TY - GEN

T1 - On the application of Algorithmic Differentiation to Newton solvers

AU - Tadjouddine, Emmanuel M.

PY - 2010

Y1 - 2010

N2 - Newton solvers have the attractive property of quadratic convergence but they require derivative information. An efficient way of computing derivatives is by Algorithmic Differentiation (AD) also known as automatic differentiation or computational differentiation. AD allows us to evaluate derivatives usually at a cheap cost without the truncation errors associated with finite-differencing. Recent years witnessed an intense activity to produce tools enabling systematic calculation of derivatives. Efficient and reliable AD tools for evaluating derivatives have been published. In this paper, we sketch some of the main theory at the heart of AD, review some of the best AD codes currently available and put into context the use of AD for iterative solution methods of nonlinear systems or adjoint equations. Our aim is to direct scientists and engineers confronted with the need of exactly calculating derivatives to the use of AD as a highly useful tool and those AD tools which they could try primarily. Moreover, we show that the use of AD increases the performance of the quadratically convergence solution of a parabolised Navier-Stokes equations.

AB - Newton solvers have the attractive property of quadratic convergence but they require derivative information. An efficient way of computing derivatives is by Algorithmic Differentiation (AD) also known as automatic differentiation or computational differentiation. AD allows us to evaluate derivatives usually at a cheap cost without the truncation errors associated with finite-differencing. Recent years witnessed an intense activity to produce tools enabling systematic calculation of derivatives. Efficient and reliable AD tools for evaluating derivatives have been published. In this paper, we sketch some of the main theory at the heart of AD, review some of the best AD codes currently available and put into context the use of AD for iterative solution methods of nonlinear systems or adjoint equations. Our aim is to direct scientists and engineers confronted with the need of exactly calculating derivatives to the use of AD as a highly useful tool and those AD tools which they could try primarily. Moreover, we show that the use of AD increases the performance of the quadratically convergence solution of a parabolised Navier-Stokes equations.

KW - Adjoint equations

KW - Algorithmic differentiation

KW - Newton solvers

KW - Vertex elimination

UR - http://www.scopus.com/inward/record.url?scp=79952385081&partnerID=8YFLogxK

M3 - Conference Proceeding

AN - SCOPUS:79952385081

SN - 9789881701282

T3 - Proceedings of the International MultiConference of Engineers and Computer Scientists 2010, IMECS 2010

SP - 1342

EP - 1347

BT - Proceedings of the International MultiConference of Engineers and Computer Scientists 2010, IMECS 2010

T2 - International MultiConference of Engineers and Computer Scientists 2010, IMECS 2010

Y2 - 17 March 2010 through 19 March 2010

ER -