Implementation of Multigrid Methods

Abstract

The Multigrid methods are invented in 1960’s. The solutions for the many physical phenomena will lie in their governing equations. Finding solution to these types of equations will depend on the complexity of the problem. Thus solution for many phenomena was solved only after the invention of the computers. Moreover with the help of the techniques for solving like multigrid methods helped researchers obtain the solution to most of the equations. But the solutions for many equations in physics are not yet available. Multigrid methods are the supporting features to solve those equations by solving them with much lesser numerical effort. Recently solving the physics equations with greater speeds without losing accuracy is the custom that has developed. And more importantly solving Navier Stokes equations has been a challenge for past many years in the field of Fluid dynamics. Thus there is a need not only to solve these equations but also to achieve maximum accuracy along with greater speed while solving computationally.

One more challenge comes when the resources like computational hardware or software is limited to certain memory or methods for greater memory cannot be accommodated which sometimes can be a compulsory for solving certain problems in the CFD field. The Algebraic Multigrid method is also one of the attempts to solve complex equations like Navier stokes equations with certain approximations. The implementation of Algebraic Multigrid on the equations over the partial differential equations which are discretized according to Finite Volume methods makes it easier to solve the problems on the complex domain by using unstructured method data representation.