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MPI

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.
2 Gray, Stephen K.
2 Grimshaw, Andrew S.
2 Gropp, William D.
2 Gunzburger, Max D.
2 Haase, Gundolf
2 Haftka, Raphael T.
2 Hammarling, Sven J.
2 Harrison, Peter G.
2 Houzeaux, Guillaume
2 Humphrey, Marty A.
2 Jambunathan, Revathi
2 Jin, Jianming
2 Jordan, Charles
2 Ju, Lili
2 Kalantzis, Vassilis
2 Larios-Cárdenas, Luis Ángel
2 Le, Minh Hoang
2 Lenci, Stefano
2 Leon, Coromoto
2 Levin, Deborah A.
2 Liew, Kim Meow
2 Martorell, Xavier
2 McInnes, Lois Curfman
2 Merino, María
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Cited in 146 Serials

52 Journal of Computational Physics
38 Computers and Fluids
23 Computer Physics Communications
14 Computer Methods in Applied Mechanics and Engineering
11 Journal of Parallel and Distributed Computing
11 SIAM Journal on Scientific Computing
10 Parallel Computing
9 Mathematics and Computers in Simulation
8 Computers & Mathematics with Applications
8 ACM Transactions on Mathematical Software
7 Applied Mathematics and Computation
7 International Journal for Numerical Methods in Engineering
7 Computing and Visualization in Science
7 Concurrency and Computation: Practice & Experience
6 International Journal for Numerical Methods in Fluids
6 International Journal of Parallel Programming
5 International Journal of Computer Mathematics
5 Numerical Linear Algebra with Applications
4 Concurrency: Practice and Experience
4 Applied Mathematical Modelling
4 Computational Statistics and Data Analysis
4 Mathematical Problems in Engineering
4 International Journal of Computational Fluid Dynamics
4 Lobachevskii Journal of Mathematics
4 Communications in Computational Physics
3 Journal of Computational and Applied Mathematics
3 Applied Numerical Mathematics
3 Journal of Scientific Computing
3 Computational Statistics
3 Computational Mathematics and Mathematical Physics
3 Physics of Fluids
3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings
3 Fractional Calculus & Applied Analysis
3 European Journal of Mechanics. B. Fluids
2 Information Processing Letters
2 Journal of Computer and System Sciences
2 Software. Practice & Experience
2 Science of Computer Programming
2 Journal of Symbolic Computation
2 Algorithmica
2 Computers & Operations Research
2 Mathematical and Computer Modelling
2 Numerical Algorithms
2 Automation and Remote Control
2 European Journal of Operational Research
2 Advances in Engineering Software
2 Computational Optimization and Applications
2 Engineering Analysis with Boundary Elements
2 Journal of Mathematical Chemistry
2 Multibody System Dynamics
2 Nonlinear Dynamics
2 Optimization Methods & Software
2 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki
2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
2 International Journal of Numerical Modelling
2 Combustion Theory and Modelling
2 Optimization and Engineering
2 IEEE Transactions on Antennas and Propagation
2 Archives of Computational Methods in Engineering
2 International Journal of Computational Methods
2 Software - Environments - Tools
2 Acta Mechanica Sinica
2 Mathematical Programming Computation
1 Acta Mechanica
1 Artificial Intelligence
1 European Journal of Physics
1 International Journal of Heat and Mass Transfer
1 International Journal for Numerical and Analytical Methods in Geomechanics
1 International Journal of Solids and Structures
1 International Journal of Systems Science
1 Journal of Fluid Mechanics
1 Mathematical Methods in the Applied Sciences
1 Physica A
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1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
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1 Chaos, Solitons and Fractals
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1 Journal of Xi’an Jiaotong University
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1 Journal of Global Optimization
1 The Journal of Supercomputing
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1 Linear Algebra and its Applications
1 Pattern Recognition
1 SIAM Review
...and 46 more Serials
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Cited in 35 Fields

247 Numerical analysis (65-XX)
148 Fluid mechanics (76-XX)
137 Computer science (68-XX)
40 Operations research, mathematical programming (90-XX)
33 Mechanics of deformable solids (74-XX)
32 Partial differential equations (35-XX)
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19 Optics, electromagnetic theory (78-XX)
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16 Geophysics (86-XX)
13 Quantum theory (81-XX)
11 Linear and multilinear algebra; matrix theory (15-XX)
10 Classical thermodynamics, heat transfer (80-XX)
7 Ordinary differential equations (34-XX)
7 Calculus of variations and optimal control; optimization (49-XX)
7 Mechanics of particles and systems (70-XX)
6 Combinatorics (05-XX)
5 Dynamical systems and ergodic theory (37-XX)
5 Information and communication theory, circuits (94-XX)
4 Probability theory and stochastic processes (60-XX)
4 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Number theory (11-XX)
3 Astronomy and astrophysics (85-XX)
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2 General and overarching topics; collections (00-XX)
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1 Algebraic geometry (14-XX)
1 Nonassociative rings and algebras (17-XX)
1 Group theory and generalizations (20-XX)
1 Special functions (33-XX)
1 Difference and functional equations (39-XX)
1 Integral equations (45-XX)
1 Convex and discrete geometry (52-XX)
1 Relativity and gravitational theory (83-XX)

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