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- W1651645171 abstract "The techniques of automatic differentiation are applied to an example partial differential equation arising from the modeling of unsaturated flow. One common paradigm for the numerical solution to some classes of two-, three-, or higher-dimensional partial differential equations is as follows: Given a PDE and boundary conditions, apply finite difference or finite element approximations on some appropriate (frequently nonuniform) grid, and enforce an approximate solution by solving a nonlinear system F(u)=0 for the residual by Newton's method. The dimension of the nonlinear system F(u)=0 is proportional to the number of grid points. In current algorithms, the Jacobian J required by Newton's method is computed by some combination of hand coding, divided differences, matrix coloring, and partial separability. We present a case study documenting the steps we took in analyzing a code provided by Robey for modeling unsaturated flow in porous media. Our purpose was to compute J by automatic differentiation using ADOL-C, a tool for automatic differentiation using overloaded operators in C++." @default.
- W1651645171 created "2016-06-24" @default.
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- W1651645171 date "1992-01-01" @default.
- W1651645171 modified "2023-09-26" @default.
- W1651645171 title "Automatic differentiation for PDES: Unsaturated flow case study" @default.
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