Browsing by Author "Tadjouddine, Mohamed"

Now showing 1 - 6 of 6
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    AD Tools and Prospects for Optimal AD in CFD Flux Jacobian Calculations.
    (2002-01-01T00:00:00Z) Tadjouddine, Mohamed; Forth, Shaun A.; Pryce, John D.
    We consider the problem of linearising the short (approximately 100 lines of) code that defines the numerical fluxes of mass, energy and momentum across a cell face in a finite volume compressible flow calculation. Typical of such formulations is the numerical flux due to Roe, widely used in the numerical approximation of flow fields containing moderate to strong shocks. Roe's flux takes as input 10 variables describing the flow either side of a cell face and returns as output the 5 variables for the numerical flux. We present results concerning the efficiency of derivative calculations for Roe's flux using several currently available AD tools. We also present preliminary work on deriving near optimal differentiated code using the node elimination approach. We show that such techniques, within a source transformation approach, will yield substantial gains for application code such as the Roe flux.
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    Adjoint Differentiation of a Structural Dynamics Solver.
    (2006-12-01T00:00:00Z) Tadjouddine, Mohamed; Forth, Shaun A.; Keane, Andy J.
    The design of a satellite boom using passive vibration control by Keane [J. of Sound and Vibration, 1995, 185(3),441-453] has previously been carried out using an energy function of the design geometry aimed at minimising mechanical noise and vibrations. To minimise this cost function, a Genetic Algorithm (GA) was used, enabling modification of the initial geometry for a better design. To improve efficiency, it is proposed to couple the GA with a local search method involving the gradient of the cost function. In this paper, we detail the generation of an adjoint solver by automatic differentiation via ADIFOR. This has resulted in a gradient code that runs in 7.4 times the time of the function evaluation. This should reduce the rather time-consuming process (over 10 CPU days by using parallel processing) of the GA optimiser for this problem.
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    Hierarchical automatic differentiation by vertex elimination and source transformation.
    (Springer-verlag, 2003-01-01T00:00:00Z) Tadjouddine, Mohamed; Forth, Shaun A.; Pryce, John D.
    We present a hierarchical scheme to extend the applicability of automatic differentiation (AD) by vertex elimination from the basic block level to code with branches and subroutine calls. We introduce the ELIAD tool that implements our scheme. Results from computational fluid dynamics (CFD) flux linearisations show runtime speedup by a typical factor of two over both finite-differencing and traditional forward and reverse modes of AD.
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    Improving the performance of the vertex elimination algorithm for derivative calculation
    (2006-01-01T00:00:00Z) Tadjouddine, Mohamed; Bodman, Frances; Pryce, John D.; Forth, Shaun A.
    In previous work [TOMS, 2004, 30(3), 266--299], we used Markowitz-like heuristics aiming to find elimination sequences that minimise the number of floating-point operations (flops) for vertex elimination Jacobian code. We also used the depth-first traversal algorithm to reorder the statements of the Jacobian code with the aim of reducing the number of memory accesses. In this work, we study the effects of reducing flops or memory accesses within the vertex elimination algorithm for Jacobian calculation. On RISC processors, we observed that for data residing in registers, the number of flops gives a good estimate of the execution time, while for out-of-register data, the execution time is dominated by the time for memory access operations. We also present a statement reordering scheme based on a greedy-list scheduling algorithm using ranking functions. This statement reordering will enable us to trade-off the exploitation of the instruction level parallelism of such processors with the reduction in memory accesses.
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    Jacobian Code Generated by Source Transformation and Vertex Elimination can be as Efficient as Hand-Coding
    (ACM Association for Computing Machinery, 2004-09-01T00:00:00Z) Forth, Shaun A.; Tadjouddine, Mohamed; Pryce, John D.; Reid, John K.
    This article presents the first extended set of results from ELIAD, a source- transformation implementation of the vertex-elimination Automatic Differentiation approach to calculating the Jacobians of functions defined by Fortran code (Griewank and Reese, Automatic Differentiation of Algorithms: Theory, Implementation, and Application, 1991, pp. 126-135). We introduce the necessary theory in terms of well known algorithms of numerical linear algebra applied to the linear, extended Jacobian system that prescribes the relationship between the derivatives of all variables in the function code. Using an example, we highlight the potential for numerical instability in vertex-elimination. We describe the source transformation implementation of our tool ELIAD and present results from five test cases, four of which are taken from the MINPACK- 2 collection (Averick et al, Report ANL/MCS-TM-150, 1692) and for which hand- coded Jacobian codes are available. On five computer/compiler platforms, we show that the Jacobian code obtained by ELIAD is as efficient as hand-coded Jacobian code. It is also between 2 to 20 times more efficient than that produced by current, state of the art, Automatic Differentiation tools even when such tools make use of sophisticated techniques such as sparse Jacobian compression. We demonstrate the effectiveness of reverse-ordered pre-elimination from the (successively updated) extended Jacobian system of all intermediate variables used once. Thereafter, the monotonic forward/reverse ordered eliminations of all other intermediates is shown to be very efficient. On only one test case were orderings determined by the Markowitz or related VLR heuristics found superior. A re-ordering of the statements of the Jacobian code, with the aim of reducing reads and writes of data from cache to registers, was found to have mixed effects but could be very beneficial.
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    Performance Issues for Vertex Elimination Methods in Computing Jacobians using Automatic Differentiation.
    (Springer-Verlag, 2002) Tadjouddine, Mohamed; Forth, Shaun A.; Pryce, John D.; Reid, John K.
    In this paper, we present first results from EliAD, a new automatic differentiation tool. EliAD uses the Elimination approach for Automatic Differentation first advocated by Griewank and Reese (Automatic Differentiation of Algorithms, SIAM, 1991 p126-135). EliAD implements this technique via source-transformation, writing new Fortran code for the Jacobians of functions defined by existing Fortran code. Our results are from applying EliAD to the Roe flux routine commonly used in computational fluid dynamics. We show that we can produce code that calculates the associated flux Jacobian approaching or in excess of twice the speed of current state-of-the-art automatic differentiation tools. However, in order to do so we must take into account the architecture on which we are running our code. In particular, on processors that do not support out-of-order execution, we must reorder our derivative code so that values may be reused while in arithmetic registers in order that the floating point arithmetic pipeline may be kept full.