Mitigating Error and Uncertainty in Partitioned Analysis: A Review of Verification, Calibration and Validation Methods for Coupled Simulations

Original Paper

Abstract

Partitioned analysis involves coupling of constituent models that resolve different scales or physics by allowing them to exchange inputs and outputs in an iterative manner. Through partitioning, simulations of complex physical systems are becoming evermore present in the scientific modeling community, making the Verification and Validation (V&V) of partitioned models to quantifying the predictive capability of their simulations increasingly important. Partitioning presents unique challenges, as well as opportunities, for the V&V community. Verification gains a new level of complexity in partitioned models, as numerical errors can easily be introduced at the coupling interface where non-matching domains and models are integrated together. For validation, partitioned analysis allows the quantification of the uncertainties and errors in constituent models through comparison against separate-effect experiments conducted in independent constituent domains. Such experimental validation is important as uncertainties and errors in the predictions of constituents can be transferred across their interfaces, either compensating for each other or accumulating during iterative coupling operations. This paper reviews published literature on methods for assessing and improving the predictive capability of strongly coupled models of physical and engineering systems with an emphasis on advancements made in the last decade.

References

  1. 1.
    Schlesinger S (1979) Terminology for model credibility. Simulation 32(3):103–104CrossRefGoogle Scholar
  2. 2.
    Sargent RG (1981) An assessment procedure and a set of criteria for use in the evaluation of computerized models and computer-based modelling tools. DTIC DocumentGoogle Scholar
  3. 3.
    Roache PJ (1997) Quantification of uncertainty in computational fluid dynamics. Annu Rev Fluid Mech 29(1):123–160MathSciNetCrossRefGoogle Scholar
  4. 4.
    AIAA (1998) Guide for the verification and validation of computational fluid dynamic simulations, Reston, VA, AIAA-G-077-1998Google Scholar
  5. 5.
    Roy CJ (2005) Review of code and solution verification procedures for computational simulation. J Comput Phys 205(1):131–156MATHCrossRefGoogle Scholar
  6. 6.
    Thacker BH, Doebling SW, Hemez F, Anderson MC, Pepin JE, and Rodriguez EA (2004) Concepts of model verification and validation. Los Alamos National Laboratory, Los Alamos, NM, LA-14167Google Scholar
  7. 7.
    Bejarano L, Jin F-F (2008) Coexistence of equatorial coupled modes of ENSO*. J Clim 21(12):3051–3067CrossRefGoogle Scholar
  8. 8.
    Kim J, Tchelepi HA, Juanes R et al (2009) Stability, accuracy and efficiency of sequential methods for coupled flow and geomechanics. In: SPE reservoir simulation symposiumGoogle Scholar
  9. 9.
    Atamturktur S, Hemez FM, Laman JA (2012) Uncertainty quantification in model verification and validation as applied to large scale historic masonry monuments. Eng Struct 43:221–234CrossRefGoogle Scholar
  10. 10.
    Freitas CJ (2002) The issue of numerical uncertainty. Appl Math Model 26(2):237–248MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Trucano TG, Swiler LP, Igusa T, Oberkampf WL, Pilch M (2006) Calibration, validation, and sensitivity analysis: what’s what. Reliab Eng Syst Saf 91(10–11):1331–1357CrossRefGoogle Scholar
  12. 12.
    Oberkampf WL, Trucano TG (2002) Verification and validation in computational fluid dynamics. Prog Aerosp Sci 38(3):209–272CrossRefGoogle Scholar
  13. 13.
    Atamturktur S, Hegenderfer J, Williams B, Egeberg M, Lebensohn RA, Unal C (2015) A resource allocation framework for experiment-based validation of numerical models. Mech Adv Mater Struct 22(8):641–654CrossRefGoogle Scholar
  14. 14.
    Felippa CA, Park KC, Farhat C (2001) Partitioned analysis of coupled mechanical systems. Comput Methods Appl Mech Eng 190(24):3247–3270MATHCrossRefGoogle Scholar
  15. 15.
    Michler C, Hulshoff SJ, van Brummelen EH, de Borst R (2004) A monolithic approach to fluid-structure interaction. Comput Fluids 33(5–6):839–848MATHCrossRefGoogle Scholar
  16. 16.
