MPI

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.


References in zbMATH (referenced in 487 articles , 1 standard article )

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  1. Botbol, Vincent; Chailloux, Emmanuel; Le Gall, Tristan: Static analysis of communicating processes using symbolic transducers (2017)
  2. Calandra, H.; Gratton, S.; Vasseur, X.: A geometric multigrid preconditioner for the solution of the Helmholtz equation in three-dimensional heterogeneous media on massively parallel computers (2017)
  3. Clay, M. P.; Buaria, D.; Gotoh, T.; Yeung, P. K.: A dual communicator and dual grid-resolution algorithm for petascale simulations of turbulent mixing at high Schmidt number (2017)
  4. Hernández-Gómez, Jorge J.; Couder-Castañeda, Carlos; Herrera-Díaz, Israel E.; Flores-Guzmán, Norberto; Gómez-Cruz, Enrique: Weakly coupled distributed calculation of Lyapunov exponents for non-linear dynamical systems (2017)
  5. Hofer, Christoph: Parallelization of continuous and discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods (2017)
  6. Jambunathan, Revathi; Levin, Deborah A.: Advanced parallelization strategies using hybrid MPI-CUDA octree DSMC method for modeling flow through porous media (2017)
  7. Jeong, Jena; Ramézani, Hamidréza; Leklou, Nordine: Porous-micro-dilatation theory for random crystallization: Monte Carlo simulation for delayed ettringite formation (2017)
  8. Kutepov, A. L.; Oudovenko, V. S.; Kotliar, G.: Linearized self-consistent quasiparticle GW method: application to semiconductors and simple metals (2017)
  9. Munguía, Lluís-Miquel; Ahmed, Shabbir; Bader, David A.; Nemhauser, George L.; Goel, Vikas; Shao, Yufen: A parallel local search framework for the fixed-charge multicommodity network flow problem (2017)
  10. Schutte, Aaron D.: A nilpotent algebra approach to Lagrangian mechanics and constrained motion (2017)
  11. Shui, Langquan; Liu, Yilun; Chen, Xi: Three dimensional wave propagation in time-varying materials: a mathematical model based on the weak solutions of continuity in the moving property interface (2017)
  12. Zhang, Shanghong; Li, Wenda; Jing, Zhu; Yi, Yujun; Zhao, Yong: Comparison of three different parallel computation methods for a two-dimensional dam-break model (2017)
  13. Briggs, J. P.; Pennycook, S. J.; Fergusson, J. R.; Jäykkä, J.; Shellard, E. P. S.: Separable projection integrals for higher-order correlators of the cosmic microwave sky: acceleration by factors exceeding 100 (2016)
  14. Ciobanu, Oana; Halpern, Laurence; Juvigny, Xavier; Ryan, Juliette: Overlapping domain decomposition applied to the Navier-Stokes equations (2016)
  15. Economon, Thomas D.; Mudigere, Dheevatsa; Bansal, Gaurav; Heinecke, Alexander; Palacios, Francisco; Park, Jongsoo; Smelyanskiy, Mikhail; Alonso, Juan J.; Dubey, Pradeep: Performance optimizations for scalable implicit RANS calculations with SU2 (2016)
  16. Fannon, James; Loiseau, Jean-Christophe; Valluri, Prashant; Bethune, Iain; Náraigh, Lennon Ó.: High-performance computational fluid dynamics: a custom-code approach (2016)
  17. Ghosh, Swarnava; Suryanarayana, Phanish: Higher-order finite-difference formulation of periodic orbital-free density functional theory (2016)
  18. Lenôtre, Lionel: A strategy for parallel implementations of stochastic Lagrangian simulation (2016)
  19. Mortensen, Mikael; Langtangen, Hans Petter: High performance python for direct numerical simulations of turbulent flows (2016)
  20. Rovenskaya, O. I.: Computational study of 3D rarefied gas flow in microchannel with 90 bend (2016)

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