Finite elements methods (FEMs) with numerical integration play a central role in numerical homogenization methods for partial differential equations with multiple scales, as the effective data in a homogenization problem can only be recovered from a microscopic solver at a finite number of points in the computational domain. In a multiscale framework the convergence of a FEM with numerical inte...

A general uniform convergence theorem for numerical integration of Cauchy principal value integrals is proved. Seven special instances of this theorem are given as corollaries.

We present an efficient approach to evaluate multivariate highly oscillatory integrals on piecewise analytic integration domains. Cubature rules are developed that only require the evaluation of the integrand and its derivatives in a limited set of points. A general method is presented to identify these points and to compute the weights of the corresponding rule. The accuracy of the constructed...

In a recent comparison of methods of highly oscillatory numerical integration the authors appear to have overlooked some works which seem to compete effectively with several of those described. It is the intention briefly to illuminate this with a number of examples reworked. In so doing, it is found that three commonly used Fortran compilers give curiously differing results on a number of occa...

cretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high accuracy solution of Laplace’s equation and the Helmholtz equation on such domains. Our approach can be adapted to many other boundary value problems as well as to the case of surfaces with singularities in three dimens...

9Yoon, S., Howe, R. M., and Greenwood, D. T., “Stability and Accuracy Analysis of Baumgarte’s Constraint Stabilization Method,” Journal of Mechanical Design, Vol. 117, No. 3, 1995, pp. 446–453. 10Lin, S. T., and Hong, M. C., “Stabilization Method for the Numerical Integration of Multibody Mechanical System,” Journal of Mechanical Design, Vol. 120, No. 4, 1998, pp. 565–572. 11Haug, E. J., Comput...

Article history: Received 14 January 2014 Received in revised form 14 August 2014 Accepted 23 August 2014 Available online 27 August 2014

The parallel version of the multidimensional numerical integration package Cuba is presented and achievable speed-ups discussed.