    Matthies HG, Niekamp R, Steindorf J (2006) Algorithms for strong coupling procedures. Comput Methods Appl Mech Eng 195(17–18):2028–2049MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Néron D, Dureisseix D (2008) A computational strategy for thermo-poroelastic structures with a time-space interface coupling. Int J Numer Meth Eng 75(9):1053–1084MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Wüchner R, Kupzok A, Bletzinger K-U (2007) A framework for stabilized partitioned analysis of thin membrane-wind interaction. Int J Numer Meth Fluids 54(6–8):945–963MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Järvinen E, Råback P, Lyly M, Salenius J-P (2008) A method for partitioned fluid–structure interaction computation of flow in arteries. Med Eng Phys 30(7):917–923CrossRefGoogle Scholar
  20. 20.
    Jahromi HZ, Izzuddin BA, Zdravkovic L (2007) Partitioned analysis of nonlinear soil-structure interaction using iterative coupling. Interact Multiscale Mech 1(1):33–51CrossRefGoogle Scholar
  21. 21.
    Badia S, Nobile F, Vergara C (2008) Fluid–structure partitioned procedures based on robin transmission conditions. J Comput Phys 227(14):7027–7051MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Houzeaux G, Codina R (2003) A chimera method based on a Dirichlet/Neumann (Robin) coupling for the Navier–Stokes equations. Comput Methods Appl Mech Eng 192(31–32):3343–3377MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Causin P, Gerbeau JF, Nobile F (2005) Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput Methods Appl Mech Eng 194(42–44):4506–4527MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Yoon GH, Jensen JS, and Sigmund O (2006) Topology optimization for acoustic–structure interaction problems. In: IUTAM symposium on topological design optimization of structures, machines and materials, pp 355–364Google Scholar
  25. 25.
    Zhili T, Jun D (2009) Couplings in multi-criterion aerodynamic optimization problems using adjoint methods and game strategies. Chin J Aeronaut 22(1):1–8CrossRefGoogle Scholar
  26. 26.
    Harris MJ, Baxter WV, Scheuermann T, and Lastra A (2003) Simulation of cloud dynamics on graphics hardware. In: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware, pp 92–101Google Scholar
  27. 27.
    Lieber M, Wolke R (2008) Optimizing the coupling in parallel air quality model systems. Environ Model Softw 23(2):235–243CrossRefGoogle Scholar
  28. 28.
    Knezevic M, McCabe RJ, Lebensohn RA, Tomé CN, Mihaila B (2012) Finite element implementation of a self-consistent polycrystal plasticity model: application to α-uranium. Evolution 100:2Google Scholar
  29. 29.
    Abdulle A and Jecker O (2014) An Optimization-based multiscale coupling methods. No. EPRL-ARTICLE-199836Google Scholar
  30. 30.
    Olson D, Bochev PB, Luskin M, Shapeev AV (2014) An optimization-based atomistic-to-continuum coupling method. SIAM J Numer Anal 52(4):2183–2204MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    Trčka M, Hensen JLM, Wetter M (2010) Co-simulation for performance prediction of integrated building And HVAC systems—an analysis of solution characteristics using a two-body system. Simul Model Pract Theory 18(7):957–970CrossRefGoogle Scholar
  32. 32.
    Farajpour I, Atamturktur S (2012) Partitioned analysis of coupled numerical models considering imprecise parameters and inexact models. J Comput Civ Eng 28(1):145–155CrossRefGoogle Scholar
  33. 33.
    Quaranta G, Bindolino G, Masarati P, and Mantegazza P (2004) Toward a computational framework for rotorcraft multi-physics analysis: adding computational aerodynamics to multibody rotor models. In: 30th European rotorcraft forum, Marseilles, FranceGoogle Scholar
  34. 34.
    Hensen JL (1999) A comparison of coupled and de-coupled solutions for temperature and air flow in a building. ASHRAE Trans 105:962Google Scholar
  35. 35.
    Valdés JG, Hernández A, and Mendoza M (2012) A fluid-structure interaction scheme applied to the analysis and design of a wind turbine generator system–an engineering solution. In: 10th World congress on computational mechanics, pp 8–13Google Scholar
  36. 36.
