DECUHR.jl

Julia
Quadrature
Numerical Analysis

Pure-Julia port of the DECUHR algorithm (Espelid & Genz, 1994) for adaptive integration of functions with vertex singularities over hyper-rectangles, pluggable into Integrals.jl.

DECUHR.jl is a pure-Julia port of the DECUHR algorithm of Espelid & Genz for the automatic adaptive integration of functions with vertex singularities over hyper-rectangles — the situation met when integrating Green functions over an inclusion.

Key features

  • Vertex-singularity handling by extrapolation, where a plain adaptive rule stalls
  • Hyper-rectangular domains in arbitrary dimension
  • SciML integration — exposed as a pluggable algorithm for Integrals.jl

Credits and license

The algorithm and the original Fortran 77 routines are due to T. O. Espelid and A. Genz, DECUHR: an algorithm for automatic integration of singular functions over a hyperrectangular region, Numerical Algorithms 8 (1994) 201–220, doi:10.1007/BF02142691. The Julia port is under the MIT license and ships the upstream copyright notice unmodified.