About#

The OTI numbers, and its corresponding computational implementation, were initially developed by Dr. Mauricio Aristizabal during his Ph.D. studies as he was researching the use of hypercomplex algebras and other automatic differentiation approaches to compute high-order shape derivatives in Finite Element analyses for optimization appliations. Although hypercomplex algebras like Hyperdual numbers and Multicomplex numbers were options for obtaining high-order derivatives, its exponential growth in size prevented its deployment for high performance multivariate analysis.

The focus has always been to provide support for linear-algebra applications, like the Finite Element analses, with a robust an efficient implementation of an algebra that allows arbitrary order multivariable derivatives.

The development of the library (otilib and pyoti), began in 2016 and has been actively developed by Dr. Aristizabal since then. Minor contrubutions to the library were provided by students who worked together with Dr. Aristizabal before 2024.

Contributors#

The following is a list of contributors for the development of the otilib/pyoti library.

Mauricio Aristizabal, Ph.D.; Samuel Roberts (Ph.D. student, UT San Antonio); Jose-Leonel Hernandez-Estrada (Master student, Universidad EAFIT)

Acknowledgements#

Special thanks to the advisorship from:

Dr. Manuel J. Garcia (Ph.D. sdvisor) Dr. Harry Millwater (Postdoc advisor)

The development of the OTIlib and pyoti libraries has been possible thanks to the support from:

  • St. Mary’s University

  • National Aeronautics and Space Administration (NASA), grant 80NSSC23K1342.

  • Army Research Office (U.S. Department of Defense), grant W911NF2010315.

  • U.S. Department of Defense, grant W911NF1510456.

  • University of Texas at San Antonio.

  • COLCIENCIAS (now Minciencias) scholarship program 647-2014.

  • Universidad EAFIT.