Parameterized Adaptive Multidimensional Integration Routines (PAMIR): Localization by Repeated 2^p Subdivision

TL;DR

This paper introduces PAMIR, a new adaptive multidimensional integration method using repeated subdivisions, with adjustable sampling and a focus on simplexes and hypercubes, supported by theoretical foundations and implementation guidelines.

Contribution

It presents a novel adaptive integration technique for p-dimensional spaces using repeated 2^p subdivision, enabling high-order routines with user-controlled sampling.

Findings

Effective for high-dimensional integrals

Supports adjustable sampling parameters

Provides a theoretical framework for the method

Abstract

This book draft gives the theory of a new method for p dimensional adaptive integration by repeated 2^p subdivision of simplexes and hypercubes. A new method of constructing high order integration routines for these geometries permits adjustable samplings of the integration region controlled by user supplied parameters. An outline of the programs and use instructions are also included in the draft. The fortran programs are not included, but will be published with this draft as a book.