相关论文: Idealized Multigrid Algorithm for Staggered Fermio…
Multigrid (MG) methods for the computation of propagators of staggered fermions in non-Abelian gauge fields are discussed. MG could work in principle in arbitrarily disordered systems. The practical variational MG methods tested so far with…
Practical modifications of deterministic multigrid and conventional relaxation algorithms are discussed. New parameters need not be tuned but are determined by the algorithms themselves. One modification can be thought of as ``updating on a…
A Dirac choice for the averaging kernel $C$ is implemented numerically. This improved kernel will be needed in gauge covariant multigrid computations for propagators of staggered fermions. Results for $C$ and the variational coarse grid…
NOTE: this is a shortened version of the abstract of the paper. Multigrid methods for propagators in gauge fields are investigated. Gauge fields are incorporated in algorithms in a covariant way. This avoids the necessity for gauge fixing…
Adaptive multi-grid methods have proven very successful in dealing with critical slow down for the Wilson-Dirac solver in lattice gauge theory. Multi-grid algorithms developed for Staggered fermions using the K\"ahler-Dirac…
The Iteratively Smoothing Unigrid algorithm (ISU), a new multigrid method for computing propagators in Lattice Gauge Theory, is explained. The main idea is to compute good (i.e.\ smooth) interpolation operators in an iterative way. This…
Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind…
Multigrid methods were invented for the solution of discretized partial differential equations in ordered systems. The slowness of traditional algorithms is overcome by updates on various length scales. In this article we discuss…
An efficient $hp$-multigrid scheme is presented for local discontinuous Galerkin (LDG) discretizations of elliptic problems, formulated around the idea of separately coarsening the underlying discrete gradient and divergence operators. We…
Lattice regularization of chiral fermions is an important development of the theory of elementary particles. Nontheless, brute force computer simulations are very expensive, if not prohibitive. In this letter I exploit the non-interacting…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the…
The parareal algorithm represents an important class of parallel-in-time algorithms for solving evolution equations and has been widely applied in practice. To achieve effective speedup, the choice of the coarse propagator in the algorithm…
Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, two-grid theory plays an important role in motivating…
Achieving an evenly distributed fertilization spread pattern is a complex technical task. A corresponding control algorithm must account for the tractor movement, the settings of the spreader, the prescribed dosage as well as machine…
Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs), but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the…
Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…
Application of multigrid solvers in shifted linear systems is studied. We focus on accelerating the rational approximation needed for simulating single flavor operators. This is particularly useful, in the case of twisted mass fermions for…
I review recent research and advances in algorithms for solvers and gauge generation, with an emphasis on practical algorithms for four dimensional simulations. Particular consideration is given to advances in multigrid solvers, fourier…
Two-grid methods with exact solution of the Galerkin coarse-grid system have been well studied by the multigrid community: an elegant identity has been established to characterize the convergence factor of exact two-grid methods. In…