arXiv subjects

Sebastian Blauth

Publications and source records attributed to Sebastian Blauth.

At least 19 recordsLinked to original sources

arXiv2024

Enforcing Mesh Quality Constraints in Shape Optimization with a Gradient Projection Method

For the numerical solution of shape optimization problems, particularly those constrained by partial differential equations (PDEs), the quality of the underlying mesh is of utmost importance. Particularly when investigating complex geometries, the mesh quality tends to deteriorate over the course of a shape optimization so that either the optimization comes to a halt or an expensive remeshing operation must be performed before the optimization can be continued. In this paper, we present a novel, semi-discrete approach for enforcing a minimum mesh quality in shape optimization. Our approach is based on Rosen's gradient projection method, which incorporates mesh quality constraints into the shape optimization problem. The proposed constraints bound the angles of triangular and solid angles of tetrahedral mesh cells and, thus, also bound the quality of these mesh cells. The method treats these constraints by projecting the search direction to the linear subspace of the currently active constraints. Additionally, only slight modifications to the usual line search procedure are required to ensure the feasibility of the method. We present our method for two- and three-dimensional simplicial meshes. We investigate the proposed approach numerically for the drag minimization of an obstacle in a two-dimensional Stokes flow, the optimization of the flow in a pipe governed by the Navier-Stokes equations, and for the large-scale, three-dimensional optimization of a structured packing used in a distillation column. Our results show that the proposed method is indeed capable of guaranteeing a minimum mesh quality for both academic examples and challenging industrial applications. Particularly, our approach allows the shape optimization of complex structures while ensuring that the mesh quality does not deteriorate.

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arXiv2024

CFD-based Shape Optimization of Structured Packings for Enhancing Separation Efficiency in Distillation

Free-form shape optimization techniques are investigated to improve the separation efficiency of structured packings in laboratory-scale distillation columns. A simplified simulation model based on computational fluid dynamics (CFD) for the mass transfer in the distillation column is used and a corresponding shape optimization problem is formulated. The goal of the optimization is to increase the mass transfer in the column by changing the packing's shape, which has been previously used as criterion for increasing the separation efficiency of the column. The computational shape optimization yields promising results, with an increased mass transfer of nearly 20 %. For validation, the resulting optimized shape is additively manufactured using 3D-printing and investigated experimentally. The experimental results are in good agreement with the performance improvement predicted by the computational model, yielding an increase in separation efficiency of around 20 %.

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arXiv2024

A Novel Deflation Approach for Topology Optimization and Application for Optimization of Bipolar Plates of Electrolysis Cells

Topology optimization problems usually feature multiple local minimizers. To guarantee convergence to local minimizers that perform best globally or to find local solutions that are desirable for practical applications due to easy manufacturability or aesthetic designs, it is important to compute multiple local minimizers of topology optimization problems. In this paper, we introduce a novel deflation approach to systematically find multiple local minimizers of general topology optimization problems. The approach is based on a penalization of previously found local solutions in the objective. We validate our approach on the so-called two-pipes five-holes example. Finally, we introduce a model for the topology optimization of bipolar plates of hydrogen electrolysis cells and demonstrate that our deflation approach enables the discovery of novel designs for such plates.

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arXiv2024

Computing Multiple Local Minimizers for the Topology Optimization of Bipolar Plates in Electrolysis Cells

In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We use the Borvall-Petersson model to describe the fluid flow and derive a criterion for a uniform flow distribution in the bipolar plate. Furthermore, we introduce a novel deflation approach to compute multiple local minimizers of topology optimization problems. The approach is based on a penalty method that discourages convergence towards previously found solutions. Finally, we demonstrate this technique on the topology optimization for bipolar plates and show that multiple distinct local solutions can be found.

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arXiv2023

Continuous Synthesis of Diazo Acetonitrile: From Experiments to Physical and Grey-Box Modeling

Diazo compounds are gathering interest for their potential in promoting greener synthesis routes. We investigate, at a lab-scale, the continuous synthesis of diazo acetonitrile (DAN) using a micro-structured flow reactor and a flow reaction calorimeter. Data concerning DAN formation in the former, and relative to reaction heat and gas flow rate in the latter, are collected. We present both a physical and a grey-box simulation model, both of which are calibrated to our measurements. Both models provide valuable insights into the DAN synthesis. The grey-box approach is useful to incorporate the complex chemical reaction pathways for DAN synthesis and decomposition that are currently hard to address with the physical model.

