Advertisement

Optimization–Based Modeling with Applications to Transport: Part 1. Abstract Formulation

  • Pavel Bochev
  • Denis Ridzal
  • Joseph Young
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)

Abstract

This paper is the first of three related articles, which develop and demonstrate a new, optimization–based framework for computational modeling. The framework uses optimization and control ideas to assemble and decompose multiphysics operators and to preserve their fundamental physical properties in the discretization process. An optimization–based monotone, linearity preserving algorithm for transport (OBT) demonstrates the scope of the framework. The second and the third parts of this work focus on the formulation of efficient optimization algorithms for the solution of the OBT problem, and computational studies of its accuracy and efficacy.

Keywords

Sandia National Laboratory Discrete Optimization Problem Discretization Process Control Idea Fundamental Physical Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berger, M., Murman, S.M., Aftosmis, M.J.: Analysis of slope limiters on irregular grids. In: Proceedings of the 43rd AIAA Aerospace Sciences Meeting. No. AIAA2005-0490, AIAA, Reno, NV, January 10-13 (2005)Google Scholar
  2. 2.
    Bochev, P., Ridzal, D.: Additive Operator Decomposition and Optimization–Based Reconnection with Applications. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2009. LNCS, vol. 5910, pp. 645–652. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Bochev, P., Ridzal, D.: An optimization-based approach for the design of PDE solution algorithms. SIAM Journal on Numerical Analysis 47(5), 3938–3955 (2009), http://link.aip.org/link/?SNA/47/3938/1 MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Bochev, P., Ridzal, D., Scovazzi, G., Shashkov, M.: Formulation, analysis and numerical study of an optimization-based conservative interpolation (remap) of scalar fields for arbitrary lagrangian-eulerian methods. Journal of Computational Physics 230(13), 5199–5225 (2011), http://www.sciencedirect.com/science/article/B6WHY-52F895B-2/2/5e30ada70a5c6053464dfe9ceb74cf26 MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Dukowicz, J.K., Baumgardner, J.R.: Incremental remapping as a transport/advection algorithm. Journal of Computational Physics 160(1), 318–335 (2000), http://www.sciencedirect.com/science/article/B6WHY-45FC8N8-6F/2/179cbfc9634bb79579b68754cebd5525 zbMATHCrossRefGoogle Scholar
  6. 6.
    Kucharik, M., Shashkov, M., Wendroff, B.: An efficient linearity-and-bound-preserving remapping method. Journal of Computational Physics 188(2), 462–471 (2003), http://www.sciencedirect.com/science/article/B6WHY-48CWYJW-2/2/d264d65dcfa253e387aea5bdebfd433f zbMATHCrossRefGoogle Scholar
  7. 7.
    Margolin, L.G., Shashkov, M.: Second-order sign-preserving conservative interpolation (remapping) on general grids. Journal of Computational Physics 184(1), 266–298 (2003), http://www.sciencedirect.com/science/article/B6WHY-47HS5PX-4/2/9acf255c80d91bf5873398d5b929303e MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Ridzal, D., Bochev, P., Young, J., Peterson, K.: Optimization–Based Modeling with Applications to Transport. Part 3. Implementation and Computational Studies. In: Lirkov, I., Margenov, S., Wanśiewski, J. (eds.) LSSC 2011. LNCS, vol. 7116, pp. 81–88. Springer, Heidelberg (2012)Google Scholar
  9. 9.
    Swartz, B.: Good neighborhoods for multidimensional Van Leer limiting. Journal of Computational Physics 154(1), 237–241 (1999), http://www.sciencedirect.com/science/article/B6WHY-45GMW6B-25/2/5ba96d929cffd2519d4a04719509a5e7 MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Young, J., Ridzal, D., Bochev, P.: Optimization–Based Modeling with Applications to Transport. Part 2. Optimization Algorithm. In: Lirkov, I., Margenov, S., Wanśiewski, J. (eds.) LSSC 2011. LNCS, vol. 7116, pp. 72–80. Springer, Heidelberg (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pavel Bochev
    • 1
  • Denis Ridzal
    • 2
  • Joseph Young
    • 1
  1. 1.Numerical Analysis and ApplicationsSandia National LaboratoriesAlbuquerqueUSA
  2. 2.Optimization and Uncertainty QuantificationSandia National LaboratoriesAlbuquerqueUSA

Personalised recommendations