Learn More
This paper surveys the techniques that are necessary for constructing compu-tationally efficient parallel multigrid solvers. Both geometric and algebraic methods are considered. We first cover the sources of parallelism, including traditional spatial partitioning and more novel additive multilevel methods. We then cover the paral-lelism issues that must be(More)
Algebraic multigrid (AMG) is a very efficient iterative solver and preconditioner for large unstructured linear systems. Traditional coarsening schemes for AMG can, however, lead to computational complexity growth as problem size increases, resulting in increased memory use and execution time, and diminished scalability. Two new parallel AMG coarsening(More)
The hypre software library provides high performance preconditioners and solvers for the solution of large, sparse linear systems on massively parallel computers. One of its attractive features is the provision of conceptual interfaces. These interfaces give application users a more natural means for describing their linear systems, and provide access to(More)
Now that the performance of individual cores has plateaued, future supercomputers will depend upon increasing parallelism for performance. Processor counts are now in the hundreds of thousands for the largest machines and will soon be in the millions. There is an urgent need to model application performance at these scales and to understand what changes(More)
Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers, however its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Additive AMG variants provide increased parallelism as well as decreased numbers of messages per(More)
The software library <i>hypre</i> provides high-performance preconditioners and solvers for the solution of large, sparse linear systems on massively parallel computers as well as conceptual interfaces that allow users to access the library in the way they naturally think about their problems. These interfaces include a stencil-based structured interface(More)