Residual-Based Isotropic and Anisotropic Mesh Adaptation for Computational Fluid Dynamics

The accuracy of a fluid flow simulation depends not only on the numerical method used for discretizing the governing equations, but also on the distribution and topology of the mesh elements. Mesh adaptation is a technique for automatically modifying the mesh in order to improve the simulation accuracy in an attempt to reduce the manual work required for mesh generation. The conventional approach to mesh adaptation is based on a feature-based criterion that identifies the distinctive features in the flow field such as shock waves and boundary layers. Although this approach has proved to be simple and effective in many CFD applications, its implementation may require a lot of trial and error for determining the appropriate criterion in certain applications. An alternative approach to mesh adaptation is the residual-based approach in which the discretization error of the fluid flow quantities across the mesh faces is used to construct an adaptation criterion. Although this approach provides a general framework for developing robust mesh adaptation criteria, its incorporation leads to significant computational overhead. The main objective of the thesis is to present a methodology for developing an appropriate mesh adaptation criterion for fluid flow problems that offers the simplicity of a feature-based criterion and the robustness of a residual-based criterion. This methodology is demonstrated in the context of a second-order accurate cell-centred finite volume method for simulating laminar steady incompressible flows of constant property fluids. In this methodology, the error of mass and momentum flows across the faces of each control volume are estimated with a Taylor series analysis. Then these face flow errors are used to construct the desired adaptation criteria for triangular isotropic meshes and quadrilateral anisotropic meshes. The adaptation results for the lid-driven cavity flow show that the solution error on the resulting adapted meshes is 80 to 90 percent lower than that of a uniform mesh with the same number of control volumes. The advantage of the proposed mesh adaptation method is the capability to produce meshes that lead to more accurate solutions compared to those of the conventional methods with approximately the same amount of computational effort

Source-Free and Image-Only Unsupervised Domain Adaptation for Category Level Object Pose Estimation

We consider the problem of source-free unsupervised category-level pose estimation from only RGB images to a target domain without any access to source domain data or 3D annotations during adaptation. Collecting and annotating real-world 3D data and corresponding images is laborious, expensive, yet unavoidable process, since even 3D pose domain adaptation methods require 3D data in the target domain. We introduce 3DUDA, a method capable of adapting to a nuisance-ridden target domain without 3D or depth data. Our key insight stems from the observation that specific object subparts remain stable across out-of-domain (OOD) scenarios, enabling strategic utilization of these invariant subcomponents for effective model updates. We represent object categories as simple cuboid meshes, and harness a generative model of neural feature activations modeled at each mesh vertex learnt using differential rendering. We focus on individual locally robust mesh vertex features and iteratively update them based on their proximity to corresponding features in the target domain even when the global pose is not correct. Our model is then trained in an EM fashion, alternating between updating the vertex features and the feature extractor. We show that our method simulates fine-tuning on a global pseudo-labeled dataset under mild assumptions, which converges to the target domain asymptotically. Through extensive empirical validation, including a complex extreme UDA setup which combines real nuisances, synthetic noise, and occlusion, we demonstrate the potency of our simple approach in addressing the domain shift challenge and significantly improving pose estimation accuracy.Comment: 36 pages, 9 figures, 50 tables; ICLR 2024 (Poster

Improved Artificial Viscosity in Finite Element Method (FEM) for Hypervelocity Impact Calculations

AbstractIn this paper we develop methods based primarily on the work of Kuropatenko and Wilkins to improve the application of artificial viscosity in 3D finite element method (FEM) codes. The primary goal is to obtain better shock predictions for hypervelocity impacts (HVI) and reduce the need for user calibration. We focus on examining factors such as geometric variability with respect to shock direction, dynamic adaptation to changes in compressibility in the shock front, and anisotropic compression in multi-dimensional formulations. We implement the methods in the Velodyne hydro-structural code and investigate the effects on shock propagation using a series of simple flyer impact test cases which cover a range of system responses including strong and weak shocks. Various initial mesh geometries are utilized to examine mesh effects. Energetic materials using the Ignition and Growth Reactive Burn (IGRB) equation of state (EOS) are also examined due to the rapid change in compressibility and energy density which occurs due to reaction. These rapid changes can lead to insufficient damping in artificial viscosity calculations and thus provide an effective test case. We employ the CTH hydrocode to evaluate baseline shock behavior. The regular, ordered mesh of CTH allows for a consistent and precise application of the artificial viscosity. Direct numerical comparisons are used rather than experimental data to eliminate uncertainty due to factors such as material characterizations, EOS models, and mesh resolution. We compare the CTH results against various FEM artificial viscosity implementations to evaluate performance. It is demonstrated that shock response in FEM codes can be significantly improved by using updated artificial viscosity methods

