17 research outputs found
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 āperformance profileā 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
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
Numerical Integration of Two-Dimensional Complex-Valued Functions for the needs of BIEM
Numerical integration is a key problem with numerous applications, including the boundary integral equation method (BIEM). GSL [7] provides powerful implementations of a broad variety of well-known numerical methods and algorithms. However, its routines have certain limitations: the numerical integration based on QUADPACK library [2] is implemented only in the case of one-dimensional functions. In this paper we present an extension of the GSL numerical integration routines for the special case of two-dimensional complex-valued functions. The presented approach is part of our effort to build a BIEM software system for solving a 3D elastodynamics problem for wave propagation in a continuously inhomogeneous half-space
Numerical product design: Springback prediction, compensation and optimization
Numerical simulations are being deployed widely for product design. However, the accuracy of the numerical tools is not yet always sufficiently accurate and reliable. This article focuses on the current state and recent developments in different stages of product design: springback prediction, springback compensation and optimization by finite element (FE) analysis. To improve the springback prediction by FE analysis, guidelines regarding the mesh discretization are provided and a new through-thickness integration scheme for shell elements is launched. In the next stage of virtual product design the product is compensated for springback. Currently, deformations due to springback are manually compensated in the industry. Here, a procedure to automatically compensate the tool geometry, including the CAD description, is presented and it is successfully applied to an industrial automotive part. The last stage in virtual product design comprises optimization. This article presents an optimization scheme which is capable of designing optimal and robust metal forming processes efficiently
Marginal Structural Illness-Death Models for Semi-Competing Risks Data
The three-state illness death model has been established as a general
approach for regression analysis of semi-competing risks data. For
observational data the marginal structural models (MSM) are a useful tool,
under the potential outcomes framework to define and estimate parameters with
causal interpretations. In this paper we introduce a class of marginal
structural illness death models for the analysis of observational semi
competing risks data. We consider two specific such models, the usual Markov
illness death MSM and the general Markov illness death MSM where the latter
incorporates a frailty term. For interpretation purposes, risk contrasts under
the MSMs are defined. Inference under the usual Markov MSM can be carried out
using estimating equations with inverse probability weighting, while inference
under the general Markov MSM requires a weighted EM algorithm. We study the
inference procedures under both MSMs using extensive simulations, and apply
them to the analysis of mid-life alcohol exposure on late life cognitive
impairment as well as mortality using the Honolulu-Asia Aging Study data set.
The R codes developed in this work have been implemented in the R package
semicmprskcoxmsm that is publicly available on CRAN