BibTeX
@ARTICLE{
         Bischof2003EIS,
       author = "C. H. Bischof and H. M. B{\"u}cker and P.T. Wu",
       title = "Exploiting Intermediate Sparsity in Computing Derivatives for a Leapfrog Scheme",
       journal = "Computational Optimization and Applications",
       volume = "24",
       number = "1",
       pages = "117--133",
       doi = "10.1023/A:1021858217693",
       abstract = "The leapfrog scheme is a commonly used second-order method for solving differential
         equations. If~$Z(t)$ denotes the state of a system at a particular time step~$t$, this integration
         scheme computes the state at the next time step as~$Z({t+1}) = H(Z(t), Z({t-1}), W)$, where $H$ is
         the nonlinear timestepping operator and $W$ are parameters that are not time-dependent. In this
         note, we show how the associativity of the chain rule of differential calculus can be used to expose
         and exploit intermediate derivative sparsity arising from the typical localized nature of the
         operator~$H$. We construct a computational harness that capitalizes on this structure while
         employing automatic differentiation tools to automatically generate the derivative code
         corresponding to the evaluation of one time step. Experimental results with a 2-D shallow water
         equations model on IBM~RS/6000 and Sun SPARCstations illustrate these issues.",
       ad_area = "Meteorology",
       ad_tools = "ADIFOR",
       year = "2003"
}