Fast higher-order derivative tensors with Rapsodia

References

• Baggeroer , A. B. , Kuperman , W. A. and Mikhalevsky , P. N. 1993 . An overview of matched field methods in ocean acoustics . IEEE J. Ocean. Eng. , 18 : 401 – 424 .
   Web of Science ®Google Scholar
• Bischof , C. H. , Green , L. , Haigler , K. and Knauff , T. Calculation of sensitivity derivatives for aircraft design using automatic differentiation . Proceedings of the 5th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA 94-4261 . pp. 73 – 84 . American Institute of Aeronautics and Astronautics .
   Google Scholar
• Brauner , M. , Briggs , J. and Klar , H. 1989 . Triply-differential cross sections for ionization of hydrogen atoms by electrons and positrons . J. Phys. B: At. Mol. Phys. , 22 : 2265 – 2287 .
   Google Scholar
• Charpentier , I. 2007 . Adjoint modelling experiments on eruptive columns . Geophys. J. Int. , 169 ( 3 ) : 1356 – 1365 .
   Google Scholar
• Charpentier , I. 2008 . Variational coupling of Plinian column models and data: application to El Chichón volcano . J. Volcanol. Geotherm. Res. , 25 : 501 – 508 .
   Google Scholar
• Charpentier , I. and Dal Cappello , C. 2005 . High order cross derivative computation for the differential cross section of double ionization of helium by electron impact . Tech. Rep. , 5546 INRIA
   Google Scholar
• Charpentier , I. and Roux , P. 2004 . Mode and wavenumber inversion in shallow water using an adjoint method . J. Comput. Acoust. , 12 : 521 – 542 .
   Google Scholar
• Charpentier , I. and Utke , J. 2008 . “ Rapsodia: user manual ” . In Tech. Rep , Argonne National Laboratory . Available at http://www.mcs.anl.gov/rapsodia/
   Google Scholar
• Griewank , A. 2000 . “ Evaluating Derivatives. Principles and Techniques of Algorithmic Differentiation ” . In Frontiers in Applied Mathematics , Philadelphia : SIAM . Number 19
   Google Scholar
• Griewank , A. , Juedes , D. and Utke , J. 1996 . ADOL–C, a package for the automatic differentiation of algorithms written in C/C++ . ACM Trans. Math. Software , 22 ( 2 ) : 131 – 167 .
   Web of Science ®Google Scholar
• Griewank , A. , Utke , J. and Walther , A. 2000 . Evaluating higher derivative tensors by forward propagation of univariate Taylor series . Math. Comput. , 69 : 1117 – 1130 .
   Web of Science ®Google Scholar
• Guillaume , Ph. and Masmoudi , M. 1994 . Computation of high order derivatives in optimal shape design . Numer. Math. , 67 ( 2 ) : 231 – 250 .
   Google Scholar
• Jensen , F. , Kuperman , W. , Porter , M. and Schmidt , H. 1994 . Computational Ocean Acoustics , New York : Springer .
   Google Scholar
• Jones , S. and Madison , D. Single and double ionization of atoms by photons, electrons, and ions . AIP Conference Proceedings 697 . pp. 70 – 73 .
   Google Scholar
• Joulakian , B. , Dal Cappello , C. and Brauner , M. 1992 . Double ionization of helium by fast electrons: use of correlated two electron wavefunctions . J. Phys. B: Atomic, Mol. Opt. Phys. , 25 : 2863 – 2871 .
   Google Scholar
• Kheifets , A. , Bray , I. , Berakdar , J. and Dal Cappello , C. 2002 . Comparative theoretical study of (e, 3e) on helium: Coulomb-waves versus close-coupling approach . J. Phys. B: Atomic, Mol. Opt. Phys. , 35 : L15 – L21 .
   Google Scholar
• Kinoshita , T. 1957 . Ground state of the helium . Phys. Rev. , 105 ( 5 ) : 1490 – 1502 .
   Google Scholar
• Portable, Extensible Toolkit for Scientific Computation. Available at http://www.mcs.anl.gov/petsc
   Google Scholar
• Pryce , J. and Reid , J. 1998 . “ AD01, a Fortran 90 code for automatic differentiation ” . Chilton, Oxfordshire, , England : Rutherford Appleton Laboratory . Tech. Rep. RAL-TR-1998-057
   Google Scholar
• Python Programming Language. Available at http://www.python.org/
   Google Scholar
• Rapsodia website – http://www.mcs.anl.gov/rapsodia
   Google Scholar
• Wengert , R. E. 1964 . A simple automatic derivative evaluation program . Comm. ACM , 7 ( 8 ) : 463 – 464 .
   Web of Science ®Google Scholar