Multimedia delivery in the future internet

The term “Networked Media” implies that all kinds of media including text, image, 3D graphics, audio and video are produced, distributed, shared, managed and consumed on-line through various networks, like the Internet, Fiber, WiFi, WiMAX, GPRS, 3G and so on, in a convergent manner [1]. This white paper is the contribution of the Media Delivery Platform (MDP) cluster and aims to cover the Networked challenges of the Networked Media in the transition to the Future of the Internet. Internet has evolved and changed the way we work and live. End users of the Internet have been confronted with a bewildering range of media, services and applications and of technological innovations concerning media formats, wireless networks, terminal types and capabilities. And there is little evidence that the pace of this innovation is slowing. Today, over one billion of users access the Internet on regular basis, more than 100 million users have downloaded at least one (multi)media file and over 47 millions of them do so regularly, searching in more than 160 Exabytes1 of content. In the near future these numbers are expected to exponentially rise. It is expected that the Internet content will be increased by at least a factor of 6, rising to more than 990 Exabytes before 2012, fuelled mainly by the users themselves. Moreover, it is envisaged that in a near- to mid-term future, the Internet will provide the means to share and distribute (new) multimedia content and services with superior quality and striking flexibility, in a trusted and personalized way, improving citizens’ quality of life, working conditions, edutainment and safety. In this evolving environment, new transport protocols, new multimedia encoding schemes, cross-layer inthe network adaptation, machine-to-machine communication (including RFIDs), rich 3D content as well as community networks and the use of peer-to-peer (P2P) overlays are expected to generate new models of interaction and cooperation, and be able to support enhanced perceived quality-of-experience (PQoE) and innovative applications “on the move”, like virtual collaboration environments, personalised services/ media, virtual sport groups, on-line gaming, edutainment. In this context, the interaction with content combined with interactive/multimedia search capabilities across distributed repositories, opportunistic P2P networks and the dynamic adaptation to the characteristics of diverse mobile terminals are expected to contribute towards such a vision. Based on work that has taken place in a number of EC co-funded projects, in Framework Program 6 (FP6) and Framework Program 7 (FP7), a group of experts and technology visionaries have voluntarily contributed in this white paper aiming to describe the status, the state-of-the art, the challenges and the way ahead in the area of Content Aware media delivery platforms

Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction

Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we combine the moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the lazy flip technique, a reversible edge removal algorithm to modify the mesh connectivity. Moreover, we utilize radial basis function (RBF) surface reconstruction to improve tetrahedral meshes with curved boundary surfaces. Numerical tests show that the combination of these techniques into a mesh improvement framework achieves results which are comparable and even better than the previously reported ones.Comment: Revised and improved versio

A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily implement various numerical algorithms.Two robust and optimised numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are implemented to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models

Computation of Ground States of the Gross-Pitaevskii Functional via Riemannian Optimization

In this paper we combine concepts from Riemannian Optimization and the theory of Sobolev gradients to derive a new conjugate gradient method for direct minimization of the Gross-Pitaevskii energy functional with rotation. The conservation of the number of particles constrains the minimizers to lie on a manifold corresponding to the unit $L^2$ norm. The idea developed here is to transform the original constrained optimization problem to an unconstrained problem on this (spherical) Riemannian manifold, so that fast minimization algorithms can be applied as alternatives to more standard constrained formulations. First, we obtain Sobolev gradients using an equivalent definition of an $H^1$ inner product which takes into account rotation. Then, the Riemannian gradient (RG) steepest descent method is derived based on projected gradients and retraction of an intermediate solution back to the constraint manifold. Finally, we use the concept of the Riemannian vector transport to propose a Riemannian conjugate gradient (RCG) method for this problem. It is derived at the continuous level based on the "optimize-then-discretize" paradigm instead of the usual "discretize-then-optimize" approach, as this ensures robustness of the method when adaptive mesh refinement is performed in computations. We evaluate various design choices inherent in the formulation of the method and conclude with recommendations concerning selection of the best options. Numerical tests demonstrate that the proposed RCG method outperforms the simple gradient descent (RG) method in terms of rate of convergence. While on simple problems a Newton-type method implemented in the {\tt Ipopt} library exhibits a faster convergence than the (RCG) approach, the two methods perform similarly on more complex problems requiring the use of mesh adaptation. At the same time the (RCG) approach has far fewer tunable parameters.Comment: 28 pages, 13 figure