A new parallel Gauss–Seidel method based on alternating group explicit method and domain decomposition method

A new parallel Gauss–Seidel method is presented for solution of system of linear equations related to finite difference discretization of partial differential equations. This method is based on domain decomposition method and local coupling between interfaces of neighbor sub-domains, same as alternating group explicit method. This method is convergent and number of iterations for achieving convergence criteria is near the original Gauss–Seidel method (sometimes better and sometimes worse but difference is very small). The convergence theory is discussed in details. Numerical results are given to justify the convergence and performance of the proposed iterative method.