction algorithm for large scale systems of differential algebraic equations

Cited by 5 publications

References 32 publications

The OpenModelica Integrated Environment for Modeling, Simulation, and Model-Based Development

The OpenModelica Integrated Environment for Modeling, Simulation, and Model-Based Development

A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

A New Block Structural Index Reduction Approach for Large-scale Differential Algebraic Equations

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