A wavelet approach to adjoint state sensitivity computation for steady state differential equations

The computation of the sensitivity matrix is the most time-consuming part of any parameter estimation algorithm that requires sensitivity coefficients. An efficient wavelet approach to adjoint sensitivity analysis is proposed to reduce the computational cost of obtaining sensitivity coefficients. The method exploits a wavelet reduction of the data space to reduce the size of the linear system encountered in steady state adjoint equations. In this regard, wavelet transform is used as a data compression tool. Numerical examples applied to spatial data are used to verify and show the effectiveness of the method.