170 research outputs found
Adaptive multigrid algorithm for the lattice Wilson-Dirac operator
We present an adaptive multigrid solver for application to the non-Hermitian
Wilson-Dirac system of QCD. The key components leading to the success of our
proposed algorithm are the use of an adaptive projection onto coarse grids that
preserves the near null space of the system matrix together with a simplified
form of the correction based on the so-called gamma_5-Hermitian symmetry of the
Dirac operator. We demonstrate that the algorithm nearly eliminates critical
slowing down in the chiral limit and that it has weak dependence on the lattice
volume
Final Report on Subcontract B591217: Multigrid Methods for Systems of PDEs
Progress is summarized in the following areas of study: (1) Compatible relaxation; (2) Improving aggregation-based MG solver performance - variable cycle; (3) First Order System Least Squares (FOSLS) for LQCD; (4) Auxiliary space preconditioners; (5) Bootstrap algebraic multigrid; and (6) Practical applications of AMG and fast auxiliary space preconditioners
First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow
This paper develops a first-order system least-squares (FOSLS) formulation
for equations of two-phase flow. The main goal is to show that this
discretization, along with numerical techniques such as nested iteration,
algebraic multigrid, and adaptive local refinement, can be used to solve these
types of complex fluid flow problems. In addition, from an energetic
variational approach, it can be shown that an important quantity to preserve in
a given simulation is the energy law. We discuss the energy law and inherent
structure for two-phase flow using the Allen-Cahn interface model and indicate
how it is related to other complex fluid models, such as magnetohydrodynamics.
Finally, we show that, using the FOSLS framework, one can still satisfy the
appropriate energy law globally while using well-known numerical techniques.Comment: 22 pages, 8 figures submitted to Journal of Computational Physic
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