相关论文: A Technical Survey of Sparse Linear Solvers in Ele…

The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…

Matrix exponential discriminant analysis (EDA) is a generalized discriminant analysis method based on matrix exponential. It can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear…

This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…

Electrical design automation (EDA) techniques have deeply influenced the computer hardware design, especially in the field of very large scale Integration (VLSI) circuits. Particularly, the popularity of FPGA, ASIC and SOC applications have…

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…

HPC systems are a critical resource for scientific research. The increased demand for computational power and memory ushers in the exascale era, in which supercomputers are designed to provide enormous computing power to meet these needs.…

The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…

Solving large, sparse linear systems is a fundamental workload in scientific computing and engineering simulations, often dominating runtime and energy consumption in high-performance computing (HPC) applications. In this work, we explore…

We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the…

Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…

Complexity of linear finite-impulse-response (FIR) equalizers is proportional to the square of the number of nonzero taps in the filter. This makes equalization of channels with long impulse responses using either zero-forcing or minimum…

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…

In this work, we are interested in solving large linear systems stemming from the Extra-Membrane-Intra (EMI) model, which is employed for simulating excitable tissues at a cellular scale. After setting the related systems of partial…

When solving linear systems arising from PDE discretizations, iterative methods (such as Conjugate Gradient, GMRES, or MINRES) are often the only practical choice. To converge in a small number of iterations, however, they have to be…

Sparse autoencoders (SAEs) have recently become central tools for interpretability, leveraging dictionary learning principles to extract sparse, interpretable features from neural representations whose underlying structure is typically…

A brief summary of direct solution approaches for finite element methods (FEM) in computational electromagnetics (CEM) is given along with an alternative direct solution based on domain decomposition (DD). Unlike recent trends in…

Preconditioned Krylov subspace (KSP) methods are widely used for solving large-scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs). These linear systems are often nonsymmetric due to the…

As integrated circuits become increasingly complex, the demand for efficient and accurate simulation solvers continues to rise. Traditional solvers often struggle with large-scale sparse systems, leading to prolonged simulation times and…

Recently, numerous sparse hardware accelerators for Deep Neural Networks (DNNs), Graph Neural Networks (GNNs), and scientific computing applications have been proposed. A common characteristic among all of these accelerators is that they…

We introduce the sparsified Cholesky and sparsified multigrid algorithms for solving systems of linear equations. These algorithms accelerate Gaussian elimination by sparsifying the nonzero matrix entries created by the elimination process.…