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arXiv2023

Multi-Criteria Shape Optimization of Flow Fields for Electrochemical Cells

We consider the shape optimization of flow fields for electrochemical cells. Our goal is to improve the cell by modifying the shape of its flow field. To do so, we introduce simulation models of the flow field with and without the porous transport layer. The latter is less detailed and used for shape optimization, whereas the former is used to validate our obtained results. We propose three objective functions based on the uniformity of the flow and residence time as well as the wall shear stress. After considering the respective optimization problems separately, we use techniques from multi-criteria optimization to treat the conflicting objective functions systematically. Our results highlight the potential of our approach for generating novel flow field designs for electrochemical cells.

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arXiv2023

Topology Optimization for Uniform Flow Distribution in Electrolysis Cells

In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We present a model for the bipolar plate using the Stokes equation with an additional drag term, which models the influence of fluid and solid regions. Furthermore, we derive a criterion for a uniform flow distribution in the bipolar plate. To obtain shapes that are well-manufacturable, we introduce a novel smoothing technique for the fluid velocity. Finally, we present some numerical results and investigate the influence of the smoothing on the obtained shapes.

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arXiv2023

Version 2.0 -- cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software

In this paper, we present version 2.0 of cashocs. Our software automates the solution of PDE constrained optimization problems for shape optimization and optimal control. Since its inception, many new features and useful tools have been added to cashocs, making it even more flexible and efficient. The most significant additions are a framework for space mapping, the ability to solve topology optimization problems with a level-set approach, the support for parallelism via MPI, and the ability to handle additional (state) constraints. In this software update, we describe the key additions to cashocs, which is now even better-suited for solving complex PDE constrained optimization problems.

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arXiv2023

Quasi-Newton Methods for Topology Optimization Using a Level-Set Method

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andr\"a (A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, 216, 2006). To do so, we introduce a new perspective on the commonly used evolution equation for the level-set method, which allows us to derive our quasi-Newton methods for topology optimization. We investigate the performance of the proposed methods numerically for the following examples: Inverse topology optimization problems constrained by linear and semilinear elliptic Poisson problems, compliance minimization in linear elasticity, and the optimization of fluids in Navier-Stokes flow, where we compare them to current state-of-the-art methods. Our results show that the proposed solution algorithms significantly outperform the other considered methods: They require substantially less iterations to find a optimizer while demanding only slightly more resources per iteration. This shows that our proposed methods are highly attractive solution methods in the field of topology optimization.

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arXiv2023

Asymptotic Analysis for Optimal Control of the Cattaneo Model

We consider an optimal control problem with tracking-type cost functional constrained by the Cattaneo equation, which is a well-known model for delayed heat transfer. In particular, we are interested the asymptotic behaviour of the optimal control problems for a vanishing delay time $\tau \rightarrow 0$. First, we show the convergence of solutions of the Cattaneo equation to the ones of the heat equation. Assuming the same right-hand side and compatible initial conditions for the equations, we prove a linear convergence rate. Moreover, we show linear convergence of the optimal states and optimal controls for the Cattaneo equation towards the ones for the heat equation. We present numerical results for both, the forward and the optimal control problem confirming these linear convergence rates.

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arXiv2022

Space Mapping for PDE Constrained Shape Optimization

The space mapping technique is used to efficiently solve complex optimization problems. It combines the accuracy of fine model simulations with the speed of coarse model optimizations to approximate the solution of the fine model optimization problem. In this paper, we propose novel space mapping methods for solving shape optimization problems constrained by partial differential equations (PDEs). We present the methods in a Riemannian setting based on Steklov-Poincar\'e-type metrics and discuss their numerical discretization and implementation. We investigate the numerical performance of the space mapping methods on several model problems. Our numerical results highlight the methods' great efficiency for solving complex shape optimization problems.

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arXiv2022

Validating a Simulation Model for Laser-Induced Thermotherapy Using MR Thermometry

Laser-induced interstitial thermotherapy (LITT) is applied to ex-vivo porcine livers. An artificial blood vessel is used to study the cooling effect of larger blood vessels in proximity to the ablation zone. The same setting is simulated using a model based on partial differential equations (PDEs) for temperature, radiation, and tissue damage. The simulated temperature distributions are compared to temperature data obtained from MR thermometry. The study shows that the quality and resolution of the thermometry data is sufficient to validate and improve modeling approaches. Furthermore, the data can be used to identify missing model parameters as well as the exact placement of the laser applicator in relation to the imaging plane.

