Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of ...
We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...
What training should engineering students receive to enable them to contribute to reducing bias, discrimination and the persistent lack of diversity in engineering? Collaboration is central to professional engineering work and, consequently, teamwork and g ...
Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...
The alkali-silica reaction (ASR), also known as concrete cancer, is one of the most prevalent causes of concrete degradation. In this chemical reaction, amorphous silica in the aggregates reacts with alkalis in the pore solution. By absorbing water, hydrop ...
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of ...
The response of the soil-structure interface can significantly affect the performance of any geotechnical structure. Thermal cycles are a new factor that influence the response to all structures that have an energy function in addition to the structural on ...
The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...