    Heil M (2004) An efficient solver for the fully coupled solution of large-displacement fluid-structure interaction problems. Comput Methods Appl Mech Eng 193(1–2):1–23MathSciNetMATHCrossRefGoogle Scholar
  37. 37.
    Ahn HT, Kallinderis Y (2006) Strongly coupled flow/structure interactions with a geometrically conservative ALE scheme on general hybrid meshes. J Comput Phys 219(2):671–696MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    Fernández MÁ, Moubachir M (2005) A newton method using exact jacobians for solving fluid-structure coupling. Comput Struct 83(2–3):127–142CrossRefGoogle Scholar
  39. 39.
    Hofman JMA (2003) Control–fluid interaction in air-conditioned aircraft cabins. Comput Methods Appl Mech Eng 192(44–46):4947–4963MATHCrossRefGoogle Scholar
  40. 40.
    Matthies HG, Steindorf J (2002) Partitioned but strongly coupled iterative schemes for nonlinear fluid-structure interaction. Comput Struct 80:1991–1999CrossRefGoogle Scholar
  41. 41.
    Joosten MM, Dettmer WG, Perić D (2009) Analysis of the block gauss-seidel solution procedure for a strongly coupled model problem with reference to fluid-structure interaction. Int J Numer Methods Eng 78(7):757–778MathSciNetMATHCrossRefGoogle Scholar
  42. 42.
    Mahrenholz J, Lumkes J (2010) Analytical coupled modeling and model validation of hydraulic on/off valves. J Dyn Syst Meas Control 132(1):011005CrossRefGoogle Scholar
  43. 43.
    Cervera M, Codina R, Galindo M (1996) On the computational efficiency and implementation of block-iterative algorithms for nonlinear coupled problems. Eng Comput 13(6):4–30MATHCrossRefGoogle Scholar
  44. 44.
    Menck J (2002) An approximate newton-like coupling of subsystems. Zeitschrift fur Angewandte Mathematik und Mechanik 82(2):101–114MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Adams M, Brezina M, Hu J, Tuminaro R (2003) Parallel multigrid smoothing: polynomial versus Gauss–Seidel. J Comput Phys 188(2):593–610MathSciNetMATHCrossRefGoogle Scholar
  46. 46.
    Yeckel A, Lun L, Derby JJ (2009) An approximate block newton method for coupled iterations of nonlinear solvers: theory and conjugate heat transfer applications. J Comput Phys 228(23):8566–8588MathSciNetMATHCrossRefGoogle Scholar
  47. 47.
    Farajpour I, Atamturktur S (2013) Error and uncertainty analysis of inexact and imprecise computer models. J Comput Civ Eng 27(4):407–418CrossRefGoogle Scholar
  48. 48.
    von Scheven M, Ramm E (2011) Strong coupling schemes for interaction of thin-walled structures and incompressible flows. Int J Numer Methods Eng 87(1–5):214–231MATHCrossRefGoogle Scholar
  49. 49.
    Küttler U, Wall WA (2008) Fixed-point fluid-structure interaction solvers with dynamic relaxation. Comput Mech 43(1):61–72MATHCrossRefGoogle Scholar
  50. 50.
    Küttler U, Wall WA (2009) Vector extrapolation for strong coupling fluid-structure interaction solvers. J Appl Mech 76(2):021205CrossRefGoogle Scholar
  51. 51.
    Wall WA, Genkinger S, Ramm E (2007) A strong coupling partitioned approach for fluid-structure interaction with free surfaces. Comput Fluids 36(1):169–183MATHCrossRefGoogle Scholar
  52. 52.
    Derby JJ, Lun L, Yeckel A (2007) Strategies for the coupling of global and local crystal growth models. J Cryst Growth 303(1):114–123CrossRefGoogle Scholar
  53. 53.
    Evans DJ (1984) Parallel SOR iterative methods. Parallel Comput 1(1):3–18MATHCrossRefGoogle Scholar
  54. 54.
    Zohdi TI (2008) On the computation of the coupled thermo-electromagnetic response of continua with particulate microstructure. Int J Numer Methods Eng 76(8):1250–1279MathSciNetMATHCrossRefGoogle Scholar
  55. 55.
    Weiβ C, Karl W, Kowarschik M, and Rüde U (1999) Memory characteristics of iterative methods. In: Proceedings of the 1999 ACM/IEEE conference on supercomputing, pp 31Google Scholar
  56. 56.
