As seen in the two iterative procedures shown above, iterative methods slowly reach the final solution rather than a large final step, as seen in the backward substitution procedures of the Gauss elimination. Thus, no further discussion is made regarding other iterative solvers. Other iterative procedures apply different and yet conceptually similar approaches. On the other hand, the Gauss–Seidel method can replace each variable as soon as a new update becomes available. As such, all variables need to be stored in memory until the iteration is finished. In terms of computational efficiency, the simultaneous displacement (Jacobi) method is perfectly designed for parallel computing, because none of the variables within each iteration change until the iteration is completed. Although this is true in most problems, some special cases may have opposite results. Convergence processes of using the Gauss–Seidel iterative procedures for the 4-node, 3-element bar problem.Ĭomparing results obtained from the Jacobi and Gauss–Seidel methods for this particular example problem, we observed that the convergence occurs much quicker for the Gauss–Seidel method.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |