Coarse-grid selection using simulated annealing

Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about underlying problem its discretization, algebraic aims to be less intrusive, requiring origin of system. A key step in is choice coarse/fine partitioning, aiming balance convergence iteration with cost. In work by MacLachlan Saad (2007), a constrained combinatorial optimization used define “best” coarse grid within setting two-level reduction-based method shown NP-complete. Here, we develop new coarsening algorithm based on simulated annealing approximate solutions this problem, which yields improved results over greedy developed previously. We present numerical test problems both structured unstructured meshes, demonstrating ability exploit structure if it available.