    Kowarschik M, Rüde U, Weiss C, Karl W (2000) Cache-aware multigrid methods for solving Poisson’s equation in two dimensions. Computing 64(4):381–399MathSciNetMATHCrossRefGoogle Scholar
  57. 57.
    Farajpour I, Atamturktur S (2012) Optimization-based strong coupling procedure for partitioned analysis. J Comput Civ Eng 26(5):648–660CrossRefGoogle Scholar
  58. 58.
    Gunzburger MD, Lee HK (2000) An optimization-based domain decomposition method for the Navier–Stokes equations. SIAM J Numer Anal 37(5):1455–1480MathSciNetMATHCrossRefGoogle Scholar
  59. 59.
    Ben-Israel A (1966) A Newton–Raphson method for the solution of systems of equations. J Math Anal Appl 15:243–252MathSciNetMATHCrossRefGoogle Scholar
  60. 60.
    Matthies HG, Steindorf J (2003) Partitioned strong coupling algorithms for fluid-structure interaction. Comput Struct 81(8–11):805–812CrossRefGoogle Scholar
  61. 61.
    Hammond GE, Valocchi AJ, Lichtner PC (2005) Application of Jacobian-free Newton–Krylov with physics-based preconditioning to biogeochemical transport. Adv Water Resour 28(4):359–376CrossRefGoogle Scholar
  62. 62.
    Erban R, Kevrekidis IG, Adalsteinsson D, Elston TC (2006) Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation. J Chem Phys 124(8):084106CrossRefGoogle Scholar
  63. 63.
    Brown PN, Saad Y (1990) Hybrid Krylov methods for nonlinear systems of equations. SIAM J Sci Stat Comput 11(3):450–481MathSciNetMATHCrossRefGoogle Scholar
  64. 64.
    Jones JE, Woodward CS (2001) Newton–Kyrlov-multigrid solvers for large-scale, highly heterogeneous, variably saturated flow problems. Adv Water Resour 24(7):763–774CrossRefGoogle Scholar
  65. 65.
    Rider WJ, Knoll DA, Olson GL (1999) A multigrid Newton–Krylov method for multimaterial equilibrium radiation diffusion. J Comput Phys 152(1):164–191MATHCrossRefGoogle Scholar
  66. 66.
    Knoll DA, Keyes DE (2004) Jacobian-free Newton–Krylov methods: a survey of approaches and applications. J Comput Phys 193(2):357–397MathSciNetMATHCrossRefGoogle Scholar
  67. 67.
    Roache PJ (1994) Perspective: a method for uniform reporting of grid refinement studies. J Fluids Eng 116:405–413CrossRefGoogle Scholar
  68. 68.
    Larson J (2005) The model coupling toolkit: a new Fortran90 toolkit for building multiphysics parallel coupled models. Int J High Perform Comput Appl 19(3):277–292CrossRefGoogle Scholar
  69. 69.
    Rangavajhala S, Sura VS, Hombal VK, Mahadevan S (2011) Discretization error estimation in multidisciplinary simulations. AIAA J 49(12):2673–2683CrossRefGoogle Scholar
  70. 70.
    Jaiman RK, Jiao X, Geubelle PH, Loth E (2005) Assessment of conservative load transfer for fluid–solid interface with non-matching meshes. Int J Numer Methods Eng 64(15):2014–2038MATHCrossRefGoogle Scholar
  71. 71.
    de Boer A, van Zuijlen AH, Bijl H (2007) Review of coupling methods for non-matching meshes. Comput Methods Appl Mech Eng 196(8):1515–1525MathSciNetMATHCrossRefGoogle Scholar
  72. 72.
    Thévenaz P, Blu T, Unser M (2000) Interpolation revisited (medical images application). IEEE Trans Med Imaging 19(7):739–758CrossRefGoogle Scholar
  73. 73.
    Farhat C, Lesoinne M, LeTallec P (1998) Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput Methods Appl Mech Eng 157:95–114MathSciNetMATHCrossRefGoogle Scholar
  74. 74.
    Cebral JR, Lohner R (1997) Conservative load projection and tracking for fluid-structure problems. AIAA J 35(4):687–692MATHCrossRefGoogle Scholar
  75. 75.
