Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium

Infiltration of water in dry porous media is subject to a powerful gravity-driven instability. Although the phenomenon of unstable infiltration is well known, its description using continuum mathematical models has posed a significant challenge for several decades. The classical model of water flow in the unsaturated flow, the Richards equation, is unable to reproduce the instability. Here, we present a computational study of a model of unsaturated flow in porous media that extends the Richards equation and is capable of predicting the instability and captures the key features of gravity fingering quantitatively. The extended model is based on a phase-field formulation and is fourth-order in space. The new model poses a set of challenges for numerical discretizations, such as resolution of evolving interfaces, stiffness in space and time, treatment of singularly perturbed equations, and discretization of higher-order spatial partial–differential operators. We develop a numerical algorithm based on Isogeometric Analysis, a generalization of the finite element method that permits the use of globally-smooth basis functions, leading to a simple and efficient discretization of higher-order spatial operators in variational form. We illustrate the accuracy, efficiency and robustness of our method with several examples in two and three dimensions in both homogeneous and strongly heterogeneous media. We simulate, for the first time, unstable gravity-driven infiltration in three dimensions, and confirm that the new theory reproduces the fundamental features of water infiltration into a porous medium. Our results are consistent with classical experimental observations that demonstrate a transition from stable to unstable fronts depending on the infiltration flux.United States. Dept. of Energy (Early Career Award Grant DE-SC0003907

Information inference for cyber-physical systems with application to aviation safety and space situational awareness

Due to the rapid advancement of technologies on sensors and processors, engineering systems have become more complex and highly automated to meet ever stringent performance and safety requirements. These systems are usually composed of physical plants (e.g., aircraft, spacecraft, ground vehicles, etc.) and cyber components (e.g., sensing, communication, and computing units), and thus called as Cyber-Physical Systems (CPSs). For safe, efficient, and sustainable operation of a CPS, the states and physical characteristics of the system need to be effectively estimated or inferred from sensing data by proper information inference algorithms. However, due to the complex nature of the interacting multiple-heterogeneous elements of the CPS, the information inference of the CPS is a challenging task, where exiting methods designed for a single-element dynamic system (or for even dynamic systems with multiple-homogenous elements) could not be applicable. Moreover, the increasing number of sensor resources in CPSs makes the task even more challenging as meaningful information needs to be accurately and effectively inferred from huge amount of data, which is usually noise corrupted. Many aerospace systems such as air traffic control systems, pilot-automation integrated systems, networked unmanned aircraft systems, and space surveillance systems are good examples of CPSs and thus have the aforementioned challenging problems. The goals of this research are to 1) overcome the challenges in complex CPSs by developing new information inference methodologies based on control, estimation, hybrid systems and information theories, and 2) successfully apply them to various complex and safety-critical aerospace systems such as air transportation systems, space surveillance systems, and integrated human-machine systems, to promote their efficiency and safety

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation

A generic computer simulation for manipulator systems (ROBSIM) was implemented and the specific technologies necessary to increase the role of automation in various missions were developed. The specific items developed are: (1) capability for definition of a manipulator system consisting of multiple arms, load objects, and an environment; (2) capability for kinematic analysis, requirements analysis, and response simulation of manipulator motion; (3) postprocessing options such as graphic replay of simulated motion and manipulator parameter plotting; (4) investigation and simulation of various control methods including manual force/torque and active compliances control; (5) evaluation and implementation of three obstacle avoidance methods; (6) video simulation and edge detection; and (7) software simulation validation

Complex-Grid Spectral Algorithms For Inviscid Linear Instability of Boundary-Layer Flows

We present a suite of algorithms designed to obtain accurate numerical solutions of the generalised eigenvalue problem governing inviscid linear instability of boundary-layer type of flow in both the incompressible and compressible regimes on planar and axisymmetric curved geometries. The large gradient problems which occur in the governing equations at critical layers are treated by diverting the integration path into the complex plane, making use of complex mappings. The need for expansion of the basic flow profiles in truncated Taylor series is circumvented by solving the boundary-layer equations directly on the same (complex) grid used for the instability calculations. Iterative and direct solution algorithms are employed and the performance of the resulting algorithms using nonlinear radiation or homogeneous Dirichlet far-field boundary conditions is examined. The dependence of the solution on the parameters of the complex mappings is discussed. Results of incompressible and supersonic flow examples are presented; their excellent agreement with established works demonstrates the accuracy and robustness of the new methods presented. Means of improving the efficiency of the proposed spectral algorithms are suggested

IST Austria Thesis

This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning non-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces

