03/10/2025 –, Salle café
Langue: English
We present the new package HAdaptiveIntegration.jl which can compute the integral of functions over simplicies (triangle, tetrahedron, ...) and axis-aligned orthotopes (rectangle, cuboid, ...). The numerical computation of the integral is based on efficient tabulated embedded cubature rules and automatic mesh refinement (h-adaptivity) guided by error estimation given by the embedded cubature.
HAdaptiveIntegration.jl is a Julia package designed for numerical integration over multidimensional domains. It computes integrals of the form I = ∫ f(x) dx over Ω where f is any Julia function and Ω represents domains such as simplices (triangle, tetrahedron, ...) and axis-aligned orthotopes (rectangle, cuboid, ...). The package employs an adaptive approach, dynamically refining the integration domain as needed. It uses embedded cubature rules to provide error estimates, aiming to achieve high accuracy while minimizing function evaluations.
Features include:
- Adaptive integration over simplices and axis-aligned orthotope of any dimension,
- Utilization of efficient tabulated cubatures for low-dimensional simplices and orthotopes,
- Support for custom embedded cubature rules,
- Arbitrary precision arithmetic.
