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Aerospace : open access aeronautics journal 8(11), 322 (2021). doi:10.3390/aerospace8110322 special issue: "Special Issue "Computational Fluid Dynamics on High-Speed and Non-Equilibrium Flows" / Special Issue Editor: Prof. Dr. Marco Fossati, Guest Editor", Published by MDPI, Basel

In the field of turbomachinery, a multidisciplinary optimization may seek to optimize an objective in the discipline of fluid dynamics, e.g. maximizing efficiency, while satisfying constraints in the discipline of structural mechanics, e.g.keeping the maximum von Mises stress beneath a defined threshhold. This enables the design of components that are both aerodynamically optimized and structurally feasible. In order to respect structural constraints, gradient-based optimization methods require the sensitivities of the structural objectives with respect to the design variables. A discrete adjoint structural solver, based on the finite element method (FEM), and differentiated using adjoint algorithmic differentiation (AD), plays a key role in computing the structural sensitivities efficiently. The gradients can be computed at a cost of a single adjoint run for each objective function, independent on the size of the design space. Not only does this give us the opportunity to include a large number of design parameters, e.g. a large number of control points for a CAD-based shape paremetrization, but even to go beyond the usual shape design parameters and include composite material design parameters [1], [2] as well. This paves the way for an efficient simultaneous shape and material optimization using adjoint AD. In this work, we introduce the ongoing developments of a discrete adjoint structural solver that has the capabilities of computing sensitivities with respect to shape design parameters, as well as composite material design parameters, with a single adjoint run for each structural objective function. The solver is written in C++ and differentiated using the AD tool CoDiPack [3]. The theory behind this concept is discussed first, followed by preliminary results and a conclusion.

Dissertation, RWTH Aachen University, 2018; Aachen 1 Online-Ressource (vii, 232 Seiten) : Illustrationen (2019). = Dissertation, RWTH Aachen University, 2018, Computer simulations and computer aided design in the past decades have evolved into a valuable instrument, penetrating just about every branch of engineering in industry and academia. More specifically, computational fluid dynamics (CFD) simulations allow to inspect flow phenomena in a variety of applications. As simulation methods evolve, mature, and are adopted by a rising number of users, the demand for methods which not only predict the result of a specific configuration, but can give indications on how to improve the design, increases. This thesis is concerned with the efficient calculation of sensitivity information of CFD algorithms, and their application to numerical optimization. The sensitivities are obtained by applying Algorithmic Differentiation (AD).A specific emphasis of this thesis is placed on the efficient application of adjoint methods, including parallelism, for commonly used CFD finite volume methods (FVM) and their implementation in the open source framework OpenFOAM., Published by Aachen

This dissertation is concerned with the computation of arbitrary-order derivative projections (tangents and adjoints) of numerical simulation programs written in C++. Thanks to the increasing computational power, simulation nowadays plays a fundamental role within a wide range of applications. On this basis, in the last decades simulation programs became the foundation for optimization problems in a wide variety of domains, e.g. design optimization in computational fluid dynamics. When using derivative-based algorithms to carry out the optimization, first- and higher-order sensitivities of the underlying simulation program are required. Since in many cases gradients of scalar objective functions need to be computed, the adjoint method should be used. Adjoint programs can either be written by hand or generated by Algorithmic (or Automatic) Differentiation (AD) tools. AD is a semantic program transformation exploiting the chain rule of differential calculus to automatically generate programs such that sensitivities are computed in addition to the original function values. Writing adjoint programs by hand can be a tedious, time-consuming, and error-prone task, but on the other hand, the well-versed programmer can possibly write much more efficient code, especially when exploiting mathematical properties by symbolic transformations. When hand-coding an adjoint simulation program, an incremental software development process is difficult. To achieve an effective development process and get an efficient program, hybridization techniques can be used to couple an AD tool with hand-written code. This makes a top-down adjoint code development possible -- beginning with a pure AD solution, going step by step to a more efficient implementation.This thesis consists of three main points. First, the software dco/c++ is presented. dco/c++ implements AD by overloading in C++ and features hybridization techniques in a flexible and efficient way. Flexibility is meant in terms of compliance with a modern C++ environment (e.g. generic concepts, exception-safety, thread-safety, or portability), and in terms of a convenient interface with emphasis on the support for arbitrary-order derivatives. Efficiency on the other hand is ensured by the newly developed AD test suite, which carries out performance tests also in comparison to other AD tools.As the second main point, arbitrary-order derivative projections of common numerical algorithms like linear and nonlinear solvers are derived symbolically, exploiting mathematical properties. Those results are shown to be of practical relevance by connecting them to the hybridization capabilities of dco/c++. This combination is presented with the help of an extensive case study demonstrating the effectiveness of the approach. In addition, dco/c++ was successfully used in many projects and its applicability is therefore shown in terms of "reference projects".When using AD to generate an adjoint program, the resulting executable typically requires a huge amount of memory. The third point of this thesis therefore covers the Call Tree Reversal (CTR) problem. CTR is a checkpointing technique, which allows for a tradeoff between additional runtime and memory requirements. The problem itself is an NP-complete optimization problem, which in this thesis is approached by a mixed integer programming formulation for the first time.

