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Transformation of Differential Algebraic Array Equations to Index One Form

2017
*
Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017
*

Several new algorithms are proposed that in effect

doi:10.3384/ecp17132565
dblp:conf/modelica/OtterE17
fatcat:kp5e46dhhbcyhn6ulqga5aszrq
*transform*DAEs (*Differential**Algebraic**Equations*)*to*a special*index**one**form*that can be simulated with standard DAE integrators. ... The*transformation**to*this*form*is performed without solving linear and/or nonlinear*equation*systems, the sparsity*of*the*equations*is kept, and*array**equations*remain*array**equations*or*differentiated*... Acknowledgements The authors would like*to*thank Martin Arnold from University Halle-Wittenberg for discussions*to*understand the fine details*of*multibody integrators. ...##
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A derivative array approach for linear second order differential-algebraic systems

2011
*
The Electronic Journal of Linear Algebra
*

At first, in Section 2, we present the basic results

doi:10.13001/1081-3810.1441
fatcat:fltmirbb4nd5rasr35mnidbf6m
*of*the analysis*of*linear second order*differential*-*algebraic**equations*as derived in [12] , including a new condensed*form*that allows*one**to*read ... We present an*index*reduction method based*on*derivative*arrays*that allows*to*determine an equivalent second order system*of*lower*index*in a numerical computable way. ... Therefore, the numerical solution*of*linear second order*differential*-*algebraic*systems*of*the*form*(1.1) typically requires the reduction*to*a first order system*on*the*one*hand and an*index*reduction ...##
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Review of applied multidimensional systems theory

1984
*
Linear Algebra and its Applications
*

Among the areas

doi:10.1016/0024-3795(84)90194-0
fatcat:azsvcaeomrebxolb444ml6lbzi
*of*~applied mathematics that heavily use linear*algebra*, systems theory is currently*one**of*the most active. ... The general heading*of*systems theory includes topics from control theory, circuit theory, and power systems*to*name a few. For the person with a strong linear*algebra*background wanting*to*learn ... The emphasis is*on*the z*transform*and difference*equations*. ...##
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A Differentiation Index for Partial Differential-Algebraic Equations

2000
*
SIAM Journal on Scientific Computing
*

This

doi:10.1137/s1064827598332229
fatcat:hwa5qf6kw5dgvivwxocfowvrxy
*index*is thus a generalization*of*the*differentiation**index**of**differential*-*algebraic**equations*. ... A*differentiation**index*for nonlinear partial*differential*-*algebraic**equations*is presented. ... From here onward the term*index*will refer*to*the*differentiation**index*.*Algebraic**equations*may be thought*of*as constraints*on*or invariants*of*the system. ...##
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Optimal Control for Navier-Stokes Takagi-Sugeno Fuzzy Equations Using Simulink
[chapter]

2011
*
Communications in Computer and Information Science
*

Since such

doi:10.1007/978-3-642-19263-0_7
fatcat:7fatu6sc6rcirkmepyiv5rd6xi
*differential**algebraic*systems have a difficulty*to*solve in their original*form*, most approaches use some kind*of**index*reduction. ... In this paper, the unsteady Navier-Stokes Takagi-Sugeno (T-S) fuzzy*equations*(UNSTSFEs) are represented as a*differential**algebraic*system*of*strangeness*index**one*by applying any spatial discretization ... Acknowledgements: The funding*of*this work by the UMRG grant (Account No: RG099/10AFR) is gratefully acknowledged. ...##
###
Eigenvalue placement in completions of DAES

2013
*
The Electronic Journal of Linear Algebra
*

*Differential*

*algebraic*

*equations*(DAEs) are used

*to*describe many physical processes. A completion

*of*a DAE is an ordinary

*differential*

*equation*whose solutions include those

*of*the DAE. ... Algorithms exists for designing stabilized completions

*of*

*differential*

*algebraic*

*equations*. ...

*Differential*

*algebraic*

*equations*(DAEs) are mixed systems

*of*

*differential*and

*algebraic*

*equations*F (x ′ , x, t) = 0 for which the Jacobian F x ′ is identically singular. ...

##
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Index reduction for differential-algebraic equations by minimal extension

2004
*
Zeitschrift für angewandte Mathematik und Mechanik
*

Based

doi:10.1002/zamm.200310127
fatcat:75xlxeia4ve35c3sjg5nccnhjm
*on*this information reduced derivative*arrays*are*formed*and instead*of*using expensive subspace computations the*index*reduction is obtained by introducing new variables. ... In this paper a new*index*reduction technique is discussed for the treatment*of**differential*-*algebraic*systems for which extra structural information is available. ... Acknowledgment We thank Diana Estevez-Schwarz and Caren Tischendorf for many helpful discussions concerning the topological characterization*of*the high*index**equations*in circuit simulation and Ingo Seufer ...##
###
Einstein summation for multidimensional arrays

2002
*
Computers and Mathematics with Applications
*

*one*

*of*the most common data structures, at least in scientific computing, is the multidimensional

*array*. ... An objectoriented implementation

*of*a C++ library that supports

*index*notation is described. ... These quantities may also vary over the computational domain, which requires the data structures

*to*be

*arrays*

*of*

*arrays*,

*one*

*array*referring

*to*the physical quantity and

*one*

*array*referring

*to*the discretization ...

