Reducing Communication Costs Associated with Parallel Algebraic Multigrid

Algebraic multigrid (AMG) is an iterative method for solving sparse linear systems of equations (Ax̂ = b), such as discretized partial differential equations arising in various fields of science and engineering. AMG is considered an optimal solver, requiring only O(n) operations to solve a system of n unknowns. Standard computers contain neither the memory nor computing power to solve increasingly large systems of equations, resulting in a demand for parallel solvers, in which the system is distributed and solved across a large number of nodes. Current implementations of parallel AMG lack scalability due to high costs of intranodal communication, yielding increasingly long solve times associated with large systems.