Algebraic multigrid methods

In CED, a number of different iterative solvers for linear algebraic systems have been applied. Two of the most successful and most widely used methods are conjugate gradient and multigrid methods. The basic idea of the conjugate gradient method is to transform the linear equation system Eq. (38) into a minimization problem... 

Multigrid methods have proven to be powerful algorithms for the solution of linear algebraic equations. They are to be considered as a combination of different techniques allowing specific weaknesses of iterative solvers to be overcome. For this reason, most state-of-the-art commercial CFD solvers offer the multigrid capability. 

CFX software focuses on one approach to solve the governing equations of motion (coupled algebraic multigrid), while the FLUENT product offers several solution approaches (density-segregated- and coupled-pressure-based methods). 

Error vector in multigrid method outline Unit vector with components e, in the i i = 1,2,3) directions Unit vector in the direction of incoming light in LDA Unit vector in the direction of scattered light in LDA Linear algebraic system source vector used in WRM Net force acting on a single particle (N)... 

Multigrid acceleration of the Gauss-Seidel point-iterative method is currently used in many commercial CFD codes to solve the system of algebraic equations resulting from the discretization of the governing equations. For this reason, the basic principles and nomenclature must be known by the users of commercial codes and in particular for researchers that are making their own codes. 

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