Hi all,
In point (Gauss-Seidel) method of iterative solution, simple algorithm is applied at each point where the function value has to be determined in successive manner, which essentially means that all point methods are a explicit methods. In fact Gauss Seidel method is explicit.
So, How point explicit G-S works ?
whereas in line method of iteration (called implicit method), a row of many grids are solved simultaneously with the known values (existing values) from neighbouring grids. So this method becomes implicit method?
I need a clarification on this form an numerical simulation expert. Please someone answer.
Waiting for a reply.
Thanks
Vivek
In some sense (as e.g. in ode-solution, where a method which requires a linear or nonlinear system solve for one time step is considered as (semi)implicit) the block method is implicit, but in fact, considering a ''small'' linear system solve as trivial, both methods have the same quality:
for i=1,...,n
solve a_{ii}x_{i,new} = b_i
- sum_{j=1 to i-1} a_{i,j} x_{j,new} - sum_{j=i+1 to n}a_{i,j}x_{j,old}
with x_i, a_{ij} scalar this is the pointwise method and the ''solve'' trivial but you may read this also with x_i of dimension m and the a_{i,j} m*m matrices and hence the whole system of dimension m*n, requiring an exact linear system solve.
In this context the block method does not help much with speed, but in the context of multigrid there are situations where you must use the block method.
- Badges
- Science topic