Sharif Digital Repository

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. © 2006 Elsevier Inc.... 

A new group explicit method for solution of diffusion equation is presented. This method is based on domain decomposition concept and using asymmetric Saul'yev schemes for internal nodes of each sub-domain and alternating group explicit method for sub-domain's interfacial nodes. This new method has several advantages such as: good parallelism, unconditional stability, fully explicit nature and better accuracy than original Saul'yev schemes. The details of implementation and proving stability are briefly discussed. Numerical experiments on stability and accuracy are also presented. © 2006 Elsevier Inc. All rights reserved