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We propose a simple and efficient one-way multigrid method for self-consistent electronic structure calculations based on iterative diagonalization. Total energy calculations are performed on several different levels of grids starting from…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method,…
Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting…
The scalability of quantum computing is currently limited by physical, technological, and architectural constraints that hinder the integration of a large number of qubits within a single quantum processor. Distributed quantum computing…
Multiple-antenna systems is a key technique to serve multiple users in future wireless systems. For low energy consumption and hardware complexity we first consider transmit symbols with constant magnitude and then 1-bit digital-to-analog…
The multigrid methodology is reviewed. By integrating numerical processes at all scales of a problem, it seeks to perform various computational tasks at a cost that rises as slowly as possible as a function of $n$, the number of degrees of…
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme…
We consider the problem of coding over the multi-user Interference Channel (IC). It is well-known that aligning the interfering signals results in improved achievable rates in certain setups involving more than two users. We argue that in…
We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among $n$ different nodes, which can communicate using a limited number of…
A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable…
Pallalel GPGPU computing for lattice QCD simulations has a bottleneck on the GPU to GPU data communication due to the lack of the direct data exchanging facility. In this work we investigate the performance of quark solver using the…
In this work, we consider solving a distributed optimization problem (DOP) in a multi-agent network with multiple agent clusters. In each cluster, the agents manage separable cost functions composed of possibly non-smooth components and aim…
We present an adaptive multigrid Dirac solver developed for Wilson clover fermions which offers order-of-magnitude reductions in solution time compared to conventional Krylov solvers. The solver incorporates even-odd preconditioning and…
In this paper, we aim to solve a distributed optimization problem with affine coupling constraints in a multi-agent network, where the cost function of the agents is composed of smooth and possibly non-smooth parts. To solve this problem,…
Lattice QCD calculations require significant computational effort, with the dominant fraction of resources typically spent in the numerical inversion of the Dirac operator. One of the simplest methods to solve such large and sparse linear…
The setup cost of a modern solver such as DD-\alpha AMG (Wuppertal Multigrid) is a significant contribution to the total time spent on solving the Dirac equation, and in HMC it can even be dominant. We present an improved implementation of…
This paper considers the multi-agent linear least-squares problem in a server-agent network. In this problem, the system comprises multiple agents, each having a set of local data points, that are connected to a server. The goal for the…
In this paper, we study FPGA based pipelined and superscalar design of two variants of conjugate gradient methods for solving Laplacian equation on a discrete grid; the first version corresponds to the original conjugate gradient algorithm,…
The performance and efficiency of distributed training of Deep Neural Networks highly depend on the performance of gradient averaging among all participating nodes, which is bounded by the communication between nodes. There are two major…