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We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU ...

This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, ...

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision ...

We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume, or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly ...

We present a structured parallel geometry-based multifrontal sparse solver using hierarchically semiseparable (HSS) representations and exploiting the inherent low-rank structures. Parallel strategies for nested dissection ordering (taking low rankness ...

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank ...

Matrices coming from elliptic partial differential equations have been shown to have a low-rank property: well-defined off-diagonal blocks of their Schur complements can be approximated by low-rank products. Given a suitable ordering of the matrix which ...

A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designed for problems with smooth solutions. The resulting system of ...

To face the advent of multicore processors and the ever increasing complexity of hardware architectures, programming models based on DAG parallelism regained popularity in the high performance, scientific computing community. Modern runtime systems offer ...

Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern and its dual cone, the cone of sparse matrices with ...

The advent of multicore processors represents a disruptive event in the history of computer science as conventional parallel programming paradigms are proving incapable of fully exploiting their potential for concurrent computations. The need for different ...

In this paper, a novel parallel algorithm is proposed for power system transient stability computation. The proposed algorithm uses the s-stage 2s-order symplectic Gauss method to convert the differential-algebraic system simultaneously at s time points ...

The inverse of an irreducible sparse matrix is structurally full, so that it is impractical to think of computing or storing it. However, there are several applications where a subset of the entries of the inverse is required. Given a factorization of the ...

On many current and emerging computing architectures, single-precision calculations are at least twice as fast as double-precision calculations. In addition, the use of single precision may reduce pressure on memory bandwidth. The penalty for using ...

We present a new scheduling algorithm for task graphs arising from parallel multifrontal methods for sparse linear systems. This algorithm is based on the theorem proved by Prasanna and Musicus [1] for tree-shaped task graphs, when all tasks exhibit the ...

Based on message passing interface (MPI) distributed-memory network, we propose a parallel realization of algebraic domain decomposition method to solve the large sparse linear systems, which were derived from the vector finite element method (FEM) for ...

In this paper, we present a new way to improve performance of the factorization of large sparse linear systems which cannot fit in memory. Instead of rewriting a large part of the code to implement an out-of-core algorithm with explicit I/O, we modify ...

An ANSI C code for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes an upper bound on ...

A new method for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The column ordering is selected to give a good a priori upper bound on fill-...

We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 × 2 pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We describe some of ...