A posteriori error estimation for acoustic wave propagation problems
The main purpose of this paper is to review a posteriori error estimators for the simulation of acoustic wave propagation problems by computational methods. Residual-type (explicit and implicit) and recovery-type estimators are presented in detail in the case of the Helmholtz problem. Recent work on goal-oriented error estimation techniques with respect to so-called quantities of interest or output functionals are also accounted for. Fundamental results from a priori error estimation are presented and issues dealing with pollution error at large wave numbers are extensively discussed.
Summary form only given, as follows. A study is presented of precision constraints imposed by a hybrid chip architecture with analog neurons and digital backpropagation calculations. Conversions between the analog and digital domains and weight storage restrictions impose precision limits on both analog and digital calculations. It is shown through simulations that a learning system of this nature can be implemented in spite of limited resolution in the analog circuits and using fixed-point arithmetic to implement the backpropagation algorithm. >