Optimized time-space domain staggered-grid finite-difference methods based on new finite-difference stencils

Abstract

Two staggered-grid finite-difference (SGFD) methods with fourthand sixth-order accuracy in time have been developed recently based on two new SGFD stencils. The SGFD coefficients are determined by Taylor-series expansion (TE), which is accurate only nearby zero wavenumber. We adopt the new two SGFD stencils and optimize the SGFD coefficients by minimizing the errors between the wavenumber responses of the SGFD operators and the first-order k (wavenumber)-space operator in a least-squares (LS) sense. We solve the LS problems by performing weighted pseudo-inverse of nonsquare matrices to obtain the SGFD coefficients, and to yield two LS based SGFD methods. Dispersion analysis and numerical examples demonstrate that our LS based SGFD methods can preserve the original fourthand sixth-order temporal accuracy and achieve higher spatial accuracy than the existing TE based time-space domain SGFD methods.