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Reliability and Accuracy of ODE Systems Solution for Modeling Environment of Heterogeneous Dynamic Systems PA10 
 


Authors 
 Zhuk D.M. 
 Kozhevnikov D.Yu. 
 Manichev V.B. 
Date of publication 
 2018 
DOI 
 10.31114/207877072018197102 

Abstract 
 For solving some problems of simulation heterogeneous dynamic systems, it is necessary to use interdisciplinary or multiphysics analysis at the concentrated and distributed level of simulation (simulation of MEMS, for example). Such approach will correspond to requirements of reliability and adequacy of simulator, even at very complex products design. Needs for precision simulation dynamic systems with illconditioned mathematical models (with stiff and superstiff ODE set) are increased now continuously. There are many challenges of mathematical simulation in the time domain on the basis of a solution the stiff ODE sets: in chemistry (for example, problems of a chemical kinetics), in physics (problems of mechanics, an isotope kinetics, laser technics, etc.), in microelectronics and nanoelectronics, in CAE systems. It is increased importance of adequate and precision simulation of heterogeneous dynamic systems. Timedomain simulation and analysis of electronic circuits (by Intel and our firms) is now realized by programs using solvers ODE of SPICE simulator. In EDA software of the foreign companies the basic attention now is given the userfriendly interface and convenience of using the programs. However with increase in the complexity of solved problems there is a necessity of mathematical simulation of wave effects and solutions of the superrigid ODE sets. EDA software mentioned above companies do not solve these problems now. The basic weakness of known programs for numerical simulation of dynamic systems (for example, MATLAB_SIMULINK) consists in deriving incorrect outcome for numerical simulation of dynamic systems at the low set requirements to a mathematical accuracy (parameter  eps) to integration of corresponding ODE set as model of dynamic system (by default eps=0.001 in MATLABSIMULINK). Low requirements to a mathematical accuracy for a solution of mathematical models of dynamic systems result from a low measurement accuracy of initial interior parameters of dynamic systems and accordingly numerical values of different factors, as a rule, and it is necessary to consider also a technological variety of these parameters and aging of modelled products. To disadvantages of known programs for simulation of dynamic systems we can add also its orientation for mathematiciansprogrammers and the design engineers of the top skills knowing mathematical English language (for example, MATLAB_SIMULINK is not localized). Development of software product PA10 (Program for Analysis, version 10) is directed on elimination of these disadvantages. Problems of reliable and accurate simulation of heterogeneous dynamic systems and objects with program PA10, surpassing similar foreign software products, are considered in this paper. Base function of PA10 is an reliable and accurate simulation and an engineering timedomain analysis of systems and objects for designing products of microelectronics, nanoelectronics and, in the main, mechatronics (MEMS). Experience of development of mathematical kernel PA10  program solver the ODE set manzhuk is considered. This solver surpasses in reliability and accuracy of calculations corresponding solvers in a package of mathematical programs MATLAB and furthermore surpass solvers ODE of SPICE simulator (Gear and Trapezoid methods). 
Keywords 
 Electronic Design Automation (EDA), simulation, Computer Aided Engineering (CAE), dynamic systems, Ordinary Differential Equations (ODE), Differential Algebraic Equations (DAE). 
Library reference 
 Zhuk D.M., Kozhevnikov D.Yu., Manichev V.B. Reliability and Accuracy of ODE Systems Solution for Modeling Environment of Heterogeneous Dynamic Systems PA10 // Problems of Perspective Micro and Nanoelectronic Systems Development  2018. Issue 1. P. 97102. 
URL of paper 
 http://www.mesconference.ru/data/year2018/pdf/D052.pdf 

