Jacob B. Schroder

Parallel Time Integration with Multigrid

We consider optimal-scaling multigrid solvers for the linear systems that arise from the discretization of problems with evolutionary behavior. Typically, solution algorithms for evolution equations are based on a time-marching approach, solving sequentially for one time step after the other. Parallelism in these traditional time-integration techniques is limited to spatial parallelism. However, current trends in computer architectures are leading toward systems with more, but not faster, processors. Therefore, faster compute speeds must come from greater parallelism. One approach to achieving parallelism in time is with multigrid, but extending classical multigrid methods for elliptic operators to this setting is not straightforward. In this paper, we present a nonintrusive, optimal-scaling time-parallel method based on multigrid reduction (MGR). We demonstrate optimality of our multigrid-reduction-in-time algorithm (MGRIT) for solving diffusion equations in two and three space dimensions in numerical ex...

A General Interpolation Strategy for Algebraic Multigrid Using Energy Minimization

Algebraic multigrid methods solve sparse linear systems

A new perspective on strength measures in algebraic multigrid

Ax=b

Smoothed aggregation for Helmholtz problems

by automatic construction of a multilevel hierarchy. This hierarchy is defined by grid transfer operators that must accurately capture algebraically smooth error relative to the relaxation method. We propose a methodology to improve grid transfers through energy minimization. The proposed strategy is applicable to Hermitian, non-Hermitian, definite, and indefinite problems. Each column of the grid transfer operator

Smoothed aggregation multigrid solvers for high-order discontinuous Galerkin methods for elliptic problems

P

Smoothed aggregation solvers for anisotropic diffusion

is minimized in an energy-based norm while enforcing two types of constraints: a defined sparsity pattern and preservation of specified modes in the range of

Non-Galerkin Coarse Grids for Algebraic Multigrid

P

Multigrid Reduction in Time for Nonlinear Parabolic Problems: A Case Study

. A Krylov-based strategy is used to minimize energy, which is equivalent to solving

A Root-Node--Based Algebraic Multigrid Method

A P_j = \boldsymbol{0}

Multigrid methods with space–time concurrency

for each column