Related papers: A Parallel and Scalable Iterative Solver for Seque…
This paper presents and analyzes a parallelizable iterative procedure based on domain decomposition for primal-dual weak Galerkin (PDWG) finite element methods applied to the Poisson equation. The existence and uniqueness of the PDWG…
The Poisson pressure solve resulting from the spectral element discretization of the incompressible Navier-Stokes equation requires fast, robust, and scalable preconditioning. In the current work, a parallel scaling study of…
In this paper we design and analyze algorithms for asynchronously solving linear programs using nonlinear signal processing structures. In particular, we discuss a general procedure for generating these structures such that a fixed-point of…
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
This paper describes a software package called EVSL (for EigenValues Slicing Library) for solving large sparse real symmetric standard and generalized eigenvalue problems. As its name indicates, the package exploits spectrum slicing, a…
One of the greatest efforts of computational scientists is to translate the mathematical model describing a class of physical phenomena into large and complex codes. Many of these codes face the difficulty of implementing the mathematical…
A new algorithm for eigenvalue problems for the fractional Jacobi type ODE is proposed. The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some…
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…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
Breakthroughs in the generative AI domain have fueled an explosion of large language model (LLM)-powered applications, whose workloads fundamentally consist of sequences of inferences through transformer architectures. Within this rapidly…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…
This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…
We devise a mixing algorithm for full-potential (FP) all-electron calculations in the linearized augmented planewave (LAPW) method. Pulay's direct inversion in the iterative subspace is complemented with the Kerker preconditioner and…
The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…