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In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
We present a Matlab code for modelling and topology optimization of hyperelastic structures, including contact modelled by the Third Medium Contact (TMC) approach. By using the so-called HuHu-regularization we penalize the skew distortion…
Aligning lattices based on local stress distribution is crucial for achieving exceptional structural stiffness. However, this aspect has primarily been investigated under a single load condition, where stress in 2D can be described by two…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
We present an efficient 140 line MATLAB code for topology optimization problems that include probabilistic parameters. It is built from the top99neo code by Ferrari and Sigmund and incorporates a stochastic sample-based approach. Old…
The purpose of this work is two-fold. First, we introduce an efficient homogenization-based approach to perform topology optimization of coated structures with orthotropic infill material. By making use of the relaxed design space, we can…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual…
The design of porous infill structures presents significant challenges due to their complex geometric configurations, such as the accurate representation of geometric boundaries and the control of localized maximum stress. In current…
We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…
This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
Large Language Models (LLMs) excel at both informal and formal (e.g. Lean 4) mathematical reasoning but still struggle with autoformalisation, the task of transforming informal into formal mathematical statements. Autoformalisation helps…
Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures, a novel asymptotic homogenisation topology optimisation…
This paper introduces a heuristic topology optimization framework for thin-walled, 2D extruded lattice structures subject to complex high-speed loading. The proposed framework optimizes the wall thickness distribution in the lattice cross…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…