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Mini-symposium on Computational and Numerical Differentiation and Its Application to Engineering Analysis

Manuel Garcia, Angelo State University

Arturo Montoya, University of Texas-San Antonio

Harry Millwater, University of Texas-San Antonio

Differentiation plays a significant role in design sensitivity analysis, design optimization, parameter tuning, reliability analysis, reduced-order models, uncertainty quantification, fracture mechanics, and structural health monitoring.  Numerical techniques to compute a function's derivatives include automatic differentiation, hypercomplex (complex and dual) step differentiation, and truncated Taylor series polynomials, among others.
Differentiation of problems solved through the finite element method has been accomplished by direct and adjoint differentiation and finite difference methods. More recently, hypercomplex algebras and automatic differentiation have been used in various applications that include: aerodynamics, computational fluid dynamics, combustion, heat conduction, fracture mechanics, and control engineering, among others. 
This mini-symposium seeks to discuss recent development in computational techniques for computing derivatives and its application to different fields.
Possible topics include but are not limited to: Efficient computation of high order derivatives, advances in multi-complex and multi(hyper)-dual methods, benchmark problems, and applications.