Related papers: Optimizing Staggered Multigrid for Exascale perfor…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
We show that using the multisplitting algorithm as a preconditioner for conjugate gradient inversion of the domain wall fermion Dirac operator could effectively reduce the inter-node communication cost, at the expense of performing more…
Complete spectra of the staggered Dirac operator $\Dirac$ are determined in quenched four-dimensional $SU(2)$ gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An…
In this work we exploit agglomeration based $h$-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature $h$-coarsened mesh…
In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by a fractional diffusion equation. Multigrid methods within the all-at-once approach to solve the first order-order…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
Bundle adjustment is an important global optimization step in many structure from motion pipelines. Performance is dependent on the speed of the linear solver used to compute steps towards the optimum. For large problems, the current state…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
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…
For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…
We describe our implementation of a multigrid solver for Wilson-clover fermions, which increases parallelism by solving for multiple right-hand sides (MRHS) simultaneously. The solver is based on Grid and thus runs on all computing…
Numerical simulations of quantum chromodynamics (QCD) on a lattice require the frequent solution of linear systems of equations with large, sparse and typically ill-conditioned matrices. Algebraic multigrid methods are meanwhile the…
In this work we construct multigrid preconditioners to accelerate the solution process of a linear-quadratic optimal control problem constrained by the Stokes system. The first order optimality conditions of the control problem form a…
At physical light quark masses, efficient linear solvers are crucial for carrying out the millions of inversions of the Dirac matrix required for obtaining high statistics in quark correlation functions. Adaptive algebraic multi-grid…
Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an…
Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite…
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…
Computing at the exascale level is expected to be affected by a significantly higher rate of faults, due to increased component counts as well as power considerations. Therefore, current day numerical algorithms need to be reexamined as to…
We investigate and clarify the role of topology and the issues surrounding the epsilon regime for staggered quarks. We study unimproved and improved staggered quark Dirac operators on quenched lattice QCD gluon backgrounds generated using a…