Related papers: An Efficient Block Circulant Preconditioner For Si…

One of the most significant challenges involved in efforts to understand the effects of repeated earthquake cycle activity are the computational costs of large-scale viscoelastic earthquake cycle models. Computationally intensive…

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to…

Using fault-tolerant constructions, computations performed with unreliable components can simulate their noiseless counterparts though the introduction of a modest amount of redundancy. Given the modest overhead required to achieve…

Ordinary state-based peridynamic (OSB-PD) models have an unparalleled capability to simulate crack propagation phenomena in solids with arbitrary Poisson's ratio. However, their non-locality also leads to prohibitively high computational…

Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically…

In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…

This paper presents a new stochastic preconditioning approach. For symmetric diagonally-dominant M-matrices, we prove that an incomplete LDL factorization can be obtained from random walks, and used as a preconditioner for an iterative…

Plastic deformation of most crystalline materials is due to the motion of lattice dislocations. Therefore, the simulation of the interaction and dynamics of these defects has become state-of-the-art method to study work hardening, size…

We propose a machine learning approach to address a key challenge in materials science: predicting how fractures propagate in brittle materials under stress, and how these materials ultimately fail. Our methods use deep learning and train…

Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…

In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…

When solving partial differential equations (PDEs) using finite difference or finite element methods, efficient solvers are required for handling large sparse linear systems. In this paper, a recursive sparse LU decomposition for matrices…

We present a robust and scalable solver for direct-forcing immersed boundary simulations, based on a preconditioned SIMPLE algorithm. The method applies block elimination to the pressure-force coupled system, and utilizes the discrete…

Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the…

The dominant cost of most lattice QCD simulations is the inversion of the Dirac operator required to calculate the force term in the RHMC update. One way to improve this situation is to use multiple pseudofermions, which reduces the size…

The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…

Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle-particle and particle-fluid interactions require an adequate representation but the computational cost has to be kept…

Fault-tolerant deep learning accelerator is the basis for highly reliable deep learning processing and critical to deploy deep learning in safety-critical applications such as avionics and robotics. Since deep learning is known to be…

In this work, we propose an absolute value block $\alpha$-circulant preconditioner for the minimal residual (MINRES) method to solve an all-at-once system arising from the discretization of wave equations. Motivated by the absolute value…

Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by…