Time integration for complex fluid dynamics

2021 Fall.Includes bibliographical references.Efficient and accurate simulation of turbulent combusting flows in complex geometry remains a challenging and computationally expensive proposition. A significant source of computational expense is in the integration of the temporal domain, where small time steps are required for the accurate resolution of chemical reactions and long solution times are needed for many practical applications. To address the small step sizes, a fourth-order implicit-explicit additive Runge-Kutta (ARK4) method is developed to integrate the stiff chemical reactions implicitly while advancing the convective and diffusive physics explicitly in time. Applications involving complex geometry, stiff reaction mechanisms, and high-order spatial discretizations are challenged by stability issues in the numerical solution of the nonlinear problem that arises from the implicit treatment of the stiff term. Techniques for maintaining a physical thermodynamic state during the numerical solution of the nonlinear problem, such as placing constraints on the nonlinear solver and the use of a nonlinear optimizer to find valid thermodynamic states, are proposed and tested. Verification and validation are performed for the new adaptive ARK4 method using lean premixed flames burning hydrogen, showing preservation of 4th-order error convergence and recovery of literature results. ARK4 is then applied to solve lean, premixed C3H8-air combustion in a bluff-body combustor geometry. In the two-dimensional case, ARK4 provides a 70× speedup over the standard explicit four-stage Runge-Kutta method and, for the three-dimensional case, three-orders-of-magnitude-larger time step sizes are achieved. To further increase the computational scaling of the algorithms, parallel-in-time (PinT) techniques are explored. PinT has the dual benefit of providing parallelization to long temporal domains as well as taking advantage of hardware trends towards more concurrency in modern high-performance computing platforms. Specifically, the multigrid reduction-in-time (MGRIT) method is adapted and enhanced by adding adaptive mesh refinement (AMR) in time. This creates a space-time algorithm with efficient solution-adaptive grids. The new MGRIT+AMR algorithm is first verified and validated using problems dominated by diffusion or characterized by time periodicity, such as Couette flow and Stokes second problem. The adaptive space-time parallel algorithm demonstrates up to a 13.7× speedup over a time-sequential algorithm for the same solution accuracy. However, MGRIT has difficulties when applied to solve practical fluid flows, such as turbulence, governed by strong hyperbolic partial differential equations. To overcome this challenge, the multigrid operations are modified and applied in a novel way by exploiting the space-time localization of fine turbulence scales. With these new operators, the coarse-scale errors are advected out of the temporal domain while the fine-scale dynamics iterate to equilibrium. This leads to rapid convergence of the bulk flow, which is important for computing macroscopic properties useful for engineering purposes. The novel multigrid operations are applied to the compressible inviscid Taylor-Green vortex flow and the convergence of the low-frequency modes is achieved within a few iterations. Future work will be focused on a performance study for practical highly turbulent flows

Semi-analytical modelling of fluid flow in unconventional fractured reservoirs including branch-fracture permeability field

Growing demand for energy and unavailability of new viable energy resources have played a crucial role in the persistent exploitation of unconventional resources through multistage hydraulic fracturing. Currently, standard modelling approaches idealize a fractured media as an interplay of several homogeneous continuum of normal diffusive characteristics. However, evolved branch-fractures generate a space with extreme heterogeneity around primary fracture plane. The precise characterization of these branch-fractures is imperative for well performance analysis along with subdiffusive behaviour of unconventional matrices. This study presents two semi-analytical models that account for the branch-fracture permeability field and subdiffusion. The first model, Induced Branch-fracture Subdiffusive Flow model (SIBFF), accounts for exponential permeability field concept and subdiffusive transport behaviour of matrices. Compared to the earlier analytical models, the SIBFF model accounts for more comprehensive transport mechanisms and medium properties. The other model, Fractal Branch-fracture model, couples fractal porosity/permeability distribution of branch-fracture and subdiffusion to account for more detailed description of stimulated reservoir volume (SRV) and unfractured inner region. The wellbore pressure solution is derived by discretizing the reservoir into several flow regions and imposing both flux and pressure continuity at the interface between contiguous segments. The inclusion of permeability field and fractional flux law introduces important complexities to the mathematical model that are carefully resolved by implementing Bessel functions and Laplace transformation (LT). Finally, the solution is inverted to time domain using Gaver-Wynn-Rho (GWR) algorithm. This study also assessed the applicability of four numerical inversion methods and found GWR method more suitable and predictive. The sensitivity of important model parameters is presented. Results were verified analytically and validated against Niobrara and Eagleford field data. It is shown that the models could be implemented to quantify the efficiency of a stimulation job, to decide on the necessity of re-fracturing a formation and to analyze horizontal well performance with better predictive capability. The proposed models could further be employed to characterize different flow regimes for unconventional reservoirs

Accelerated iterative solvers for the solution of electromagnetic scattering and wave propagation propagation problems

The aim of this work is to contribute to the development of accelerated iterative methods for the solution of electromagnetic scattering and wave propagation problems. In spite of recent advances in computer science, there are great demands for efficient and accurate techniques for the analysis of electromagnetic problems. This is due to the increase of the electrical size of electromagnetic problems and a large amount of design and analytical work dependent on simulation tools. This dissertation concentrates on the use of iterative techniques, which are expedited by appropriate acceleration methods, to accurately solve electromagnetic problems. There are four main contributions attributed to this dissertation. The first two contributions focus on the development of stationary iterative methods while the other two focus on the use of Krylov iterative methods. The contributions are summarised as follows: • The modified multilevel fast multipole method is proposed to accelerate the performance of stationary iterative solvers. The proposed method is combined with the buffered block forward backward method and the overlapping domain decomposition method for the solution of perfectly conducting three dimensional scattering problems. The proposed method is more efficient than the standard multilevel fast multipole method when applied to stationary iterative solvers. • The modified improvement step is proposed to improve the convergence rate of stationary iterative solvers. The proposed method is applied for the solution of random rough surface scattering problems. Simulation results suggest that the proposed algorithm requires significantly fewer iterations to achieve a desired accuracy as compared to the conventional improvement step. • The comparison between the volume integral equation and the surface integral equation is presented for the solution of two dimensional indoor wave propagation problems. The linear systems resulting from the discretisation of the integral equations are solved using Krylov iterative solvers. Both approaches are expedited by appropriate acceleration techniques, the fast Fourier transform for the volumetric approach and the fast far field approximation for the surface approach. The volumetric approach demonstrates a better convergence rate than the surface approach. • A novel algorithm is proposed to compute wideband results of three dimensional forward scattering problems. The proposed algorithm is a combination of Krylov iterative solvers, the fast Fourier transform and the asymptotic waveform evaluation technique. The proposed method is more efficient to compute the wideband results than the conventional method which separately computes the results at individual frequency points