    Jiao X, Heath MT (2004) Common-refinement-based data transfer between non-matching meshes in multiphysics simulations. Int J Numer Methods Eng 61(14):2402–2427MathSciNetMATHCrossRefGoogle Scholar
  76. 76.
    Tan E, Choi E, Thoutireddy P, Gurnis M, Aivazis M (2006) Geoframework: coupling multiple models of mantle convection within a computational framework: Geoframework-mantle convection models. Geochem Geophys Geosyst 7:6CrossRefGoogle Scholar
  77. 77.
    Baker TJ (1997) Mesh adaptation strategies for problems in fluid dynamics. Finite Elem Anal Des 25:243–273MathSciNetMATHCrossRefGoogle Scholar
  78. 78.
    van Loon R, Anderson PD, van de Vosse FN, Sherwin SJ (2007) Comparison of various fluid-structure interaction methods for deformable bodies. Comput Struct 85(11–14):833–843CrossRefGoogle Scholar
  79. 79.
    Johansen H, Colella P (1998) A Cartesian grid embedded boundary method for Poisson’s equation on irregular domains. J Comput Phys 147:60–85MathSciNetMATHCrossRefGoogle Scholar
  80. 80.
    Fu P, Johnson SM, Hao Y, and Carrigan CR (2011) Fully coupled geomechanics and discrete flow network modeling of hydraulic fracturing for geothermal applications. In: The 36th Stanford geothermal workshopGoogle Scholar
  81. 81.
    Zhen F, Chen Z, Zhang J (2000) Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method. IEEE Trans Microw Theory Tech 48(9):1550–1558CrossRefGoogle Scholar
  82. 82.
    Zhang K, Hopperstad OS, Holmedal B, Dumoulin S (2014) A robust and efficient substepping scheme for the explicit numerical integration of a rate-dependent crystal plasticity model: adaptive substepping scheme for rate-dependent crystal plasticity. Int J Numer Methods Eng 99(4):239–262MATHCrossRefGoogle Scholar
  83. 83.
    Zhang Q, Dasgupta A, Haswell P (2004) Partitioned viscoplastic-constitutive properties of the Pb-free Sn3. 9Ag0. 6Cu solder. J Electron Mater 33(11):1338–1349CrossRefGoogle Scholar
  84. 84.
    Berrone S (2009) A local-in-space-timestep approach to a finite element discretization of the heat equation with a posteriori estimates. SIAM J Numer Anal 47(4):3109–3138MathSciNetMATHCrossRefGoogle Scholar
  85. 85.
    Pegon P and Magonette G (2005) Continuous PsD testing with non-linear substructuring: using the operator splitting technique to avoid iterative procedures. Joint Research Centre, ELSE, Ispra, Italy, Technical Report SPI.05.30Google Scholar
  86. 86.
    Bonelli A, Bursi OS, He L, Magonette G, Pegon P (2008) Convergence analysis of a parallel interfield method for heterogeneous simulations with dynamic substructuring. Int J Numer Methods Eng 75(7):800–825MATHCrossRefGoogle Scholar
  87. 87.
    Döscher R, Willén U, Jones C, Rutgersson A, Meier HEM, Hansson U, Graham LP (2002) The development of the regional coupled ocean-atmosphere model RCAO. Boreal Environ Res 7(3):183–192Google Scholar
  88. 88.
    Kumar M, Ghoniem AF (2012) Multiphysics simulations of entrained flow gasification. Part I: Validating the nonreacting flow solver and the particle turbulent dispersion model. Energy Fuels 26(1):451–463CrossRefGoogle Scholar
  89. 89.
    Farajpour I, Atamturktur S (2014) Partitioned analysis of coupled numerical models considering imprecise parameters and inexact models. J Comput Civ Eng 28(1):145–155CrossRefGoogle Scholar
  90. 90.
    Hemez FM and Doebling SW (2001) Uncertainty, validation of computer models and the myth of numerical predictability. In: 2nd European COST-F3 conference on structural system identification, Kassel, GermanyGoogle Scholar
  91. 91.
    Werker C and Brenner T (2004) Empirical calibration of simulation models. In: Papers on economics and evolutionGoogle Scholar
  92. 92.
