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Books (** Especially Recommended)
- *** R.C. Smith, Uncertainty Quantification: Theory, Implementation and Applications}, SIAM, Philadelphia, PA 2014.
- ** D.G. Cacuci, Sensitivity and Uncertainty Analysis, Theory, Chapman and Hall/CRC, 2003.
- P. Knupp and K. Salari, Verification of Computer Codes in Computational
Science and Engineering, Chapman and Hall/CRC, Boca Raton, FL, 2003.
- ** W.L. Oberkampf and C.J. Roy, Verification and Validation in Scientific Computing},
Cambridge University Press, 2010.
- P.J. Roache, Verification and Validataion in Computational Science
and Engineering, Hermosa Publishers, Albuquerque, NM, 1998.
- T.J. Santner, B.J. Williams and W.I. Notz, The Design and Analysis of
Computer Experiments, Springer, Berlin, 2003.
- R.C. Smith, Smart Material Systems: Model Development, SIAM, Philadelphia, PA, 2005
(Chapter 7: Rod, Beam, Plate and Shell Models PDF;
Chapter 8: Numerical Techniques PDF;
Appendix C: Legendre Transforms, Calculus of Variations, and Mechanics Principles
PDF;
Bibliography PDF).
Tutorial Slides on MATLAB, Linear Algebra and Numerical Analysis
- "Introduction to MATLAB and Linear Algebra'', PDF
- "Introduction to Numerical Integration, Optimization, Differentiation and Differential Equations'', PDF
MATLAB-R-Python
- D. Hiebeler, "MATLAB/R Reference'', PDF
- "MATLAB-Python-R'', PDF
Papers
- A. Alexanderian, "A brief note on the Karhunen-Loeve expansion'' PDF.
- B.M. Adams, H.T. Banks, M. Davidian, H-D. Kwon, H.T. Tran, S.N. Wynne and E.S. Rosenberg,
"HIV dynamics: Modeling, data analysis, and optimal treatment protocols,''
Journal of Computational and Applied Mathematics,'' 184, pp. 10-49, 2005
PDF.
- C. Andrieu and J. Thomas, "A tutorial on adaptive MCMC,'' Statistics and Computing,
18, pp. 343-373, 2008.
- I. Babuska, F. Nobile and R. Tempone, "Reliability of computational
science,'' in Numerical Methods for Partial Differential Equations,
23(4), pp. 753-784, 2007.
- H.T. Banks, M. Davidian, J.R. Samuels, Jr., and K.L. Sutton,
"An inverse problem statistical methodology summary,'' Workshop
on Biomedical Modeling and Cardiovascular-Respiratory Control,
Schloss Seggau, Leibnitz, Austria, 2007; CRSC Technical Report
CRSC-TR08-01 PDF.
- R.G. Hills and T.G. Trucano, "Statistical validation of engineering and
scientific models: Background, Sandia Report SAND99-1256, 1999.
- W.L. Oberkampf and T.G. Trucano, "Verification and validation in computational
fluid dynamics,'' Progress in Aerospace Sciences, 38, pp. 209-272, 2002.
- W.L. Oberkampf, T.G. Trucano and C. Hirsch, "Verification, validation, and
predictive capability in computational engineering and physics,'' Applied
Mechanics Review, 57(5), pp. 345-384, 2004.
- A. O'Hagan, "Bayesian analysis of computer code outputs: A tutorial,''
Reliability Engineering and System Safety, 91, pp. 1290-1300, 2006.
- M.C. Kennedy and A. O'Hagan, "Bayesian callibration of computer models,''
Journal of the Royal Statistical Society B, 63, pp. 425-464, 2001.
- C.J. Roy, "Review of code and solution verification procedures for
computational simulation,'' Journal of Computational Physics, 205, pp. 131-156,
2005.
- C.J. Roy and A. Raju, "Estimation of discretization errors using
the method of nearby problems,'' AIAA Journal, 45(6), pp. 1232-1243, 2007.
- R.D. Skeel, "Thirteen ways to estimate global error,'' Numerische Mathematik,
48(1), pp. 1-20, 1986.
- P.E. Zadunaisky, "On the estimation of errors propogated in the numerical
integration of ordinary differential equations,'' Numerische Mathematik, 27,
pp. 21-29, 1976.
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