This article proposes an open-source implementation of a phase-field model for brittle fracture using a recently developed finite element toolbox, Gridap in Julia. The present work exploits the advantages of both the phase-field model and Gridap toolbox for simulating fracture in brittle materials. On one hand, the use of the phase-field model, which is a continuum approach and uses a diffuse representation of sharp cracks, enables the proposed implementation to overcome such well-known drawbacks of the discrete approach for predicting complex crack paths as the need for re-meshing, enrichment of finite element shape functions and an explicit tracking of the crack surfaces. On the other hand, the use of Gridap makes the proposed implementation very compact and user-friendly that requires low memory usage, and provides a high degree of flexibility to the users in defining weak forms of partial differential equations. A test on a notched beam under symmetric three-point bending and a set of tests on a notched beam with three holes under asymmetric three-point bending is considered to demonstrate how the proposed Gridap based phase-field Julia code can be used to simulate fracture in brittle materials.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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The impending termination of Moore's law motivates the search for new forms of computing to continue the performance scaling we have grown accustomed to. Among the many emerging Post-Moore computing candidates, perhaps none is as salient as the Field-Programmable Gate Array (FPGA), which offers the means of specializing and customizing the hardware to the computation at hand. In this work, we design a custom FPGA-based accelerator for a computational fluid dynamics (CFD) code. Unlike prior work -- which often focuses on accelerating small kernels -- we target the entire Poisson solver on unstructured meshes based on the high-fidelity spectral element method (SEM) used in modern state-of-the-art CFD systems. We model our accelerator using an analytical performance model based on the I/O cost of the algorithm. We empirically evaluate our accelerator on a state-of-the-art Intel Stratix 10 FPGA in terms of performance and power consumption and contrast it against existing solutions on general-purpose processors (CPUs). Finally, we propose a data movement-reducing technique where we compute geometric factors on the fly, which yields significant (700+ Gflop/s) single-precision performance and an upwards of 2x reduction in runtime for the local evaluation of the Laplace operator. We end the paper by discussing the challenges and opportunities of using reconfigurable architecture in the future, particularly in the light of emerging (not yet available) technologies.
Generative Adversarial Networks are a popular method for learning distributions from data by modeling the target distribution as a function of a known distribution. The function, often referred to as the generator, is optimized to minimize a chosen distance measure between the generated and target distributions. One commonly used measure for this purpose is the Wasserstein distance. However, Wasserstein distance is hard to compute and optimize, and in practice entropic regularization techniques are used to improve numerical convergence. The influence of regularization on the learned solution, however, remains not well-understood. In this paper, we study how several popular entropic regularizations of Wasserstein distance impact the solution in a simple benchmark setting where the generator is linear and the target distribution is high-dimensional Gaussian. We show that entropy regularization promotes the solution sparsification, while replacing the Wasserstein distance with the Sinkhorn divergence recovers the unregularized solution. Both regularization techniques remove the curse of dimensionality suffered by Wasserstein distance. We show that the optimal generator can be learned to accuracy $\epsilon$ with $O(1/\epsilon^2)$ samples from the target distribution. We thus conclude that these regularization techniques can improve the quality of the generator learned from empirical data for a large class of distributions.
A promising option for storing large-scale quantities of green gases (e.g., hydrogen) is in subsurface rock salt caverns. The mechanical performance of salt caverns utilized for long-term subsurface energy storage plays a significant role in long-term stability and serviceability. However, rock salt undergoes non-linear creep deformation due to long-term loading caused by subsurface storage. Salt caverns have complex geometries and the geological domain surrounding salt caverns has a vast amount of material heterogeneity. To safely store gases in caverns, a thorough analysis of the geological domain becomes crucial. To date, few studies have attempted to analyze the influence of geometrical and material heterogeneity on the state of stress in salt caverns subjected to long-term loading. In this work, we present a rigorous and systematic modeling study to quantify the impact of heterogeneity on the deformation of salt caverns and quantify the state of stress around the caverns. A 2D finite element simulator was developed to consistently account for the non-linear creep deformation and also to model tertiary creep. The computational scheme was benchmarked with the already existing experimental study. The impact of cyclic loading on the cavern was studied considering maximum and minimum pressure that depends on lithostatic pressure. The influence of geometric heterogeneity such as irregularly-shaped caverns and material heterogeneity, which involves different elastic and creep properties of the different materials in the geological domain, is rigorously studied and quantified. Moreover, multi-cavern simulations are conducted to investigate the influence of a cavern on the adjacent caverns.
Coupled hydro-mechanical processes are of great importance to numerous engineering systems, e.g., hydraulic fracturing, geothermal energy, and carbon sequestration. Fluid flow in fractures is modeled after a Poiseuille law that relates the conductivity to the aperture by a cubic relation. Newton's method is commonly employed to solve the resulting discrete, nonlinear algebraic systems. It is demonstrated, however, that Newton's method will likely converge to nonphysical numerical solutions, resulting in estimates with a negative fracture aperture. A Quasi-Newton approach is developed to ensure global convergence to the physical solution. A fixed-point stability analysis demonstrates that both physical and nonphysical solutions are stable for Newton's method, whereas only physical solutions are stable for the proposed Quasi-Newton method. Additionally, it is also demonstrated that the Quasi-Newton method offers a contraction mapping along the iteration path. Numerical examples of fluid-driven fracture propagation demonstrate that the proposed solution method results in robust and computationally efficient performance.