    Park B, Qi H (1934) Development and evaluation of a procedure for the calibration of simulation models. Transp Res Rec J Transp Res Board 208–217:2005Google Scholar
  93. 93.
    Higdon D, Gattiker J, Williams B, Rightley M (2007) Computer model calibration using high-dimensional output. American Statistical Association, BostonMATHGoogle Scholar
  94. 94.
    Hemez F, Atamturktur HS, Unal C (2010) Defining predictive maturity for validated numerical simulations. Comput Struct 88(7–8):497–505CrossRefGoogle Scholar
  95. 95.
    Atamturktur S, Hemez F, Williams B, Tome C, Unal C (2011) A forecasting metric for predictive modeling. Comput Struct 89(23–24):2377–2387CrossRefGoogle Scholar
  96. 96.
    Roy CJ, Oberkampf WL (2011) A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing. Comput Methods Appl Mech Eng 200(25):2131–2144MathSciNetMATHCrossRefGoogle Scholar
  97. 97.
    Unal C, Williams B, Hemez F, Atamturktur SH, McClure P (2011) Improved best estimate plus uncertainty methodology, including advanced validation concepts, to license evolving nuclear reactors. Nucl Eng Des 241(5):1813–1833CrossRefGoogle Scholar
  98. 98.
    Atamturktur S, Brown DA (2015) State-aware calibration for inferring systematic bias in computer models of complex systems. NAFEMS World Congress 2015, June 21–24, San Diego, CAGoogle Scholar
  99. 99.
    Rizzi F, Najm HN, Debusschere BJ, Sargsyan K, Salloum M, Adalsteinsson H, Knio OM (2012) Uncertainty quantification in MD simulations. Part I: forward propagation. Multiscale Model Simul 10(4):1428–1459MathSciNetMATHCrossRefGoogle Scholar
  100. 100.
    Liang C, Mahadevan S, Sankararaman S (2015) Stochastic multidisciplinary analysis under epistemic uncertainty. J Mech Des 137(2):021404CrossRefGoogle Scholar
  101. 101.
    Stevens G, Atamturktur S, Lebensohn R, Kaschner G (2014) Experiment-based validation and uncertainty quantification of coupled multi-scale plasticity models. In: Atamturktur HS, Moaveni B, Papadimitriou C, Schoenherr T (eds) Model validation and uncertainty quantification, vol 3. Springer, pp 203–213Google Scholar
  102. 102.
    Liu C, Muraleetharan KK (2012) Coupled hydro-mechanical elastoplastic constitutive model for unsaturated sands and silts. II: integration, calibration, and validation. Int J Geomech 12(3):248–259CrossRefGoogle Scholar
  103. 103.
    Oliver TA, Terejanu G, Simmons CS, Moser RD (2015) Validating predictions of unobserved quantities. Comput Methods Appl Mech Eng 283:1310–1335CrossRefGoogle Scholar
  104. 104.
    Lin H, Yim SC (2006) Coupled surge-heave motions of a moored system. I: Model calibration and parametric study. J Eng Mech 132(6):671–680CrossRefGoogle Scholar
  105. 105.
    Konyukhov A, Vielsack P, Schweizerhof K (2008) On coupled models of anisotropic contact surfaces and their experimental validation. Wear 264(7–8):579–588CrossRefGoogle Scholar
  106. 106.
    Avramova MN, Ivanov KN (2010) Verification, validation and uncertainty quantification in multi-physics modeling for nuclear reactor design and safety analysis. Prog Nucl Energy 52(7):601–614CrossRefGoogle Scholar
  107. 107.
    Kumar M, Ghoniem AF (2012) Multiphysics simulations of entrained flow gasification. Part II: Constructing and validating the overall model. Energy Fuels 26(1):464–479CrossRefGoogle Scholar
  108. 108.
    Korzekwa DA (2009) Truchas—a multi-physics tool for casting simulation. Int J Cast Met Res 22(1–4):187–191CrossRefGoogle Scholar
  109. 109.
    Tawhai MH, Bates JHT (2011) Multi-scale lung modeling. J Appl Physiol 110(5):1466–1472CrossRefGoogle Scholar
  110. 110.
    Thompson DE, McAuley KB, McLellan PJ (2010) Design of optimal sequential experiments to improve model predictions from a polyethylene molecular weight distribution model. Macromol React Eng 4(1):73–85CrossRefGoogle Scholar
  111. 111.
