# Numerical integration over 3D domain of vector-valued function

**URL:** https://discourse.julialang.org/t/numerical-integration-over-3d-domain-of-vector-valued-function/112284
**Category:** General Usage
**Tags:** integral
**Created:** [March 29, 2024, 12:27pm UTC](https://discourse.julialang.org/t/numerical-integration-over-3d-domain-of-vector-valued-function/112284 "2024-03-29T12:27:23Z")
**Posts on this page:** 1
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### Author: ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [March 29, 2024, 2:05pm UTC](https://discourse.julialang.org/t/numerical-integration-over-3d-domain-of-vector-valued-function/112284/10 "2024-03-29T14:05:50Z")

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For adaptive integration, your allocations won’t be zero because of the data structures needed to keep track of the dynamic subdivision of the domain, though pre-allocation can help.

Your integrand has a singularity at the corner — you really want to do a transformations to eliminate this singularity to make the integration more efficient. Algorithms to do this are widely known in the integral-equation community (indeed, your integral looks much like a panel integral for a surface integral equation).

You might also want to lower the tolerance — by default it integrates to at least 8 digits, which might be more than you need.

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