In many applications of numerical simulation, for example fluid and structural mechanics, the structures and geometries are discretized by complex grids. In general, the finer such a grid is, the more accurate the simulation, but the larger the systems of equations resulting from the discretization process that have to be solved numerically. With the simulation accuracies required today, the time in which these systems of equations can be solved is a critical variable. Classical numerical solution methods are not able to solve the resulting large systems of equations in an economically justifiable computation time.
SAMG’s solution modules are based on modern hierarchical method approaches (algebraic multigrid methodology, AMG): Instead of working only with the given (extremely large) system of equations, algebraic multigrid methods combine the numerical information in a hierarchy of increasingly coarser systems of equations to solve the given problem faster. The underlying coarsening process is automatic and transparent to the SAMG user.