Towards efficient backward-in-time adjoint computations using data compression techniques

摘要: Abstract In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, state-of-the-practice is to use adjoint approaches which require solution backward-in-time problem defined by linearization forward problem. One major obstacles in practical application these need store, or recompute, define and evaluate representation. This study considers data compression techniques approximate solutions employed integration. The development derives an representation that accounts difference between standard-approach compressed approximation solution. algorithmically similar standard only requires computation quantity interest data-compressed reconstructed (i.e. scalar quantities can be evaluated as integrated). approach then compared with existing techniques, such checkpointing time-averaged adjoints. Finally, we provide numerical results indicating potential efficiency our on transient diffusion–reaction equation Navier–Stokes equations. These demonstrate memory ratios up 450 × while maintaining reasonable accuracy error-estimates.