Fully and Semi-Automated Shape Differentiation in NGSolve

Gangl, Peter; Sturm, Kevin; Neunteufel, Michael; Schöberl, Joachim

doi:10.48550/arxiv.2004.06783

Cited by 5 publications

(5 citation statements)

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“…All computations were conducted using the NGSolve [12,32] framework with its python interface. Three sets of results are presented in this section to validate the proposed strategy.…”

Section: Application To the Magnetostatics Problemmentioning

confidence: 99%

Multi-Material Topology Optimization with Continuous Magnetization Direction for Permanent Magnet Synchronous Reluctance Motors

Gauthey,

Gangl,

Hassan

2021

Preprint

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Permanent magnet-assisted synchronous reluctance motors (PMSynRM) have a significantly higher average torque than synchronous reluctance motors. Thus, determining an optimal design results in a multi-material topology optimization problem, where one seeks to distribute ferromagnetic material, air and permanent magnets within the rotor in an optimal manner.This study proposed a novel density-based distribution scheme, which allows for continuous magnetization direction instead of a finite set of angles. Thus, an interpolation scheme is established between properties pertaining to magnets and non-linear materials. This allows for new designs to emerge without introducing complex geometric parameterization or relying on the user's biases and intuitions. Toward reducing computation time, Nitsche-type mortaring is applied, allowing for free rotation of the rotor mesh relative to the stator mesh. The average torque is approximated using only four-point static positions. This study investigates several interpolation schemes and presents a new one inspired by the topological derivative. We propose to filter the final design for the magnetization angle using K-mean clustering accounting for technical feasibility constraints of magnets. Finally, the design of the electrical motor is proposed to maximize torque value.

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“…All computations were conducted using the NGSolve [12,32] framework with its python interface. Three sets of results are presented in this section to validate the proposed strategy.…”

Section: Application To the Magnetostatics Problemmentioning

confidence: 99%

Multi-Material Topology Optimization with Continuous Magnetization Direction for Permanent Magnet Synchronous Reluctance Motors

Gauthey,

Gangl,

Hassan

2021

Preprint

Self Cite

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“…Consequently, it is not feasible to carry it out by hand anymore (see, e.g., [7]). For these reasons, there has been a lot of effort recently to automate the tasks for solving PDE constrained optimization problems, resulting in software such as dolfin-adjoint [8], Fireshape [9], NGSolve [10], and our software cashocs. What distinguishes cashocs from these other packages is its novel approach of using automatic differentiation solely to derive the adjoint system and (shape) derivatives, while implementing and automating a discretization of the continuous adjoint approach in all remaining aspects.…”

Section: Motivation and Significancementioning

confidence: 99%

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

Blauth

2020

Preprint

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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 a new software package for Python, called cashocs, which automatically solves such problems in the context of optimal control and shape optimization. Our software 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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“…In AD, code tools are used to differentiate the discretization 7,8 rather than taking the approach of the volume method, which is to discretize the shape derivative. 9 AD is a promising method for shape differentiation, but without the strip method, it suffers from the same invasiveness as the volume method.…”

Section: Introductionmentioning

confidence: 99%

The strip method for shape derivatives

Hardesty

Antil

Kouri

et al. 2022

Numerical Meth Engineering

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A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. The volume and boundary methods are two approaches to computing shape derivatives. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. As an added benefit, its computational complexity is comparable to that of the boundary method, that is, it is faster than the volume method. We illustrate the benefits of the strip method with numerical examples.

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Fully and Semi-Automated Shape Differentiation in NGSolve

Cited by 5 publications

References 0 publications

Multi-Material Topology Optimization with Continuous Magnetization Direction for Permanent Magnet Synchronous Reluctance Motors

Multi-Material Topology Optimization with Continuous Magnetization Direction for Permanent Magnet Synchronous Reluctance Motors

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

The strip method for shape derivatives

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