Access to correct derivative information is crucial in numerical simulations andoptimization. While finite differences easily provide derivative approximationsthrough perturbing a function's inputs, the adjoint derivative model is the onlyway of acquiring a function's gradient both at machine precision and at the sametime complexity as the initial function evaluation. However, the adjoint model implies acomplete data flow reversal of an executed program. The same implication holds for the Message Passing Interface (MPI) of a parallel implementation. Everycommunication pattern has to be reversed when the adjoint model is applied. This work establishes a framework forthe semantic analysis of MPI communication patterns. It formulates a semanticdriven generation of adjoint patterns of the corresponding original patterns. The MPI standarddefines the semantics of every MPI communication in English language. A moreabstract representation of the MPI semantics is extracted and used in order toapply the logic of Algorithmic Differentiation (AD). Based on these adjointpattern representations a generic adjoint MPI library is implemented that may be usedsemi-automatically with any AD tool. Moreover, theruntime expectation of such an implementation on current cluster systems isanalyzed. The outcome is tested with two software packages used in numericalscience. One is the Portable Extensible Toolkit for Scientific computation(PETSc). It is currently one of the most robust frameworks for parallel linearand nonlinear solvers that exist. The other one is Sisyphe, a sedimenttransport simulation software used in the context of the fluid solver OpenTELEMAC.

International Conference on Computational Science 2016, ICCS 2016, 6-8 June 2016, San Diego, California, USA / Edited by Ilkay Altintas, Michael Norman, Jack Dongarra, ValeriaV. Krzhizhanovskaya, Michael Lees and Peter M.A. Sloot International Conference on Computational Science 2016, ICCS 2016, San Diego, California, USA, 6 Jun 2016 - 8 Jun 2016; Amsterdam [u.a.] : Elsevier, Procedia computer science, 80, 201-211 (2016). doi:10.1016/j.procs.2016.05.310, Published by Elsevier, Amsterdam [u.a.]

Sensitivity analysis with the aim of design optimization is a growing area of interest in Computational Fluid Dynamics (CFD) simulations. However, one of the major challenges is to deal with a large number of design variables for largescale industrial applications. One of the effective solution approaches is to compute adjoint-based sensitivities in the differentiated CFD code. In this paper, we develop a discrete adjoint code for an unstructured pressure-based steady Navier-Stokes solver using Algorithmic Differentiation (AD) by operator overloading (OO) tool. To reduce the huge memory requirement of the adjoint code we apply effective techniques by implementation of checkpointing schemes and by symbolic differentiation of the iterative linear solver. We combine the flexibility of an operator overloading tool with the efficiency of an adjoint code generated by source transformation through coupling these approaches. Moreover, we improve the performance of the adjoint computation by exploiting the mathematical aspects of the involved fixed-point iteration through reverse accumulation. We compare the effectiveness of these methods in terms of reduction of the numerical cost and accuracy of the sensitivities for the optimization of a vehicle climate duct industrial test case.

This is the user's manual for the version 2.1 of the Automatic Differentiation tool TAPENADE. Given a source computer program that computes a differentiable mathematical function $F$, TAPENADE builds a new source program that computes some of the derivatives of $F$, specifically directional derivatives ("tangent mode") and gradients ("reverse mode"). This report summarizes the mathematical justifications of Automatic Differentiation, then describes in full detail the differentiation model that TAPENADE implements. Our goal is to give the users of TAPENADE a precise understanding of the actions and choices made while differentiating programs, so as to improve their confidence in the produced source programs. This report documents all the available options and parameterizations that the users can give to TAPENADE, and conversely all the diagnosis and requirements that TAPENADE may issue towards the users. After a brief description of TAPENADE's architecture and performances, this report describes more fully the validation and improvement techniques for differentiated codes.