# SAMG SOLVER

### Efficient Linear Solving of Groundwater Simulations in GMS

Application:n/a
Method:n/a
Model Type:3D
Developer:Fraunhofer Gesellshaft

Why SAMG Solver with GMS?
GMS provides a custom interface to the SAMG Solver utility offering a simple way to set model parameters and a graphical user interface to run the model and visualize the results. Gather background data from a variety of sources from GIS to CAD and access online data from numerous databases of maps, images, and elevation data. GMS allows you to interact with models in true 3D taking advantage of optimized OpenGL graphics and to create photo-realistic renderings and animations for PowerPoint, print, and web presentations.

SAMG Solver Description:
GMS now has the support for the SAMG mulitgrid solver for MODFLOW and MODFLOW-USG! A Parallel Option is available for quicker solving as well as a less expensive Serial option. SAMG is the most efficient solver available for use with MODFLOW. Depending on the application and problem size, the computational cost can be reduced by one to two magnitudes.

SAMG (Algebraic Multigrid Methods for Systems) developed by the Fraunhofer Institute for Algorithms and Scientific Computing (FhG-SCAI), is a library of subroutines for the highly efficient solution of large linear systems of equations with sparse matrices. Such systems of equations form the numerical basis of most simulation software packages. Usually, the numerical solution of these linear systems of equations needs most of the computational expense of the whole simulation compared to classical methods (e.g., the ILU-preconditioned conjugate gradient method), SAMG has the advantage of being almost unconditionally numerically scalable. This means that the computational cost using SAMG depends linearly on the number of unknowns.

The algebraic multigrid solution was developed by generalizing the method of "geometric" multigrid for the solution of partial differential equations in such a way, that it can be applied directly to linear systems of equations without using geometrical information. For this reason, algebraic multigrid methods are particularly suitable for the solution of differential equations resulting from unstructured two or three dimensional problems, and also for the solution of structurally similar problems. The solution to the MODFLOW system of equations is an excellent application for the SAMG model.