Title:
Reading Course: A Monotone Spectral Gradient Method for (Linear) Elastic Problems

Abstract:

We consider the minimum compliance problem in the context of linear elastic topology optimization problems und show how to use classcial gradient-based optimization methods e.g. the optimality criteria method and the feasible direction method to solve it. A Helmholtz-based sensitivity filter is used to guarantee the existence of a solution and for avoiding the formation of checkerboard patterns. Since the goal of the presented work is to provide a framework for solving non-linear elastic topology optimization problems, we use algorithmic differentiation already in the linear case. We compare the numerical results of the different gradient-based optimization methods.

Dr. Praveen C., TIFR Center for Applicable Mathematics

Title:
Well-balanced discontinuous Galerkin method for Euler equations with gravity

Abstract:

We discuss a well-balanced discontinuous Galerkin scheme for compressible Euler equations with gravity. The DG scheme is based on nodal discontinuous Lagrange basis functions supported at Gauss-Lobatto-Legendre (GLL) nodes together with GLL quadrature using the same nodes. The scheme is able to preserve isothermal and polytropic stationary solutions upto machine precision on any mesh composed of quadrilateral cells. We provide numerical examples to show the performance of the scheme.

Lisa Kusch, SciComp

Title:
Robust Design in the Context of Deterministic Multi-Objective Optimization

Abstract:

Realistic engineering design involves the optimization of different competing objectives. Here, the aim is to find a set of solutions that fulfill the concept of Pareto optimality. A further significant step to realistic multiobjective designs is to take into account uncertainties for finding robust optimal solutions. So far, multi-objective robust design is mainly treated in an evolutionary context. There exist different methods to propagate uncertainties in the model. As the costs of a multi-objective optimization are already very high, it is important to use efficient approaches.

The aim is to find robust designs in multi-objective airfoil design. We apply a nonintrusive polynomial chaos approach for uncertainty quantification and the deterministic Epsilon-Constraint method for solving the multi-objective optimization problem. The concept of the Epsilon-Constraint Method is to optimize one objective function while imposing inequality constraints on the remaining competing objective functions. The constraints as well as the objective function to be optimized is varied to find different Pareto optimal solutions that are evenly distributed. For solving the sequence of these constrained single-objective
optimization problems we will make use of deterministic optimization strategies using algorithmic differentiation (AD) for the computation of derivatives.

The first significant steps towards multi-objective robust airfoil design are presented in the seminar talk.

Dr. Emre Özkaya, SciComp

Title:
A Discrete Adjoint Approach for Extended Helmholtz Resonator Model in Aeroacoustic Design Optimization

Abstract:

In this talk, we present a novel discrete adjoint approach for aeroacoustic design optimization. The main motivation behind the work is the noise minimization of turbofan engines using Extended Helmoltz type of acoustic liners. This type of optimization problems is characterized by a large number of design parameters and high computational cost caused by the unsteadiness of the physical phenomena and numerical methods that use forcibly higher order schemes in space and time to resolve the aeroacoustic sound propagation. In the first part of the talk, a brief review on the numerical methods used in Computational Aeroacoustics (CAA) will be given. Then, we focus on the Linearized Euler Equations (LEE) and liner impedance modelling using extended Helmholtz resonators. Finally, a discrete adjoint method that is used to compute the sensitivities of sound level with respect to liner parameters will be presented.

Stephanie Friedhoff, Ph.D., KU Leuven, Numerical Analysis and Applied Mathematics Section

Title:
Multigrid reduction techniques for parallel-in-time integration

Abstract:

With current trends in computer architectures leading towards systems with more, but not faster, processors, faster time-to-solution must come from greater parallelism. In this talk, we present an optimal-scaling, true multilevel approach to parallel-in-time integration based on multigrid reduction (MGR) principles. The resulting multigrid-reduction-in-time (MGRIT) algorithm is a non-intrusive approach, which directly uses an existing time propagator and, thus, can easily exploit substantially more computational resources than standard sequential time-stepping. Furthermore, we demonstrate that MGRIT offers excellent strong and weak parallel scaling up to thousands of processors for solving diffusion equations in two and three space dimensions. A complementary semi-algebraic mode analysis methodology will also be presented, which provides a predictive analysis tool for MGRIT and related algorithms on space-time grids.

Dr. H.C. Krahl, P. Wassermann, Robert Bosch GmbH, Fluid Dynamics.

Title:
Fluid Dynamics and Adjoint-based Optimization at Bosch Corporate Sector Research and Advance Engineering

Abstract:

We will introduce the group for Fluid Dynamics at the Corporate Sector Research and Advance Engineering of Robert Bosch GmbH and present the current activities with respect to adjoint methods in fluid dynamics. The first results of a feasibility study focusing on the optimization of an ECU cooling device will be presented, showing both the high potential of the approach and the limitations of the methods currently available in industry. The requirements for adjoint methods and sensitivity post-processing techniques will be discussed from an industrial point of view.

