SAMG (Algebraic Multigrid Methods for Systems) is a library of subroutines for highly efficient solution of large linear systems of equations with sparse matrices. Such systems of equations form the numerical core of most simulation software packages.

SAMG Groundwater simulation | © DHI Wasy

Benefit & value

Compared to classical methods (for example, conjugate gradient methods preconditioned by ILU), SAMG has the great advantage of being largely numerically scalable. This means that the computational effort with SAMG depends only linearly on the number of unknowns. Depending on the application and problem size, the resulting gain in computing time can be one to two orders of magnitude. SAMG can be integrated into an existing simulation package just as easily as a classic process.

  • Optimality principle: The computational effort with SAMG depends only linearly on the number of unknowns
  • Versatile and extensible: SAMG includes all known algorithms of the multigrid technology and further newly developed specializations.
  • High-performance and portable: Highly optimized cores achieve high performance on diverse computer systems.
  • Scalable: SAMG is highly parallel and runs on up to 10000 cores.

Target groups

The SAMG library is of interest to anyone developing or using software tools to perform large-scale numerical simulations. In addition to our solver technology, we also offer analysis and consulting on application problems as well as the adaptation of our software to customer-operated computer systems, especially parallel computers.

Developed by

Fraunhofer SCAI

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SAMG modules

SAMG is grouped around the core package SAMG-Core and offers optional modules that enable the targeted optimized use of SAMG in several specific application areas.

Application areas

  • Fluid Mechanics
  • Structural Mechanics
  • Foundry Technology
  • Oil reservoir simulation
  • Groundwater simulation
  • Hydrothermal ore deposition simulation
  • Process simulation in semiconductor physics
  • Device simulation in semiconductor physics
  • Circuit simulation

Outstanding properties of SAMG

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.

Customer reviews

SAMG has been the key to improving both the robustness and performance of our General Purpose Research Simulator – GPRS. With SAMG as the workhorse linear solver, we now routinely solve problems that were simply beyond our reach. SAMG is indispensable for reservoir flow simulation of large-scale, highly heterogeneous, unstructured reservoir models.

Prof. Hamdi Tchelepi, Petroleum Engineering Department, Stanford University

For our applications, SAMG is the fastest solver in the world. SAMG has enabled us to tackle large problems faster than ever before and attempt larger problems that were ever possible – for the first time we can make multi-million cell simulations routine where we properly capture the reservoir structure.

Prof. Martin Blunt, Petroleum Engineering, Imperial College

SAMG is in a world of its own when it comes to linear solvers. It is robust, fast, and easy to implement on any platform, and has given our company a clear competitive edge. It has been a reliable work requiring little or no maintenance, allowing us to concentrate on our core business. Small or big, simple or complex, sparse or full, structured or unstructured – SAMG will solve it.

Marco Thiele, Co-Founder & President StreamSim Technologies