    Kennard RW, Stone LA (1969) Computer aided design of experiments. Technometrics 11(1):137MATHCrossRefGoogle Scholar
  112. 112.
    Federov VV, Hackl P (1997) Model-oriented design of experiments 125. Springer Science & Business Media, BerlinCrossRefGoogle Scholar
  113. 113.
    Li G, Aute V, Azarm S (2010) An accumulative error based adaptive design of experiments for offline metamodeling. Struct Multidiscip Optim 40(1–6):137–155CrossRefGoogle Scholar
  114. 114.
    Prabhu S, Atamturktur S (2013) Selection of optimal sensor locations based on modified effective independence method: case study on a gothic revival cathedral. J Archit Eng 19(4):288–301CrossRefGoogle Scholar
  115. 115.
    Williams BJ, Loeppky JL, Moore LM, Macklem MS (2011) Batch sequential design to achieve predictive maturity with calibrated computer models. Reliab Eng Syst Saf 96(9):1208–1219CrossRefGoogle Scholar
  116. 116.
    Atamturktur S, Williams B, Egeberg M, Unal C (2013) Batch sequential design of optimal experiments for improved predictive maturity in physics-based modeling. Struct Multidisc Optim 48(3):549–569CrossRefGoogle Scholar
  117. 117.
    Atamturktur S, Egeberg MC, Hemez FM, Stevens GN (2015) Defining coverage of an operational domain using a modified nearest-neighbor metric. Mech Syst Signal Process 50–51:349–361CrossRefGoogle Scholar
  118. 118.
    Stull CJ, Hemez FM, Williams BJ, Unal C, and Rogers ML (2011) An improved description of predictive maturity for verification and validation activities. Los Alamos National Laboratory, Los Alamos, NM, LA-UR-11-05659Google Scholar
  119. 119.
    Alvin KF and Reese GM (2000) A plan for structural dynamics code and model verification and validation. In: Proceedings of the 18th international modal analysis conference, San Antonio, TX, pp 342–348Google Scholar
  120. 120.
    Vlachos DG, Mhadeshwar AB, Kaisare NS (2006) Hierarchical multiscale model-based design of experiments, catalysts, and reactors for fuel processing. Comput Chem Eng 30(10–12):1712–1724CrossRefGoogle Scholar
  121. 121.
    Sankararaman S, McLemore K, Mahadevan S, Bradford SC, Peterson LD (2013) Test resource allocation in hierarchical systems using Bayesian networks. AIAA J 51(3):537–550CrossRefGoogle Scholar
  122. 122.
    Tomlin AS, Ziehn T (2011) Use of global sensitivity methods for the analysis, evaluation and improvement of complex modelling systems. In: Gorban AN, Roose D (eds) Coping with complexity: model reduction and data analysis 75. Springer, BerlinGoogle Scholar
  123. 123.
    Liu Z, Atamturktur S, Juang CH (2014) Reliability based multi-objective robust design optimization of steel moment resisting frame considering spatial variability of connection parameters. Eng Struct 76:393–403CrossRefGoogle Scholar
  124. 124.
    Salt JD (1993) Simulation should be easy and fun! In: Proceedings of the 25th conference on Winter simulation, pp 1–5Google Scholar
  125. 125.
    Law AM and McComas MG (1991) Secrets of successful simulation studies. In: Proceedings of the 23rd conference on winter simulation, pp 21–27Google Scholar
  126. 126.
    Hegenderfer J, Atamturktur S (2013) Prioritization of code development efforts in partitioned analysis. Comput Aided Civ Infrastruct Eng 28(4):289–306CrossRefGoogle Scholar
  127. 127.
    Atamturktur S, Farajpour I (2015) Resource allocation for code development in partitioned models. Eng Comput 32(7):1981–2004CrossRefGoogle Scholar
  128. 128.
    Brooks RJ, Tobias AM (1996) Choosing the best model: level of detail, complexity, and model performance. Math Comput Model 24(4):1–14MATHCrossRefGoogle Scholar

Copyright information

© CIMNE, Barcelona, Spain 2016

Authors and Affiliations

  1. 1.Glenn Department of Civil EngineeringClemson UniversityClemsonUSA

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