Prof. Charles Swanson, NASA Langley Research Center and Old Dominion University, USA

Title:
Design of RK/Implicit Schemes for Solving the Navier-Stokes Equations

Abstract:

The design and construction of accurate, robust, and efficient solution algorithms for solving the Navier-Stokes equations requires a complete understanding of the role and effectiveness of each component of the algorithm. One class of solution algorithms allowing substantial flexibility in the design process is the RK/Implicit schemes that have been developed in the last several years. Such numerical schemes are constructed with an explicit Runge-Kutta (RK) framework. The usual limitations of explicit schemes with respect to stability and solving stiff systems of equations are removed with an implicit preconditioner. The resulting contractive algorithm has good h-ellipticity and is used as a preconditioner for a full approximation scheme (FAS) multigrid. To ensure that the algorithm has certain properties various analysis techniques are employed. For example, Fourier analysis, and in particular eigensystem analysis, are applied to examine the stabiity and smoothing properties of such schemes. In this presentation the design of the various components and the analysis of these components will be discussed. The distinction between weak and strong solution algorithms will also be included in the discussion, as well as the consequences of numerial difficulties that arise with weak algorithms and the possibility of incorrect physical solutions.

Boyan Stefanov Lazarov, Ph.D., Technical University of Denmark, Department of Mechanical Engineering

Title:
On the length scale, robustness and manufacturability in topology optimization

Abstract:

Topology optimization has gained the status of being the preferred optimization tool in the mechanical, automotive, and aerospace industries. It has undergone tremendous development since its introduction in 1988, and nowadays it has spread to a number of other disciplines such as acoustics, optics, and material design. The basic idea is to distribute material in a predefined domain by minimizing a selected objective and fulfilling a set of constraints. The procedure consists of repeated system analyses, gradient evaluation steps by adjoint sensitivity analysis, and design updates based on mathematical programming methods. Existence of a solution is ensured by regularization techniques which result in intermediate density material regions. Manufacturing of the final optimized design requires post processing. However, any amendments can easily nullify the effect of the optimization. Therefore, the aim of this talk is to present recent developments in obtaining black and white manufacturable designs with clearly defined length scale. The focus is on the mathematical modeling of the material density, its link to micro- and nano- scale production techniques, and on the introduction of uncertainties in the optimization. The unified model results in manufacturable black and white designs with performance which is robust with respect to variations in the production process.

The result of the topology optimization procedure is a bitmap image of the design. The ability of the method to modify every pixel/voxel results in design freedom unavailable with any other alternative approach. However, this freedom requires the computational power of large parallel machines. Incorporating an uncertainty model in the optimization and the high contrast between the material phases further increase the computational cost. Hence, methods for reducing the computational complexity and handling the high material contrast will be presented and discussed as well. The development will be demonstrated in the design of compliant mechanisms, heat sinks, material microstructures for additive manufacturing, and photonic devices.

Prof. Olaf Frommann, Hochschule Bremen, Institut für Aerospace Technologie

Title:
About the Dilemma of Contradictory Goals in Multi-Objective Optimization

Abstract:

Multi-Objective Optimization often leads to the problem of dealing with competing and contradictory goals, that need to be satisfied. The question is, how much each single one of them is fulfilled in relation to the others. The inderdependencies can be visualized by the so-called Pareto Front, which shows the limit, where one goal can only be improved if the quality of another is degraded. Nevertheless, one needs to decide which combination of qualities is satisfactory. Usually, this is accomplished by the application of a weighted sum for the criteria within the objective function. Despite the fact that the choice of the weighting factors is rather arbitrary, it will only work on convex Pareto Fronts. It will be shown that, if there are concave sections, this approach cannot describe every possible combination of goals. As a solution to this limitation an alternative way to set up the objective function will be proposed. An additional advantage is the inherent simplicity in assessing single criteria and their interdependencies.

Prof. Stefan Becker, Christoph Scheit, Lehrstuhl für Prozessmaschinen und Anlagentechnik, Universität Erlangen-Nürnberg

Title: Aeroacoustics of Small Vertical Wind Turbines: Simulation and Experiment

Abstract:

The contents of the presentation is to validate two different numerical methods for noise prediction of the H-Darrieus wind turbine using a complementary approach consisting of experimental measurements and numerical simulations. The acoustic measurements of a model scale rotor were performed in an anechoic wind tunnel. This data is the basis for the validation of the computational aeroacoustic simulations. Thereby, we have applied two different numerical schemes for noise prediction using hybrid methods. As usual in hybrid aeroacoustic approaches, flow field and acoustic calculations are carried out in separate software packages. For both schemes the time-dependent turbulent flow field is solved with SAS. In the first scheme the acoustic source terms are computed according to Lighthill’s acoustic analogy which gives source terms located on the original CFD grid. The second scheme uses the Ffowcs Williams-Hawkings (FW-H) method which is based on a free field Green’s function. The scheme uses a porous integration surface and implements an advanced time formulation. Both methodologies are compared with experimental data.

