By Aldo Ghizzetti (auth.), Aldo Ghizzetti (eds.)
A. Ghizzetti: a) Lezioni sui procedimenti di quasilinearizzazione e applicazioni. b) Nozioni fondamentali sulle equazioni alle differenze e sulle frazioni continue.- P. Wynn: 4 lectures at the numerical program of persevered fractions.- W. Gautschi: power and weak point of three-term recurrence relation.- F.L. Bauer: Use of persisted fractions and algorithms relating to them.
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A. Ghizzetti: a) Lezioni sui procedimenti di quasilinearizzazione e applicazioni. b) Nozioni fondamentali sulle equazioni alle differenze e sulle frazioni proceed. - P. Wynn: 4 lectures at the numerical program of persisted fractions. - W. Gautschi: power and weak spot of three-term recurrence relation.
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The driver is then modified for use with Rapsodia, and the library is generated with the appropriate settings for the order and the number or directions. For first orderÁ the number of directions is simply the number of inputs. Once the derivatives dy d xQ are calculated , the full derivatives can be reconstructed by multiplying the Rapsodia results by the Qr matrix used as input. With an effective rank of r D 3 and therefore a Qr matrix of dimension 50 3, the reconstructed derivatives were found to have relative errors on the order of 10 13 compared with results obtained from an unreduced Rapsodia calculation.
OpenAD/F: User Manual. Tech. , Argonne National Laboratory. pdf Application of Automatic Differentiation to an Incompressible URANS Solver ¨ Emre Ozkaya, Anil Nemili, and Nicolas R. Gauger Abstract This paper deals with the task of generating a discrete adjoint solver from a given primal Unsteady Reynolds Averaged Navier-Stokes (URANS) solver for incompressible flows. This adjoint solver is to be employed in active flow control problems to enhance the performance of aerodynamic configurations.
MATWS. A more realistic test problem was done with the MATWS (a subset of SAS4A ) Fortran code for nuclear reactor simulations. Single-channel calculations were performed by using as inputs the axial expansion coefficient, Doppler coefficient, moderator temperature coefficient, control rod driveline, and core radial expansion coefficient. The outputs of interest are temperatures within the channel in the coolant, the structure, the cladding, and the fuel. These give a 4 5 output for the first-order derivatives and 15 and 35 directions for second and third order, respectively.