Figure 6 Simulation domains with sinuous shapes make it diffi- cult to geometrically coarsen a mesh in a way suitable for multigrid—clustering unstructured tetrahedra does not cre- ate larger tetrahedra. This problem can occur even for regu- lar hexahedral grids on irregularly shaped domains. We cir- cumvent this problem with algebraic multigrid, which uses only the finite volume matrices, and not the geometry, to construct the prolongation and restriction operators. From the prolongation and restriction operators the system matri- ces can be defined by Ay_1 = Ry—1,xAgPhk-1- V-cycle multigrid begins by applying a relaxation oper- ator S(Ax,X,,b,), which returns an approximation solution (usually with poor accuracy) to the system A,x, = by. We use two Gauss-Seidel iterations. Next, it computes the resid- ual of the system, restricts it to the next coarser grid, and recursively solves the coarse problem on the restricted resid- ual. It prolongs the coarse solution and adds it, as a correc- tive term, to the fine solution. Finally, the relaxation operator is applied again. We use full-cycle multigrid, which uses V- cycle multigrid as a subroutine as follows. VCvecr eMintricein(y, h. /L)
Related Figures (7)
