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The design optimizaton of flow processes and the corresponding flow components for industrial applications is inherently complex due to the complexity of the associated computational fluid dynamics and multi-physics simulations. To practically optimize such processes, we apply techniques from PDE constrained optimization and focus on the following points: The efficiency of the solution algorithms and the quality of the employed mesh deformations. The former is significant as a single simulation of such a process can take hours to days and many simulations are required to perform an optimization. The latter has an enormous importance both on the performance of the optimization algorithm as well as the manufacturability of the obtained design. Mathematical research carried out in recent years in these directions has helped the field of shape optimization to mature. Moreover, improvements of additive manufacturing techniques allow the manufacturability of completely novel designs and facilitate the application of shape optimization to large-scale industrial applications.
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In this talk, we present our shape optimization approach for fluid dynamical applications. This includes our open-source software package cashocs, which automates the solution of shape optimization problems, as well as the shape optimization methods implemented within the software. As applications, we consider the optimization of structured packings for distillation processes, the arrangement of fiber patterns for industrial spinning processes, the design of flow fields for electrochemical cells as well as the optimization of chemical reactors. For all of these applications, shape optimization provides novel design ideas and can help to identify and leverage previously undiscovered potentials.
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Past activities
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* | **Kaiserslautern Applied and Industrial Mathematics Days (KLAIM) 2025**
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|*Talk: Fluid Dynamical Shape Optimization for Industrial Applications*
The design optimization of flow components for industrial applications is inherently complex. Techniques from PDE constrained shape optimization, which do not rely on a-priori parametrization of the domain, can facilitate the solution of such problems. The mathematical research carried out in recent years, which is primarily focused on the advancement of solution algorithms and mesh deformations, has helped these methods to mature. Moreover, improvements in additive manufacturing allow the manufacturability of completely novel designs and facilitate the application of shape optimization to industrial applications.
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In this talk, we will present our shape optimization approach for fluid dynamical applications. This includes our open-source software package cashocs, which automates the solution of shape optimization problems, as well as the methods implemented within the software. As applications, we consider the optimization of structured packings for distillation columns, the optimization of fiber patterns for industrial spinning processes, as well as the optimization of (electro-) chemical reactors. For all of these applications, shape optimization provides novel design ideas and helps to leverage previously undiscovered potentials.
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* | **European Conference on Computational Optimization (EUCCO) 2025**
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|*Organization of Focus Session: Shape and Topology Optimization together with Kevin Sturm*
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|September 29 - October 01, 2025, Klagenfurt, Austria
In shape optimization, the quality of the underlying mesh is of crucial importance. The mesh quality is particularly important when shape optimization problems constrained by partial differential equations (PDEs) are considered, as the mesh quality is essential for the numerical approximation of the PDE’s solutions. Even when starting with a very good mesh, the mesh quality usually tends to deteriorate over the course of a shape optimization. This either results in a premature stop of the optimization algorithm or a costly remeshing operation must be performed to continue with the optimization. In this talk, we present a novel approach for enforcing constraints on the mesh quality in shape optimization which guarantee a minimum mesh quality over the entire optimization. To do so, the angle of triangular and the solid angle of tetrahedral mesh cells is bounded from below. These constraints are treated with with Rosen’s gradient projection method which ensures that in each iteration the mesh is feasible w.r.t. the constraints. We present some numerical results of the proposed approach which highlights the applicability and performance of approach. In particular, with our approach, new shape optimization problems, particularly those relevant for industrial applications, which could not been solved with alternative approaches, can now be treated
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* | **European Symposium on Computer Aided Process Engineering (ESCAPE) 2025**
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|*Poster: CFD-Based Shape Optimization of Structured Packings for Enhancing Separation Efficiency in Distillation*
In past years the research in the field of structured packing development for laboratory-scale separation processes has intensified, where one of the main objectives is to miniaturize laboratory columns regarding the column diameter. This reduction has several advantages such as reduced operational costs and lower safety requirements due to a reduced amount of chemicals being used. However, a reduction in diameter also causes problems due to the increased surface-to-volume ratio, e.g., stronger impact of heat losses or liquid maldistribution issues. There are a lot of different approaches to design structured packings, such as using repeatedly stacked unit cells, but all of these approaches have in common that the development of new structures and the improvement of existing ones is based on educated guesses by the engineers.