Unmanned aerial vehicles (UAVs) have become very popular for many military and civilian applications including in agriculture, construction, mining, environmental monitoring, etc. A desirable feature for UAVs is the ability to navigate and perform tasks autonomously with least human interaction. This is a very challenging problem due to several factors such as the high complexity of UAV applications, operation in harsh environments, limited payload and onboard computing power and highly nonlinear dynamics. The work presented in this report contributes towards the state-of-the-art in UAV control for safe autonomous navigation and motion coordination of multi-UAV systems. The first part of this report deals with single-UAV systems. The complex problem of three-dimensional (3D) collision-free navigation in unknown/dynamic environments is addressed. To that end, advanced 3D reactive control strategies are developed adopting the sense-and-avoid paradigm to produce quick reactions around obstacles. A special case of navigation in 3D unknown confined environments (i.e. tunnel-like) is also addressed. General 3D kinematic models are considered in the design which makes these methods applicable to different UAV types in addition to underwater vehicles. Moreover, different implementation methods for these strategies with quadrotor-type UAVs are also investigated considering UAV dynamics in the control design. Practical experiments and simulations were carried out to analyze the performance of the developed methods. The second part of this report addresses safe navigation for multi-UAV systems. Distributed motion coordination methods of multi-UAV systems for flocking and 3D area coverage are developed. These methods offer good computational cost for large-scale systems. Simulations were performed to verify the performance of these methods considering systems with different sizes.
As a mean to assess the risk dam structures are exposed to during earthquakes, we employ an abstract mathematical, three dimensional, elasto-acoustic coupled wave-propagation model taking into account (i) the dam structure itself, embedded into (ii) its surrounding topography, (iii) different material soil layers, (iv) the seismic source as well as (v) the reservoir lake filled with water treated as an acoustic medium. As a case study for extensive numerical simulations we consider the magnitude 7 seismic event of the 30$^{\rm th}$ of October 2020 taking place in the Icarian Sea (Greece) and the Tahtali dam around 30 km from there (Turkey). A challenging task is to resolve the multiple length scales that are present due to the huge differences in size between the dam building structure and the area of interest, considered for the propagation of the earthquake. Interfaces between structures and highly non-conforming meshes on different scales are resolved by means of a discontinuous Galerkin approach. The seismic source is modeled using inversion data about the real fault plane. Ultimately, we perform a real data driven, multi-scale, full source-to-site, physics based simulation based on the discontinuous Galerkin spectral element method, which allows to precisely validate the ground motion experienced along the Tahtali dam, comparing the synthetic seismograms against actually observed ones. A comparison with a more classical computational method, using a plane wave with data from a deconvolved seismogram reading as an input, is discussed.
In this article we formulate and implement a computational multiphase periporomechanics model for unguided fracturing in unsaturated porous media. The same governing equation for the solid phase applies on and off cracks. Crack formation in this framework is autonomous, requiring no prior estimates of crack topology. As a new contribution, an energy-based criterion for arbitrary crack formation is formulated using the peridynamic effective force state for unsaturated porous media. Unsaturated fluid flow in the fracture space is modeled in a simplified way in line with the nonlocal formulation of unsaturated fluid flow in bulk. The formulated unsaturated fracturing periporomechanics is numerically implemented through a fractional step algorithm in time and a two-phase mixed meshless method in space. The two-stage operator split converts the coupled periporomechanics problem into an undrained deformation and fracture problem and an unsaturated fluid flow in the deformed skeleton configuration. Numerical simulations of in-plane open and shear cracking are conducted to validate the accuracy and robustness of the fracturing unsaturated periporomechanics model. Then numerical examples of wing cracking and non-planar cracking in unsaturated soil specimens are presented to demonstrate the efficacy of the proposed multiphase periporomechanics model for unguided cracking in unsaturated porous media.
In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of the data fitting in this formulation allows for reasonable assumptions to be made about the solution that can improve the computational performance further. In particular, we employ a well known dual formulation of this problem and solve the corresponding equations in a restricted domain. We present experimental results that explore the dependence of the solution on this restriction and quantify imrovements in the computational performance. This approach can be extended to analogous methods simply and could provide an efficient alternative for problems of this type.
In this paper, a novel image moments based model for shape estimation and tracking of an object moving with a complex trajectory is presented. The camera is assumed to be stationary looking at a moving object. Point features inside the object are sampled as measurements. An ellipsoidal approximation of the shape is assumed as a primitive shape. The shape of an ellipse is estimated using a combination of image moments. Dynamic model of image moments when the object moves under the constant velocity or coordinated turn motion model is derived as a function for the shape estimation of the object. An Unscented Kalman Filter-Interacting Multiple Model (UKF-IMM) filter algorithm is applied to estimate the shape of the object (approximated as an ellipse) and track its position and velocity. A likelihood function based on average log-likelihood is derived for the IMM filter. Simulation results of the proposed UKF-IMM algorithm with the image moments based models are presented that show the estimations of the shape of the object moving in complex trajectories. Comparison results, using intersection over union (IOU), and position and velocity root mean square errors (RMSE) as metrics, with a benchmark algorithm from literature are presented. Results on real image data captured from the quadcopter are also presented.
In this paper, we develop the continuous time dynamic topic model (cDTM). The cDTM is a dynamic topic model that uses Brownian motion to model the latent topics through a sequential collection of documents, where a "topic" is a pattern of word use that we expect to evolve over the course of the collection. We derive an efficient variational approximate inference algorithm that takes advantage of the sparsity of observations in text, a property that lets us easily handle many time points. In contrast to the cDTM, the original discrete-time dynamic topic model (dDTM) requires that time be discretized. Moreover, the complexity of variational inference for the dDTM grows quickly as time granularity increases, a drawback which limits fine-grained discretization. We demonstrate the cDTM on two news corpora, reporting both predictive perplexity and the novel task of time stamp prediction.
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