Sparse interpolatory reduced-order models for simulation of light-induced molecular transformations

References

• U. M. Ascher and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential Algebraic Equations, SIAM, Philadelphia, 1998.
   Google Scholar
• V. Barthelmann, E. Novak, and K. Ritter, High dimensional polynomial interpolation on sparse grids, Adv. Comput. Math. 12 (2000), pp. 273–288. doi: 10.1023/A:1018977404843
   Web of Science ®Google Scholar
• D. Bonchev, Chemical Group Theory: Techniques and Applications, Taylor and Francis, New York, 1995.
   Google Scholar
• C. G. Broyden, A new double-rank minimization algorithm, AMS Notices 16 (1969), p. 670
   Web of Science ®Google Scholar
• A. Byhkovski and D. Woolard, Physics and modeling of DNA-derivative architectures for long-wavelength bio-sensing, Proceedings of CMOS Emerging Technologies, Whistler, BC, Canada, 2011.
   Google Scholar
• J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia, 1996. Classics in Applied Mathematics Vol. 16
   Google Scholar
• R. Fletcher, A new approach to variable metric methods, Comput. J. 13 (1970), pp. 317–322. doi: 10.1093/comjnl/13.3.317
   Web of Science ®Google Scholar
• M. J. Frisch, A. Frisch, F. R. Clemente, and G. W. Trucks, Gaussian 09 User's Reference, Gaussian Inc., Wallingford, CT, 2009.
   Google Scholar
• D. Goldfarb, A family of variable metric methods derived by variational means, Math. Comp. 24 (1970), pp. 23–26. doi: 10.1090/S0025-5718-1970-0258249-6
   Web of Science ®Google Scholar
• C. T. Kelley, Iterative Methods for Optimization, Frontiers in Applied Mathematics Vol. 18, SIAM, Philadelphia, 1999.
   Google Scholar
• Y. Luo, B. Gelmont, and D. Woolard, Bio-molecular devices for terahertz frequency sensing, in Molecular and Nano Electronics: Analysis, Design, and Simulation, J. Seminario, ed., Elsevier, New York, 2006, pp. 55–81. Available at http://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=0444527257.
   Google Scholar
• D. Mokrauer, C. T. Kelley, and A. Bykhovski, Parallel computation of surrogate models for potential energy surfaces, 2010 International Symposium on Distributed Computing and Applications to Business, Engineering and Science, Q. Qingping and G. Yucheng, eds., IEEE, Los Alamitos, CA, pp. 14, 2010.
   Google Scholar
• D. Mokrauer, C. T. Kelley, and A. Bykhovski, Efficient parallel computation of molecular potential surfaces for the study of light-induced transition dynamics in multiple coordinates, IEEE Trans. Nanotechnol. 10 (2011), pp. 70–74. doi: 10.1109/TNANO.2010.2058862
   Web of Science ®Google Scholar
• D. Mokrauer, C. T. Kelley, and A. Bykhovski, Simulations of light-induced molecular transformations in multiple dimensions with incremental sparse surrogates, J. Algorithms Comput. Technol. Forthcoming.
   Google Scholar
• E. Novak and K. Ritter, High dimensional integration of smooth functions over cubes, Numer. Math. 75 (1996), pp. 79–97. doi: 10.1007/s002110050231
   Web of Science ®Google Scholar
• E. Novak and K. Ritter, Simple cubature formulas with high polynomial exactness, Constr. Approx. 15 (1999), pp. 499–522. doi: 10.1007/s003659900119
   Web of Science ®Google Scholar
• I. J. Palmer, I. N. Ragazos, F. Bemardi, M. Olivucci, and M. A. Robb, An mc-scf study of the s1 and s2 photochemical reactions of benzene, J. Am. Chem. Soc. 115 (1993), pp. 673–682. doi: 10.1021/ja00055a042
   Web of Science ®Google Scholar
• L. F. Shampine, Numerical Solution of Ordinary Differential Equations, Chapman & Hall, New York, 1994.
   Google Scholar
• D. F. Shanno, Conditioning of quasi-Newton methods for function minimization, Math. Comp. 24 (1970), pp. 647–657. doi: 10.1090/S0025-5718-1970-0274029-X
   Web of Science ®Google Scholar
• A. Simeonov, M. Matsushita, E. A. Juban, E. H.Z. Thompson, T. Z. Hoffman, A. E.B. IV, M. J. Taylor, P. Wirsching, W. Rettig, J. K. McCusker, R. C. Stevens, D. P. Millar, P. G. Schultz, R. A. Lerner, and K. D. Janda, Blue-fluorescent antibodies, Science 290 (2000), pp. 307–313. doi: 10.1126/science.290.5490.307
   PubMed Web of Science ®Google Scholar
• S. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Math. Dokl. 4 (1963), pp. 240–243.
   Google Scholar
• C. Van Caillie and R. D. Amos, Geometric derivatives of density functional theory excitation energies using gradient-corrected functionals, Chem. Phys. Letters 317 (2000), pp. 159–164. doi: 10.1016/S0009-2614(99)01346-9
   Web of Science ®Google Scholar
• G. Wasilkowski and H. Wozniakowski, Explicit cost bounds of algorithms for multivariate tensor product problems, J. Complexity 11 (1995), pp. 1–56. doi: 10.1006/jcom.1995.1001
   Web of Science ®Google Scholar