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In this talk, we investigate the novel approach of applying techniques from free-form shape optimization to increase the separation efficiency of structured packings in laboratory-scale distillation columns. A simplified single-phase computational fluid dynamics (CFD) model for the mass transfer in the distillation column is used and a corresponding shape optimization problem is solved numerically with the optimization software cashocs. The optimization approach uses a free-form shape optimization, where the shape is not parametrized, e.g., with the help of a CAD model, but all nodes of the computational mesh are moved to alter the shape. Particularly, this approach allows for more freedom in the packing design than the classical, parametrized approach. The goal of the shape optimization is to increase the mass transfer in the column by changing the packing's shape. The numerical shape optimization yields promising results and shows a greatly increased mass transfer for the simplified CFD model. To validate our findings, the optimized shape is additively manufactured and investigated experimentally. The experimental results are in great agreeement with the simulation-based prediction and show that the separation efficiency of the packing increased by around 20 % as consequence of the optimization. Our results show that the proposed approach of using free-form shape optimization for improving structured packings in distillation is extremely promising and will be pursued further in future research.
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|June 12-14, 2024, Oslo, Norway
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|:bdg-link-primary-line:`Conference website <https://fenicsproject.org/fenics-2024/>` :bdg-link-secondary-line:`Recording of the talk <https://youtu.be/mZerFCRLtgQ?si=MDl3SmvU3GcQz-7w>`
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.. dropdown:: Abstract
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As the computational solution of PDE constrained shape optimization problems is still a very challenging task, there is high demand for efficient solution algorithms, particularly for complex problems arising from industrial applications. In this talk, we present cashocs, a software package which automates the solution of such problems and facilitates their efficient solution.
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The software allows users to formulate their problems in the high-level Unified Form Language (UFL), which closely resembles mathematical notation. As users only have to change a few lines in their code, switching from a simulation in FEniCS to an optimization with cashocs is straightforward. Moreover, cashocs uses the UFL to derive the corresponding adjoint systems and shape derivatives with automatic differentiation, so that there is no more need for tedious and error-prone calculations by hand.
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In cashocs, many state-of-the-art solution algorithms for shape and topology optimization problems are implemented, e.g., space mapping methods for shape optimization as well as quasi-Newton and nonlinear CG methods for both shape and topology optimization. Additionally, cashocs provides many sophisticated methods to ensure a sufficiently high mesh quality and even has support for automated remeshing, which is crucial for shape optimization. Finally, we present several industrial applications from fluid dynamical shape optimization which are optimized with cashocs. The results highlight the performance as well as the efficiency and applicability of cashocs even for very complex problems.
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* | **ACHEMA 2024**
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|*Talk: Multi-Criteria Shape Optimization of Flow Fields for Electrolyzers and Electrochemical Cells*
Even with modern hard- and software developments, the computational solution of PDE constrained shape optimization problems is still a very challenging task. There is high demand for efficient solution algorithms, particularly for complex problems arising from industrial applications. In this talk, we present cashocs, a software package which automates the solution of such problems and facilitates their efficient solution. The software cashocs allows users to formulate their problems in a high-level language closely resembling the underlying mathematics. Moreover, cashocs automatically derives adjoint systems and shape derivatives using automatic differentiation, so that there is no more need for tedious and error-prone manual calculations. Further, this automation also makes it very easy to make modifications to the cost functional or PDE constraints without having to re-perform these calculations.
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Our software implements many state-of-the-art solution algorithms for shape and topology optimization problems, such as space mapping methods for shape optimization, quasi-Newton methods for topology optimization, as well as BFGS and nonlinear CG methods for shape optimization. Additionally, cashocs provides many sophisticated methods to ensure a sufficiently high mesh quality and even has support for automated remeshing.
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To highlight the capabilities of cashocs, we present several industrial applications from fluid dynamical shape optimization which are solved with cashocs. The results showcase the wide variety of highly-performant solution methods as well as the efficiency and applicability of cashocs even for very complex problems.
Even with modern hard- and software developments, the numerical solution of PDE-constrained shape optimization problems can be very diffcult in pratice. In particular, for complex PDE models, the cost of a single simulation can be prohibitively large for solving the corresponding design optimization problem.
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The space mapping technique, originally introduced by Bandler in the context of microwave filter design, can facilitate and enable the solution of such complex problems by means of iteratively computing and refining a sequence of coarse model approximations.
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In this talk, we extend the space mapping technique to the case of infinite-dimensional shape optimization problems which are investigated with methods from shape calculus. In particular, we use recently developed Steklov-Poincar\'e-type metrics to derive aggressive space mapping algorithms in the context of PDE-constrained shape optimization. These algorithms are implemented and available in our open-source software cashocs, which can be used to easily solve arbitrary shape optimization problems numerically. Our investigation of the proposed space mapping method for several numerical examples validates our approach and shows its efficiency.
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