##
###
Introduction to maple

2004
*
Computers and Mathematics with Applications
*

The war

doi:10.1016/s0898-1221(04)90103-4
fatcat:vqqmhhwhjng4nj4tcbzcobgutm
*of*attrition. 7.4.1. The discrete war*of*attrition. 7.4.2. The continuous war*of*attrition. 7.4.3. The discrete war*of*aggression. 7.5. The finitely repeated prisoner's dilemma game. 7.5.1. ... Centipede games*of*lengths two and three. ... Introduction*to*computer*algebra*. 1.1. What is computer*algebra*? 1.2. Computer*algebra*systems. 1.3. Some properties*of*computer*algebra*systems. 1.4. Advantages*of*computer*algebra*. 1.5. ...##
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Matrix tensor notation part I. Rectilinear orthogonal coordinates

1993
*
Computers and Mathematics with Applications
*

This is achieved by the introduction

doi:10.1016/0898-1221(93)90110-h
fatcat:dtn4dtng3rfptaif3m3ggvog5e
*of*the base as a tensor quantity in the fundamental*equation*for the relation between a tensor and its representation as a matrix. ... It is also shown that the same notation is equally useful for vectors in abstract higher dimensional space and*transformations*and*transforms*in function space. ... We apply now the same*transformation**algebra**to*the base and*to*the*transformation**equation*(11) This*equation*shows that g is the Unit space tensor and the base is merely a mixed*form**of*the unit tensor ...##
###
Characterization of classes of singular linear differential-algebraic equations

2005
*
The Electronic Journal of Linear Algebra
*

In particular, three different characterizations are given for

doi:10.13001/1081-3810.1169
fatcat:veur6fcp4zbfpeszmowapiueui
*differential*-*algebraic**equations*, namely by means*of*solution spaces, canonical*forms*, and derivative*arrays*. ... Linear, possibly over-or underdetermined,*differential*-*algebraic**equations*are studied that have the same solution behavior as linear*differential*-*algebraic**equations*with well-defined strangeness*index*... For regular DAEs, it has been shown in [1] that (1.1) has a well-defined*differentiation**index*and that (1.1) can be*transformed**to*a canonical*form*. ...##
###
Page 867 of Mathematical Reviews Vol. , Issue 98B
[page]

1998
*
Mathematical Reviews
*

In particular, an

*index*notion called the strangeness*index*was introduced. The*transformation*algorithm*to*the canonical*form*was not efficiently implementable. ... In the present paper, linear*index*2*differential*-*algebraic**equations*are considered. ...##
###
Index and Characteristic Analysis of Linear PDAE Systems

2003
*
SIAM Journal on Scientific Computing
*

These packages take as input the

doi:10.1137/s1064827599363411
fatcat:5x3ag6navjamllgxfpchp24cdy
*differential*and*algebraic*model*equations*that describe the physical behaviors*of*the process, processing tasks, and discrete events, and provide tools such as model inheritance ... Measures*of*the degeneracy*of*the system, rather than a*differentiation**index*, bound the order*of*derivatives*of*forcing functions that appear in the solution. 1. Introduction. ... If the governing PDE has a*differentiation**index*[17]*of*2 or higher with respect*to*the evolution variable,*one*expects a high-*index**differential*-*algebraic**equation*(DAE)*to*result from any reasonable ...##
###
Mathieu-Bragg photonic lattices
[article]

2021
*
arXiv
*
pre-print

The dynamics is shown

arXiv:2107.06273v2
fatcat:zxh4plmq25fobdwf5ftmkkw52m
*to*be fully integrable and therefore described in closed*form*. We examine the trajectories*of*classical light propagating in such structures. ... We show that Bragg diffraction may be modeled by classical light propagation in photonic lattices having a square power law for the refraction*index*coefficient. ...*To*increase the*index**of*refraction in a lattice, as the*one*shown in Fig. 1 , may be a difficult task, as the coupling has*to*grow quadratically; therefore, ways*of*simulating such waveguide*array*may ...##
###
The additional dynamics of least squares completions for linear differential algebraic equations

2007
*
Linear Algebra and its Applications
*

Several approaches have been proposed for numerically solving lower dimensional, nonlinear, higher

doi:10.1016/j.laa.2007.02.005
fatcat:nxgy7wwl4jaijm4wrq3ptpiydq
*index**differential**algebraic**equations*(DAEs) for which more classical numerical methods such as backward ...*One**of*these approaches is called explicit integration (EI). This approach is based*on*solving nonlinear DAE derivative*arrays*using nonlinear singular least squares methods. ... Acknowledgments We would like*to*thank Hongguo Xu for his helpful comments*on*Lemma 3. ...
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