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DECUHR.jl

Pure-Julia port of the DECUHR algorithm (Espelid & Genz, 1994): adaptive cubature for integrands that blow up at a vertex of a hyper-rectangle, in dimension 2 to 15, pluggable into Integrals.jl and differentiable with ForwardDiff.

Julia
Quadrature
Numerical Analysis

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-rectangular regions — the situation met whenever a Green function is integrated over an inclusion. Where a plain adaptive rule keeps subdividing without ever converging, the algorithm couples the subdivision to an extrapolation that removes the singular contribution. Part of the MicroPoroChemoMechanics ecosystem.

Key features

  • Vertex singularities — subdivision coupled to an extrapolation in the cell size, which is what removes the singular contribution instead of chasing it; logarithmic singularities too
  • Hyper-rectangular regions — boxes of dimension 2 to 15, with rules of degree 13 and 11 dedicated to 2D and 3D
  • Strength known or not — the algebraic exponent can be supplied when the analysis gives it, or estimated from the samples when it does not
  • Vector-valued integrands — a whole tensor of integrals shares one subdivision history rather than being recomputed component by component
  • A SciML algorithm — DecuhrAlgorithm plugs into Integrals.jl like any other solver, and ForwardDiff passes through it, estimated exponent included

Installation

DECUHR.jl is registered in Julia’s General registry:

using Pkg
Pkg.add("DECUHR")

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. This package is an independent Julia port of that work, under the MIT license, shipping the upstream copyright notice unmodified.