Title: Parallelization and Optimization of Fastest-3D for Multicore Systems

Abstract:

In this case study, we demonstrate in detail how the performance, scalability, and flexibility of an existing, vector computer based CFD Code, namely Fastest-3D, could be improved to make it compatible with modern, highly parallel cluster systems. First, a node-level performance analysis is carried out in order to pinpoint the main bottlenecks and identify sweet spots for energy-efficient execution. In addition, a single-precision version of the solver for the linear equation system arising from the discretization of the governing equations is devised, which significantly increases the single-core performance. Then the communication mechanisms are analyzed and a new communication strategy based on non-blocking calls is implemented. Performance results with the revised version show significantly increased single-node performance and considerably improved communication patterns along with much better parallel scalability.

Prof. Qiqi Wang, MIT, Cambridge, USA

Title:
Design in Chaos — the Least Squares Shadowing technique for Sensitivity Analysis of Chaotic High Fidelity Simulations

Chaos is widespread in high fidelity simulations of engineering and natural systems. These systems, including turbulent flow and combustion, can exhibit sensitivity to initial conditions and other perturbations, a defining characteristic of chaos. High fidelity simulations of these systems, such as Large Eddy Simulations, are becoming increasingly practical through advances in high performance computing. They have the potential to introduce a step change in our ability to reliably predict performance of airplane and engine components. These simulations often capture the chaotic characteristics of the system they simulate.

High fidelity simulations of chaotic systems challenge existing techniques of extracting sensitivity information from simulations. Sensitivity analysis computes how output quantities of interest respond to changes in input parameters, and is widely used in design optimization, data assimilation, inverse problems and uncertainty quantification. Traditional techniques for sensitivity analysis fails for long time averages of chaotic systems, due to presence of the “sampling error.” The derivative of the sampling error increases as the objective function is averaged over longer time, due to the “butterfly effect” of chaotic dynamics. Corrupted by the large derivative of the sampling error, traditional sensitivity analysis produces erroneous results for chaotic unsteady flows.

This talk introduces the Least Squares Shadowing technique to overcome the challenge of sensitivity analysis in chaotic simulations. The shadowing condition replaces the initial condition, and enforces that similar design variables develop similar trajectories that “shadow” each other. Similar design variables thus have similar sampling errors. The derivative of the sampling error to the design variables is small, and the derivative computed by Least Squares Shadowing approximates the derivative of the true objective function. This talk will discuss the theory, computation and potential applications of the Least Squares Shadowing technique.

Gang Wang, Associate Professor at the Dept. of Fluid Dynamics/School of Aeronautics, Northwestern Polytechnical University, Xi’an, China

Title:
Flow Fluctuation Analysis Based on the Unsteady Flow Simulation with Variable Physical Time Stepping Scheme

Abstract:

An analysis technique on flow fluctuation combined with Non-Uniform Fast Fourier Transform (NUFFT) is developed and presented in this talk, which is based on the unsteady flow simulation with variable physical time stepping scheme. This technique is suitable to analyze fluctuation features of an unsteady flow in both time domain and frequency domain. The developed method has been integrated in a hybrid unstructured Navier-Stokes flow solver, HUNS3D. The buffeting flow around supercritical OAT15A airfoil and wake bursting flow around MD 30P/30N airfoil are simulated and analyzed for the validation and assessment of the presented technique. The ability and accuracy of this technique on predicting the fluctuation variables are verified by comparing the predicted results with the experimental data. The results show that the presented NUFFT flow fluctuating analysis technique achieves the balance between the computational cost and resolution requirements on the frequency spectral analysis.

Jonas Kusch, RWTH Aachen/TU Kaiserslautern

Title:
Frequency Based Preconditioning And Smoothing for Shape Optimization

Abstract:

In this talk, a preconditioner for shape optimization in the case of small Reynolds numbers will be derived. The preconditioner mimics the local Hessian behavior, which is derived analytically for the Stokes equations and investigated numerically for the Navier-Stokes equations. The derivation will show that the Hessian symbol has smoothing behavior, which is why we can think of the method as a local smoothing technique that will accelerate the optimization process. This acceleration is crucial as the raw steepest descent method will need a large number of computationally expensive optimization steps. In order to ensure a computationally cheap approximation of the Hessian symbol, the pseudo-differential Hessian behavior of order one is approximated by even order differential operators. To obtain a good approximation of the linear scaling behavior caused by the pseudo-differential Hessian behavior, we will make use of the windowed Fourier transform. We will use the knowledge of local frequencies to locally adapt the preconditioner, such that we have linear scaling for relevant frequencies.