Abstract: We present a quadrature method for mixed boundary integral equations of stable problems,which provides high accuracy and less complexity.Discrete equations are solved in parallel according to the coarse mesh partitions.Approximations with high accuracy are obtained by splitting extrapolation methods based on multivariate asymptotic expansion of errors.Besides,a posteriori asymptotic error estimate is derived.

Key words: stable problem, mixed boundary integral equation, quadrature method, splitting extrapolation