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The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by…
Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and…
We introduce an algorithm for efficiently representing convolution with zero-padding and stride as a sparse transformation matrix, applied to a vectorized input through sparse matrix-vector multiplication (SpMV). We provide a theoretical…
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.,…
This paper provides a zeroth-order optimisation framework for non-smooth and possibly non-convex cost functions with matrix parameters that are real and symmetric. We provide complexity bounds on the number of iterations required to ensure…
We contribute a third-party survey of sparse matrix-vector (SpMV) product performance on industrial-strength, large matrices using: (1) The SpMV implementations in Intel MKL, the Trilinos project (Tpetra subpackage), the CUSPARSE library,…
The $k$-method is the isogeometric method based on splines (or NURBS, etc.) with maximum regularity. When implemented following the paradigms of classical finite element methods, the computational resources required by the $k-$method are…
This paper introduces a parallel directional fast multipole method (FMM) for solving N-body problems with highly oscillatory kernels, with a focus on the Helmholtz kernel in three dimensions. This class of oscillatory kernels requires a…
We explore the trade-offs of performing linear algebra using Apache Spark, compared to traditional C and MPI implementations on HPC platforms. Spark is designed for data analytics on cluster computing platforms with access to local disks…
Architectures with multiple classes of memory media are becoming a common part of mainstream supercomputer deployments. So called multi-level memories offer differing characteristics for each memory component including variation in…
We construct quasi-Monte Carlo methods to approximate the expected values of linear functionals of Galerkin discretizations of parametric operator equations which depend on a possibly infinite sequence of parameters. Such problems arise in…
Quantum chemistry provides a target for quantum simulation of considerable scientific interest and industrial importance. The majority of algorithms to date have been based on a second-quantized representation of the electronic structure…
We propose a quantum data fitting algorithm for non-sparse matrices, which is based on the Quantum Singular Value Estimation (QSVE) subroutine and a novel efficient method for recovering the signs of eigenvalues. Our algorithm generalizes…
A class of splitting alternating algorithms is proposed for finding the sparse solution of linear systems with concatenated orthogonal matrices. Depending on the number of matrices concatenated, the proposed algorithms are classified into…
General sparse matrix-matrix multiplication (SpGEMM) is an integral part of many scientific computing, high-performance computing (HPC), and graph analytic applications. This paper presents a new compressed sparse vector (CSV) format for…
We study faster algorithms for producing the minimum degree ordering used to speed up Gaussian elimination. This ordering is based on viewing the non-zero elements of a symmetric positive definite matrix as edges of an undirected graph, and…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is…