By Michael Förster
Numerical courses frequently use parallel programming suggestions similar to OpenMP to compute the program's output values as effective as attainable. additionally, by-product values of those output values with appreciate to definite enter values play a very important position. to accomplish code that computes not just the output values at the same time but in addition the spinoff values, this paintings introduces a number of source-to-source transformation ideas. those principles are in line with a strategy referred to as algorithmic differentiation. the focus of this paintings lies at the vital opposite mode of algorithmic differentiation. The inherent data-flow reversal of the opposite mode has to be dealt with effectively through the transformation. the 1st a part of the paintings examines the ameliorations in a really basic approach when you consider that pragma-based parallel areas happen in lots of other forms resembling OpenMP, OpenACC, and Intel Phi. the second one half describes the transformation principles of an important OpenMP constructs.
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Extra info for Algorithmic Differentiation of Pragma-Defined Parallel Regions: Differentiating Computer Programs Containing OpenMP
The number of threads used to execute both parallel regions is the same. [. " private clause To declare thread local data one can use the private clause. 1 Citation 30 (p. 96). "The private clause declares one or more list items to be private to a task. The syntax of the private clause is as follows: p r i v a t e ( list ) 50 1 Motivation and Introduction Each task that references a list item that appears in a private clause in any statement in the construct receives a new list item whose language-specific attributes are derived from the original list item.
Let us illustrate how we apply dcc to obtain the tangent-linear model F (1) and the adjoint model F(1) of F. 1 since the dcc input language does not allow OpenMP pragmas at the moment. c contains the adjusted implementation of F, we apply the forward mode by calling dcc as follows: d c c F . c which contains the implementation of F (1) . Analogously, the adjoint model F(1) is obtained by the command line d c c F . c. When speaking about the implementations of the tangent-linear or the adjoint model we often speak about the tangent-linear and the adjoint code, respectively.
As a result, this heterogeneous approach allows to use the maximum number of cores that a certain cluster configuration has available, and the number of equations is not limited by the machine’s hardware constraints because the equations are distributed among cluster nodes with the help of MPI. Hybrid approaches with MPI/OpenMP usually show good scaling properties as presented for example in . Mathematical models in process engineering become more and more complex and with an increasing complexity the number of equations usually grows as well.