论文信息 - Applying the Checkpointing Routine treeverse to Discretizations of Burgers’ Equation*

Applying the Checkpointing Routine treeverse to Discretizations of Burgers’ Equation*

We consider the inviscid Burgers’ equation augmented by a control term and its adjoint equation. For several discretization schemes of the inviscid Burgers’ equation the adjoint finite difference methods are derived. Applying these discretization methods and the checkpointing routine treeverse, approximations of the solution of both differential equations are calculated and compared.

Andreas Griewank | Andrea Walther | A. Griewank | A. Walther

[1] Andreas Griewank,et al. Treeverse: an Implementation of Checkpointing for the Reverse or Adjoint Mode of Computational Diierentiation , 1997 .

[2] Peter Eberhard,et al. Automatic differentiation of numerical integration algorithms , 1999, Math. Comput..

[3] K. Tanabe,et al. Mathematical Programming: Recent Developments and Applications. , 1990 .

[4] Andreas Griewank,et al. Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation , 1992 .

[5] C. Hirsch. Computational methods for inviscid and viscous flows , 1990 .

[6] C. Hirsch,et al. Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[7] R. LeVeque. Numerical methods for conservation laws , 1990 .