787 research outputs found
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
We present two new adaptive quadrature routines. Both routines differ from
previously published algorithms in many aspects, most significantly in how they
represent the integrand, how they treat non-numerical values of the integrand,
how they deal with improper divergent integrals and how they estimate the
integration error. The main focus of these improvements is to increase the
reliability of the algorithms without significantly impacting their efficiency.
Both algorithms are implemented in Matlab and tested using both the "families"
suggested by Lyness and Kaganove and the battery test used by Gander and
Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases
less efficient, than other commonly-used adaptive integrators.Comment: 32 pages, submitted to ACM Transactions on Mathematical Softwar
On the subdivision strategy in adaptive quadrature algorithms
AbstractThe subdivision procedure used in most available adaptive quadrature codes is a simple bisection of the chosen interval. Thus the interval is divided in two equally sized parts. In this paper we present a subdivision strategy which gives three nonequally sized parts. The subdivision points are found using only available information. The strategy has been implemented in the QUADPACK code DQAG and tested using the “performance profile” testing technique. We present test results showing a significant reduction in the number of function evaluations compared to the standard bisection procedure on most test families of integrands
Efficient and Accurate Computation of Non-Negative Anisotropic Group Scattering Cross Sections for Discrete Ordinates and Monte Carlo Radiation Transport
A new method for approximating anisotropic, multi-group scatter cross sections for use in discretized and Monte Carlo multi-group neutron transport is presented. The new method eliminates unphysical artifacts such as negative group scatter cross sections and falsely positive cross sections. Additionally, when combined with the discrete elements angular quadrature method, the new cross sections eliminate the lack of angular support in the discrete ordinates quadrature method. The new method generates piecewise-average group-to-group scatter cross sections. The accuracy and efficiency for calculating the discrete elements cross sections has improved by many orders of magnitude compared to DelGrande and Mathews previous implementation. The new cross sections have extended the discrete elements method to all neutron-producing representations in the Evaluated Nuclear Data Files. The new cross section method has been validated and tested with the cross section generation code, NJOY. Results of transport calculations using discrete elements, discrete ordinates, and Monte Carlo methods for two, one-dimensional slab geometry problems are compared
Mathematical computer programs: A compilation
Computer programs, routines, and subroutines for aiding engineers, scientists, and mathematicians in direct problem solving are presented. Also included is a group of items that affords the same users greater flexibility in the use of software
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