Computing sensitivity coefficients by using complex differentiation: Application to heat conduction problem

Abstract

A simple and efficient computational method for Sensitivity Coefficient calculation is presented. Sensitivity analysis are carried out for a simple one-dimensional heat conduction problem with respect to two parameters: thermal conductivity (k) and volumetric heat capacity (c). Results obtained by finite difference and complex step differentiation are compared with analytical solution in non-dimensional form. With an arbitrary small step-size, the complex differentiation method can achieve near analytical accuracy in languages that support complex arithmetic. Further implementation of complex step differentiation in Matlab environment is explained with some precautions.

Acknowledgments

The authors have appreciated and thank the anonymous reviewers for their useful comments and suggestions that helped them to improve the quality and the presentation of the manuscript.

Notes

1 A computer program, written in Matlab [37] is available to readers by sending an email to the corresponding author.