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arXiv2022

Shape Optimization with Nonlinear Conjugate Gradient Methods

In this chapter, we investigate recently proposed nonlinear conjugate gradient (NCG) methods for shape optimization problems. We briefly introduce the methods as well as the corresponding theoretical background and investigate their performance numerically. The obtained results confirm that the NCG methods are efficient and attractive solution algorithms for shape optimization problems.

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arXiv2020

cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software

The solution of optimization problems constrained by partial differential equations (PDEs) plays an important role in many areas of science and industry. In this work we present cashocs, a new software package written in Python, which automatically solves such problems in the context of optimal control and shape optimization. The software cashocs implements a discretization of the continuous adjoint approach, which derives the necessary adjoint systems and (shape) derivatives in an automated fashion. As cashocs is based on the finite element software FEniCS, it inherits its simple, high-level user interface. This makes it straightforward to define and solve PDE constrained optimization problems with our software. In this paper, we discuss the design and functionalities of cashocs and also demonstrate its straightforward usability and applicability.

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arXiv2020

Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov-Poincar\'e-Type Metrics

Shape optimization based on shape calculus has received a lot of attention in recent years, particularly regarding the development, analysis, and modification of efficient optimization algorithms. In this paper we propose and investigate nonlinear conjugate gradient methods based on Steklov-Poincar\'e-type metrics for the solution of shape optimization problems constrained by partial differential equations. We embed these methods into a general algorithmic framework for gradient-based shape optimization methods and discuss the numerical discretization of the algorithms. We numerically compare the proposed nonlinear conjugate gradient methods to the already established gradient descent and limited memory BFGS methods for shape optimization on several benchmark problems. The results show that the proposed nonlinear conjugate gradient methods perform well in practice and that they are an efficient and attractive addition to already established gradient-based shape optimization algorithms.

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arXiv2020

Optimal Control of the Sabatier Process in Microchannel Reactors

We consider the optimization of a chemical microchannel reactor by means of PDE constrained optimization techniques, using the example of the Sabatier reaction. To model the chemically reacting flow in the microchannels, we introduce a three- and a one-dimensional model. As these are given by strongly coupled and highly nonlinear systems of partial differential equations (PDEs), we present our software package cashocs which implements the adjoint approach and facilitates the numerical solution of the subsequent optimization problems. We solve a parameter identification problem numerically to determine necessary kinetic parameters for the models from experimental data given in the literature. The obtained results show excellent agreement to the measurements. Finally, we present two optimization problems for optimizing the reactor's product yield. First, we use a tracking-type cost functional to maximize the reactant conversion, keep the flow rate of the reactor fixed, and use its wall temperature as optimization variable. Second, we consider the wall temperature and the inlet gas velocity as optimization variables, use an objective functional for maximizing the flow rate in the reactor, and ensure the quality of the product by means of a state constraint. The results obtained from solving these problems numerically show great potential for improving the design of the microreactor.

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arXiv2020

Shape Sensitivity Analysis for a Microchannel Cooling System

We analyze the theoretical framework of a shape optimization problem for a microchannel cooling system. To this end, a cost functional based on the tracking of absorbed energy by the cooler as well as some desired flow on a subdomain of the cooling system is introduced. The flow and temperature of the coolant are modeled by a Stokes system coupled to a convection diffusion equation. We prove the well-posedness of this model on a domain transformed by the speed method. Further, we rigorously prove that the cost functional of our optimization problem is shape differentiable and calculate its shape derivative by means of a recent material derivative free adjoint approach.

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arXiv2019

Model Hierarchy for the Shape Optimization of a Microchannel Cooling System

We model a microchannel cooling system and consider the optimization of its shape by means of shape calculus. A three-dimensional model covering all relevant physical effects and three reduced models are introduced. The latter are derived via a homogenization of the geometry in 3D and a transformation of the three-dimensional models to two dimensions. A shape optimization problem based on the tracking of heat absorption by the cooler and the uniform distribution of the flow through the microchannels is formulated and adapted to all models. We present the corresponding shape derivatives and adjoint systems, which we derived with a material derivative free adjoint approach. To demonstrate the feasibility of the reduced models, the optimization problems are solved numerically with a gradient descent method. A comparison of the results shows that the reduced models perform similarly to the original one while using significantly less computational resources.

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