Factors involved in the performance of computations on Beowulf clusters.
Fast and correctly rounded logarithms in double-precision
This article is a case study in the implementation of a portable, proven and efficient correctly rounded elementary function in double-precision. We describe the methodology used to achieve these goals in the crlibm library. There are two novel aspects to this approach. The first is the proof framework, and in general the techniques used to balance performance and provability. The second is the introduction of processor-specific optimization to get performance equivalent to the best current...
Fast Fourier analysis for over a finite field and related numerical experiments.
Fast multigrid solver
In this paper a black-box solver based on combining the unknowns aggregation with smoothing is suggested. Convergence is improved by overcorrection. Numerical experiments demonstrate the efficiency.
Fast solution of MSC/NASTRAN sparse matrix problems using a multilevel approach.
Fifth-order numerical methods for heat equation subject to a boundary integral specification.
Filter factor analysis of an iterative multilevel regularizing method.
Finding nonoverlapping substructures of a sparse matrix.
Finite element modeling of wood structure
This work is focused on a weak solution of a coupled physical task of the microwave wood drying process with stress-strain effects and moisture/temperature dependency. Due to the well known weak solutions for the individual physical fields, the author concerns with the coupled stress-strain relation coupled with the moisture and temperature distributions. For the scale dependency the subgrid upscaling method was used. The solved region is assumed to be divided into discontinuous subregions according...
Finite element modelling of some incompressible fluid flow problems
We deal with modelling of flows in channels or tubes with abrupt changes of the diameter. The goal of this work is to construct the FEM solution in the vicinity of these corners as precise as desired. We present two ways. The first approach makes use of a posteriori error estimates and the adaptive strategy. The second approach is based on the asymptotic behaviour of the exact solution in the vicinity of the corner and on the a priori error estimate of the FEM solution. Then we obtain the solution...
FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials
In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate...
From classical numerical mathematics to scientific computing.