swMATH ID: 6496
Software Authors: Fike, Jeffrey A.; Alonso, Juan J.
Description: Automatic differentiation through the use of hyper-dual numbers for second derivatives. Automatic differentiation techniques are typically derived based on the chain rule of differentiation. Other methods can be derived based on the inherent mathematical properties of generalized complex numbers that enable first-derivative information to be carried in the non-real part of the number. These methods are capable of producing effectively exact derivative values. However, when second-derivative information is desired, generalized complex numbers are not sufficient. Higher-dimensional extensions of generalized complex numbers, with multiple non-real parts, can produce accurate second-derivative information provided that multiplication is commutative. One particular number system is developed, termed hyper-dual numbers, which produces exact first- and second-derivative information. The accuracy of these calculations is demonstrated on an unstructured, parallel, unsteady Reynolds-averaged Navier-Stokes solver.
Homepage: http://www.brown.edu/Departments/CCV/doc/mpi-cuda
Keywords: hyper-dual numbers; generalized complex numbers; operator overloading; second derivatives; Hessian; forward mode; C ++; CUDA; MPI; numerical examples; automatic differentiation; chain rule of differentiation; Reynolds-averaged Navier-Stokes solver
Related Software: LAPACK; CUDA; PETSc; ScaLAPACK; BLAS; PVM; METIS; MPI/MPICH; OpenCL; Matlab; ParMETIS; Trilinos; Gmsh; MUMPS; FFTW; Python; BLACS; SparseMatrix; OpenMPI; LINPACK
Cited in: 475 Publications
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Cited by 1,253 Authors

7 Arias, Enrique
6 di Serafino, Daniela
6 Gorobets, Andrey V.
6 Hernández, Vicente G.
5 D’Ambra, Pasqua
5 Ibáñez González, Jacinto Javier
5 Quintana-Ortí, Enrique S.
4 Filippone, Salvatore
4 Knottenbelt, William J.
4 Koomullil, Roy P.
4 Soni, Bharat K.
4 Wittum, Gabriel
4 Zhao, Yong
3 Alonso, Juan J.
3 Cai, Xing
3 Demmel, James Weldon
3 Dongarra, Jack J.
3 Galiano, Vicente
3 Gratton, Serge
3 Lirkov, Ivan D.
3 Margaritis, Konstantinos G.
3 Migallón, Violeta
3 Mo, Zeyao
3 Peinado, Jesús
3 Penadés, José
3 Quintana-Ortí, Gregorio
3 Robert, Yves
3 Rossi, Tuomo
3 Rovenskaya, Olga I.
3 Sanders, Peter
3 Sarkar, Abhijit
3 Siegel, Stephen F.
3 Tai, Chin Hoe
3 Trias, Francesc Xavier
3 Vasseur, Xavier
2 Al-Rawahi, Nabeel
2 Alberto, Angelines
2 Aldasoro, Unai
2 Allen, Christian B.
2 Aprovitola, Andrea
2 Aslan, Selahattin
2 Aspnäs, Mats
2 Bahi, Jacques Mohcine
2 Bailey, David Harold
2 Benet, Jesús
2 Benner, Peter
2 Benoit, Anne
2 Bethune, Iain
2 Borrell, Ricard
2 Calandra, Henri
2 Carazo, Jose-Maria
2 Caromel, Denis
2 Casoni, E.
2 Che, Yonggang
2 Couturier, Raphaël
2 Cuartero, Fernando
2 Decyk, Viktor K.
2 Delestre, Olivier
2 Denaro, Filippo Maria
2 Digalakis, Jason G.
2 Dingle, Nicholas J.
2 Dotti, Fernando Luís
2 Drummond, L. Anthony
2 Escudero, Laureano Fernando
2 Fahringer, Thomas
2 Fernández, José-Jesús
2 Fregly, Benjamin J.
2 Ganzha, Maria
2 García, Inmaculada F.
2 George, Alan D.
2 Ghendrih, Philippe
2 Ghosh, Swarnava
2 Gibou, Frédéric
2 Godoy, William F.
2 Goldfield, Evelyn M.
2 Grant, P. S.
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2 Gropp, William D.
2 Gunzburger, Max D.
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2 Houzeaux, Guillaume
2 Humphrey, Marty A.
2 Jambunathan, Revathi
2 Jin, Jianming
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2 Ju, Lili
2 Kalantzis, Vassilis
2 Larios-Cárdenas, Luis Ángel
2 Le, Minh Hoang
2 Lenci, Stefano
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2 Levin, Deborah A.
2 Liew, Kim Meow
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