ADIC: an extensible automatic differentiation tool for ANSI‐C

Bischof, Christian; Roh, Lucas; Mauer-Oats, A. J.

doi:10.1002/(sici)1097-024x(199712)27:12<1427::aid-spe138>3.3.co;2-h

Cited by 59 publications

(26 citation statements)

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“…It is up to the user to write additional code that calls the differentiated routines and incorporates the derivatives in whatever way necessary. This approach has been most successful for languages such as Fortran through tools such as ADIFOR [10], Tapenade [26], and OpenAD [51], but has also been used for C (e.g., ADIC [11]) and recently some C++ (e.g., OpenAD and TAC++ [55]). This approach is ideal in the sense that it provides the automatic differentiation tool a global view of the code to be differentiated, allowing optimization of the resulting derivative calculation.…”

Section: Automatic Differentiation Software Toolsmentioning

confidence: 99%

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Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part I: Template-Based Generic Programming

Pawlowski

Phipps

Salinger

2012

Scientific Programming

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An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering.

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Section: Automatic Differentiation Software Toolsmentioning

confidence: 99%

“…Comparison of Jacobian evaluation times for a simple vector PDE using several approaches: the original Sacado FAD AD tools in Sacado based on the original FAD library, the new Sacado FAD tools incorporating expression-level reverse mode and caching, source transformation with ADIC[11]…”

mentioning

confidence: 99%

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part I: Template-Based Generic Programming

Pawlowski

Phipps

Salinger

2012

Scientific Programming

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“…As such, software differentiation uses a discretize-then-differentiate approach to differentiating the governing equations for sensitivity analysis. Software differentiation pre-processors have been developed for C [27], Fortran [28,29], and MATLAB [30][31][32], among others. Software differentiation is not considered further in the present study.…”

Section: Software Differentiationmentioning

confidence: 99%

Sensitivity analysis of low Reynolds number channel flow using the finite volume method

Kirkman

Metzger

2007

Numerical Methods in Fluids

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SUMMARYAn unsteady finite volume-based fractional step algorithm solved on a staggered grid has been developed for computing design sensitivity parameters in two-dimensional flows. Verification of the numerical code is performed for the case of low Reynolds number, pressure-driven flow through a straight channel, which has an exact steady-state solution to the Navier-Stokes equations. Sensitivity of the flow to the channel height, fluid viscosity, and imposed pressure gradient is considered. Three different numerical techniques for computing the design sensitivity parameters: finite difference, complex-step differentiation, and sensitivity equation method (SEM), are compared in terms of numerical error (relative to the exact solution), computational expense, and ease of implementation. Results indicate that, of all the three methods, complex step is the most accurate and requires the least computational time. In addition, treatment of the boundary conditions in SEM is addressed, within the framework of the present finite volume approach, with special attention given to parameter dependence in the boundary conditions. Error estimation based on the Grid Convergence Index provides a good indication of the exact error in the SEM solutions. An example of application of the use of sensitivity parameters to estimate the propagation of input uncertainty through the numerical simulation is also provided.

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“…which, taking into account (7), is equivalent to The recursive evaluation of an adjoint associated with Z is shown in Figure 5. While all the extended state vectors are of length 2n, the exploitation of the matrix structure apparent in (9) implies that the amount of linear algebra work per time step remains, to rst order, unchanged. However, since we now have a linear recursion, the overall number of matrix-vector multiplications is 2(T ?…”

Section: A High-level Adjoint Recursionmentioning

confidence: 99%

Time-Parallel Computation of Pseudo-Adjoints for a Leapfrog Scheme

Bischof

Bücker

2004

Int. J. High Speed Comp.

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The leapfrog scheme is a commonly used second-order di erence scheme for solving di erential equations. If Z (t) denotes the state of the system at time t, the leapfrog scheme computes the state at the next time step as Z (t + 1) = H (Z(t); Z (t ? 1); W ), where H is the nonlinear timestepping operator and W are parameters that are not time dependent. In this article, we show how the associativity of the chain rule of di erential calculus can be used to compute a so-called adjoint x T (dZ(t)=d Z (0);W]) e ciently in a parallel fashion. To this end, we (1) employ the reverse mode of automatic di erentiation at the outermost level, (2) use a sparsity-exploiting incarnation of the forward mode of automatic di erentiation to compute derivatives of H at every time step, and (3) exploit chain rule associativity to compute derivatives at individual time steps in parallel. We report on experimental results with a 2-D shallow-water equation model problem on an IBM SP parallel computer and a network of Sun SPARCstations.

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ADIC: an extensible automatic differentiation tool for ANSI‐C

Cited by 59 publications

References 0 publications

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part I: Template-Based Generic Programming

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part I: Template-Based Generic Programming

Sensitivity analysis of low Reynolds number channel flow using the finite volume method

Time-Parallel Computation of Pseudo-Adjoints for a Leapfrog Scheme

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