===affil2:
Stony Brook University
===firstname:
Cao
===firstname4:

===firstname3:
Xiongfei
===lastname2:
Jiao
===lastname:
Lu
===firstname5:

===affil6:

===lastname3:
Wei
===email:
clu@ams.sunysb.edu
===lastname6:

===affil5:

===otherauths:

===lastname4:

===affil4:

===lastname7:

===affil7:

===firstname7:

===postal:
Dept. of Applied Math. \& Stat., Stony Brook University, Stony Brook,  NY 11794
===firstname6:

===ABSTRACT:
We propose a hybrid geometric+algebraic multigrid method, or HyGA, for weighted residual methods with hierarchical basis functions. We present a unified derivation of restriction and prolongation operators for these methods. Based on this derivation, we propose a hybrid multigrid method HyGA, which combines a high-quality hierarchical mesh generator, a geometric multigrid solver with a multilevel weighted residual formulation, and an algebraic multigrid solver at the coarsest levels. Our method combines the rigor, high accuracy and runtime-and-memory efficiency of geometric multigrid with the robustness and flexibility of algebraic multigrid, and at the same time it is relatively easy to implement. We apply HyGA to weighted-residual finite element methods in both 2-D and 3-D, and present numerical experiments to demonstrate the effectiveness of HyGA compared with both geometric and algebraic multigrid methods.
===affil3:
Stony Brook University
===lastname5:

===affilother:

===title:
HyGA: A Hybrid Geometric+Algebraic Multigrid Solver for Weighted-Residual Methods with Hierarchical Meshes
===firstname2:
Xiangmin