Rapid Bessel Integration

A common problem—particularly in condensed-matter physics and for topics such as mutual inductance—is computing large numbers of integrals of Bessel functions with variations in parameters.

Our Rapid Bessel Integration Suite (RBIS) utilizes highly-optimized algorithms to compute such integrals. The algorithms are fully parallelizable and can be used to generate massive look-up tables, where a single value might represent the sum of a half-million similar integrals. The RBIS then allows you to rapidly search these tables for particular values, and further interpolate using actual integrals to calculate solutions with arbitrary additional precision as needed.

Our algorithms are more than 75,000 times faster than performing the same computations in Mathematica, but they agree to the very last decimal place.


Although our algorithms are proprietary, our software’s calculations are easily checked. The computations that our software performs are hard, but the opposite computations to verify our results are trivial. This is similar to factoring: Finding the prime factors of a large integer is difficult, but verifying that multiplying those factors produces that integer is trivial.


If your experimental data is not already binned, our ZBIN data binning software can do this for you as a preliminary step.

What You Need

The Windows software runs on a single machine; the Linux software is designed for cluster use.

Your hardware will be the greatest determining factor in processing time. Very little RAM is required, however, the more cores available, the better. This software does not utilize GPU computations and requires Intel CPUs. It requires the GNU Scientific Library to be available for numerical integration. Ivy-Bridge or Haswell Xeon processors are strongly recommended.

For some calculations, you may need to define an exact interpolation geometry in order for the RBIS to calculate your results. Our installation support includes the calculation of one geometry for you, typically from a manufacturer's data sheet. If you need additional interpolation geometries, you can either calculate them yourself (with your own tools) or we can calculate them for you for a nominal additional fee.


The RBIS software consists of three distinct components:

  • RBIS-SWW—Rapid Bessel Integration Suite for 64-bit Microsoft Windows (single machine use)
  • RBIS-SWL—Rapid Bessel Integration Suite for 64-bit Linux (MPICH cluster use)
  • RBIS-FC—RBIS Format Conversion Software for Python

Minimum Hardware and Software

  • Intel Gainestown or newer Xeon processors
  • 1 GB RAM per core
  • 64-bit Ubuntu 14.04 LTS for RBIS-SWL
  • Windows 7 for RBIS-SWW
  • Python 3.4.2 or later for RBIS-FC

Recommended Hardware and Software (2016)

  • 32 or more CPU cores
  • Intel Ivy-Bridge or Haswell Xeon processors, 3 GHz or higher
  • 2 GB RAM per core
  • 64-bit Ubuntu 16.04 LTS for RBIS-SWL
  • Windows Server 2016 for RBIS-SWW
  • Python 3.6 or later for RBIS-FC