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A Primer on Laplacians
Published in Kai Hormann, N. Sukumar, Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics, 2017
In this chapter we review some important properties of Laplacians, smooth and discrete. We place special emphasis on a unified framework for treating smooth Laplacians on Riemannian manifolds alongside discrete Laplacians on graphs and simplicial manifolds. We cast this framework into the language of linear algebra, with the intent to make this topic as accessible as possible. We combine perspectives from smooth geometry, discrete geometry, spectral analysis, machine learning, numerical analysis, and geometry processing within this unified framework. The connection to generalized barycentric coordinates is established through harmonic functions that interpolate given boundary conditions.
Embedding Kalker's variational theory into railway vehicle system dynamics and its efficiency improvement
Published in Vehicle System Dynamics, 2023
On the other side, automatic wheel–rail geometry processing for online simulation is specifically needed to facilitate the integration of KVT into railway vehicle dynamics and guarantee the accuracy of the contact analysis. A completely workable wheel–rail geometry processing method was proposed in Ref. [31,32], which had also been extended to conformal contacts [33]. Based on this method, Ref. [31,34] imported the results of the wheelset kinematics from multi-body software to CONTACT for more accurate local contact results, but this is an offline integration. Recently, Liu [35] and Spiryagin [36–38] implemented contact evaluation in online simulations with Vollebregt's CONTACT [32]. Liu [35] used SIMPACK Rail to develop the multi-body model of the vehicle, where the normal forces calculated by SIMPACK were as input for CONTACT, and CONTACT returned the creep forces to the multi-body model. This seems to be a relatively weak coupling between the multi-body model and wheel–rail contact. Spiryagin [36–38] investigated heavy haul locomotives with multi-body software GENSYS integrated with Vollebregt's CONTACT for normal and creep forces, using a fourth order Runge–Kutta integrator.
Spectral decomposition and illustration-inspired visualisation of highly disturbed cerebrovascular blood flow dynamics
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2020
Thangam Natarajan, Daniel E. MacDonald, Mehdi Najafi, Peter W. Coppin, David A. Steinman
After the silhouette extraction, colouring and shading are processed on the surfaces of the flow structures. A toon or cel-shading approach is adopted, which offers two main advantages. First, when the surfaces are rendered with a two-tone toon shading approach, the lit surfaces provide focus emphasis and the unlit dark areas or shadows provide depth and increase the amount of cues for spatial perception. This substantially increases the visual comprehensibility of the image as opposed to a conventional visualisation. Secondly, since the toon-shaded surfaces are less reflective and transmissive, the memory footprint on both CPU’s and GPU’s is much lower as compared to rendering a photo-realistic image allowing the user to visualise in real-time. ParaView (Ayachit 2015) was used for the velocity reconstruction and surface extraction as we took advantage of its access to VTK functionalities including gradient filters, geometry processing subroutines and its inbuilt Python API. The subsequent rendering and animations are performed with Blender’s Python API (Blender Online Community 2017).
Capturing simulation intent in an ontology: CAD and CAE integration application
Published in Journal of Engineering Design, 2019
Flavien Boussuge, Christopher M. Tierney, Harold Vilmart, Trevor T. Robinson, Cecil G. Armstrong, Declan C. Nolan, Jean-Claude Léon, Federico Ulliana
Similarly, Rule 2 associates a pressure boundary condition as a simulation attribute attached to the CellInterfaces between a heat-shield protection component and a fluid domain. Such inference allows the robust location and selection of all the faces of the heat shield component in contact with the fluid domain. In addition, as the cellular model generates the imprints of one object onto another, the tedious task to delimit the fluid domain is also avoided. Currently, the rule does not distinguish between the interior and exterior fluid domains. Future work will develop a geometry processing and partitioning algorithm to distinguish the cavities from the exterior fluid domain in order to enrich the knowledge base allowing the user to specify an even more precise simulation intent. Additional rules are provided in Appendix.