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libMoM : a library for stochastic simulations in engineering using statistical moments

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Abstract

Stochastic simulations are becoming increasingly important in numerous engineering applications. The solution to the governing equations are complicated due to the high-dimensional spaces and the presence of randomness. In this paper we present libMoM (http://libmom.sourceforge.net), a software library to solve various types of Stochastic Differential Equations (SDE) as well as estimate statistical distributions from the moments. The library provides a suite of tools to solve various SDEs using the method of moments (MoM) as well as estimate statistical distributions from the moments using moment matching algorithms. For a large class of problems, MoM provide efficient solutions compared with other stochastic simulation techniques such as Monte Carlo (MC). In the physical sciences, the moments of the distribution are usually the primary quantities of interest. The library enables the solution of moment equations derived from a variety of SDEs, with closure using non-standard Gaussian quadrature. In engineering risk assessment and decision making, statistical distributions are required. The library implements tools for fitting the Generalized Lambda Distribution (GLD) with the given moments. The objectives of this paper are (1) to briefly outline the theory behind moment methods for solving SDEs/estimation of statistical distributions; (2) describe the organization of the software and user interfaces; (3) discuss use of standard software engineering tools for regression testing, aid collaboration, distribution and further development. A number of representative examples of the use of libMoM in various engineering applications are presented and future areas of research are discussed.

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Notes

  1. http://libmom.sourceforge.net

  2. http://www.gnu.org/software/gsl/

  3. The choice of the variables \(W_i {\tilde{\xi}}_i\) instead of \({\tilde{\xi}}_i\) is purely a convention. In the literature, the method that uses this choice of variables has been called the Direct Quadrature Method of Moments (DQMOM) [8]. Either choice is possible. The form of the Jacobian matrix is different for each choice.

  4. http://www.gnu.org/software/gsl/

  5. http://gslwrap.sourceforge.net/

  6. http://www.gnu.org/software/autoconf/

  7. http://www.gnu.org/software/automake/

  8. http://www.gnu.org/software/libtool/

  9. http://www.stack.nl/~dimitri/doxygen/index.html

  10. https://sourceforge.net/projects/libmom/

  11. http://web.maths.unsw.edu.au/~fkuo/sobol/

  12. http://libmesh.sourceforge.net

  13. http://www.openfoam.com

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Acknowledgments

The research was supported in part by the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28615.

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Authors and Affiliations

  1. Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station C0200, Austin, TX, 78712, USA

    Rochan R. Upadhyay

  2. Department of Mechanical Engineering, The University of Texas at Austin, 1 University Station C2200, Austin, TX, 78712-0292, USA

    Ofodike A. Ezekoye

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  1. Rochan R. Upadhyay
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  2. Ofodike A. Ezekoye
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Correspondence to Rochan R. Upadhyay.

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Upadhyay, R.R., Ezekoye, O.A. libMoM : a library for stochastic simulations in engineering using statistical moments. Engineering with Computers 28, 83–94 (2012). https://doi.org/10.1007/s00366-011-0219-9

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