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In this paper, we analyze the convergence %semi-convergence properties of projected non-stationary block iterative methods (P-BIM) aiming to find a constrained solution to large linear, usually both noisy and ill-conditioned, systems of…
Simulation of the Hubbard model is a leading candidate for the first useful applications of a fault-tolerant quantum computer. A recent study of quantum algorithms for early simulations of the Hubbard model [Kivlichan \textit{et al.}…
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…
We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering the multi-physics nature of the problem, which involves solid…
Block elimination algorithms for solving sparse discrete optimization problems are considered. The numerical example is provided. The benchmarking is done in order to define real computational capabilities of block elimination algorithms…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
In distributed synchronous gradient descent (GD) the main performance bottleneck for the per-iteration completion time is the slowest \textit{straggling} workers. To speed up GD iterations in the presence of stragglers, coded distributed…
Predicting fracture load in laminated composites with stress raisers is challenging due to complex failure mechanisms such as delamination, fibre breakage, and matrix cracking, which are heavily influenced by fibre orientation, layup…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain due to fluctuating…
This paper provides modified Distributed Arithmetic based technique to compute sum of products saving appreciable number of Multiply And accumulation blocks and this consecutively reduces circuit size. In this technique multiplexer based…
We present a dynamically load-balanced parallel $ p $-adaptive implicit high-order flux reconstruction method for under-resolved turbulence simulation. The high-order explicit first stage, singly diagonal implicit Runge-Kutta (ESDIRK)…
The safety and integrity of engineered structures are critically dependent on maintaining sufficient preload in their bolted joints. This preload can be dynamically lost due to sustained vibrations or sudden shock that are large enough to…
In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…
Large-scale cosmological simulations are an indispensable tool for modern cosmology. To enable model-space exploration, fast and accurate predictions are critical. In this paper, we show that the performance of such simulations can be…
Contingency screening for transient stability of large-scale, strongly nonlinear, interconnected power systems is one of the most computationally challenging parts of Dynamic Security Assessment and requires huge resources to perform…
In power system dynamic simulation, up to 90% of the computational time is devoted to solve the network equations, i.e., a set of linear equations. Traditional approaches are based on sparse LU factorization, which is inherently sequential.…
In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware…
Scalable machine learning over big data is an important problem that is receiving a lot of attention in recent years. On popular distributed environments such as Hadoop running on a cluster of commodity machines, communication costs are…
Basic-block throughput models such as uiCA, IACA, GRANITE, Ithemal, llvm-mca, OSACA, or CQA guide optimizing compilers and help performance engineers identify and eliminate bottlenecks. For this purpose, basic-block throughput models should…