Related papers: Multiple right hand side multigrid for domain wall…
We develop a parallel-in-time multigrid preconditioner for augmented systems. These saddle-point systems are foundational to numerical optimization. Our preconditioner, when paired with a suitable optimization method, accelerates the…
Results of porting parts of the Lattice Quantum Chromodynamics code to modern FPGA devices are presented. A single-node, double precision implementation of the Conjugate Gradient algorithm is used to invert numerically the Dirac-Wilson…
An idealized multigrid algorithm for the computation of propagators of staggered fermions is investigated. Exemplified in four-dimensional $SU(2)$ gauge fields, it is shown that the idealized algorithm preserves criticality under…
An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared…
Simulations at physical quark masses are affected by the critical slowing down of the solvers. Multigrid preconditioning has proved to deal effectively with this problem. Multigrid accelerated simulations at the physical value of the pion…
A structured preconditioned conjugate gradient (PCG) solver is developed for the Newton steps in second-order methods for a class of constrained network optimal control problems. Of specific interest are problems with discrete-time dynamics…
Convolution-type integral equations arise from various fields, \textit{e.g.}, finite impulse response filters in signal processing and deblurring problems in image processing. When solving these equations, conventional numerical methods,…
Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient…
We present multiplexed gradient descent (MGD), a gradient descent framework designed to easily train analog or digital neural networks in hardware. MGD utilizes zero-order optimization techniques for online training of hardware neural…
Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system…
In this paper, we develop a multigrid method on unstructured shape-regular grids. For a general shape-regular unstructured grid of ${\cal O}(N)$ elements, we present a construction of an auxiliary coarse grid hierarchy on which a geometric…
In order to develop fast inversion algorithms we have used overlap solvers in two dimensions. Lattice QED theory with U(1) group symmetry in two dimensional space-times dimensions has always been a testing ground for algorithms. By the…
We present our implementation of the RHMC algorithm for staggered fermions on Graphics Processing Units using the NVIDIA CUDA programming language. While previous studies exclusively deal with the Dirac matrix inversion problem, our code…
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…
The aim of this paper is to solve large-and-sparse linear Semidefinite Programs (SDPs) with low-rank solutions. We propose to use a preconditioned conjugate gradient method within second-order SDP algorithms and introduce a new efficient…
It is now a noticeable trend in High Performance Computing that the systems are becoming more and more heterogeneous. Compute nodes with a host CPU are being equipped with accelerators, the latter being a GPU or FPGA cards or both. In many…
The convergence of GMRES for solving linear systems can be influenced heavily by the structure of the right hand side. Within the solution of eigenvalue problems via inverse iteration or subspace iteration, the right hand side is generally…
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…
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…
We present a multigrid algorithm for the solution of the linear systems of equations stemming from the $p-$version of the Virtual Element discretization of a two-dimensional Poisson problem. The sequence of coarse spaces are constructed…