An Alternating Mesh Quality Metric Scheme for Efficient Mesh Quality Improvement

AbstractIn the numerical solution of partial differential equations (PDEs), high-quality meshes are crucial for the stability, accuracy, and convergence of the associated PDE solver. Mesh quality improvement is often performed to improve the quality of meshes before use in numerical solution of the PDE. Mesh smoothing (performed via optimization) is one popular technique for improving the mesh quality; it does so by making adjustments to the vertex locations. When an inefficient mesh quality metric is used to design the optimization problem, and hence also to measure the mesh quality within the optimization procedure, convergence of the optimization method can be much slower than desired. However, for many applications, the choice of mesh quality metric and the optimization problem should be considered fixed. In this paper, we propose a simple mesh quality metric alternation scheme for use in the mesh optimization process. The idea is to alternate the use of the original inefficient mesh quality metric with a more efficient mesh quality metric on alternate iterations of the mesh optimization procedure in order to reduce the time to convergence, while solving the original mesh quality improvement problem. Typical results of using our application scheme to solve mesh quality improvement problems yield approximately 40-55% improvement in comparison to the original mesh optimization procedure. More frequent use of the efficient metric results in greater speed-ups

Collaborative simulation and scientific big data analysis: Illustration for sustainability in natural hazards management and chemical process engineering

Classical approaches for remote visualization and collaboration used in Computer-Aided Design and Engineering (CAD/E) applications are no longer appropriate due to the increasing amount of data generated, especially using standard networks. We introduce a lightweight and computing platform for scientific simulation, collaboration in engineering, 3D visualization and big data management. This ICT based platform provides scientists an “easy-to-integrate” generic tool, thus enabling worldwide collaboration and remote processing for any kind of data. The service-oriented architecture is based on the cloud computing paradigm and relies on standard internet technologies to be efficient on a large panel of networks and clients. In this paper, we discuss the need of innovations in (i) pre and post processing visualization services, (ii) 3D large scientific data set scalable compression and transmission methods, (iii) collaborative virtual environments, and (iv) collaboration in multi-domains of CAD/E. We propose our open platform for collaborative simulation and scientific big data analysis. This platform is now available as an open project with all core components licensed under LGPL V2.1. We provide two examples of usage of the platform in CAD/E for sustainability engineering from one academic application and one industrial case study. Firstly, we consider chemical process engineering showing the development of a domain specific service. With the rise of global warming issues and with growing importance granted to sustainable development, chemical process engineering has turned to think more and more environmentally. Indeed, the chemical engineer has now taken into account not only the engineering and economic criteria of the process, but also its environmental and social performances. Secondly, an example of natural hazards management illustrates the efficiency of our approach for remote collaboration that involves big data exchange and analysis between distant locations. Finally we underline the platform benefits and we open our platform through next activities in innovation techniques and inventive design

Finite Element Modeling Driven by Health Care and Aerospace Applications

This thesis concerns the development, analysis, and computer implementation of mesh generation algorithms encountered in finite element modeling in health care and aerospace. The finite element method can reduce a continuous system to a discrete idealization that can be solved in the same manner as a discrete system, provided the continuum is discretized into a finite number of simple geometric shapes (e.g., triangles in two dimensions or tetrahedrons in three dimensions). In health care, namely anatomic modeling, a discretization of the biological object is essential to compute tissue deformation for physics-based simulations. This thesis proposes an efficient procedure to convert 3-dimensional imaging data into adaptive lattice-based discretizations of well-shaped tetrahedra or mixed elements (i.e., tetrahedra, pentahedra and hexahedra). This method operates directly on segmented images, thus skipping a surface reconstruction that is required by traditional Computer-Aided Design (CAD)-based meshing techniques and is convoluted, especially in complex anatomic geometries. Our approach utilizes proper mesh gradation and tissue-specific multi-resolution, without sacrificing the fidelity and while maintaining a smooth surface to reflect a certain degree of visual reality. Image-to-mesh conversion can facilitate accurate computational modeling for biomechanical registration of Magnetic Resonance Imaging (MRI) in image-guided neurosurgery. Neuronavigation with deformable registration of preoperative MRI to intraoperative MRI allows the surgeon to view the location of surgical tools relative to the preoperative anatomical (MRI) or functional data (DT-MRI, fMRI), thereby avoiding damage to eloquent areas during tumor resection. This thesis presents a deformable registration framework that utilizes multi-tissue mesh adaptation to map preoperative MRI to intraoperative MRI of patients who have undergone a brain tumor resection. Our enhancements with mesh adaptation improve the accuracy of the registration by more than 5 times compared to rigid and traditional physics-based non-rigid registration, and by more than 4 times compared to publicly available B-Spline interpolation methods. The adaptive framework is parallelized for shared memory multiprocessor architectures. Performance analysis shows that this method could be applied, on average, in less than two minutes, achieving desirable speed for use in a clinical setting. The last part of this thesis focuses on finite element modeling of CAD data. This is an integral part of the design and optimization of components and assemblies in industry. We propose a new parallel mesh generator for efficient tetrahedralization of piecewise linear complex domains in aerospace. CAD-based meshing algorithms typically improve the shape of the elements in a post-processing step due to high complexity and cost of the operations involved. On the contrary, our method optimizes the shape of the elements throughout the generation process to obtain a maximum quality and utilizes high performance computing to reduce the overheads and improve end-user productivity. The proposed mesh generation technique is a combination of Advancing Front type point placement, direct point insertion, and parallel multi-threaded connectivity optimization schemes. The mesh optimization is based on a speculative (optimistic) approach that has been proven to perform well on hardware-shared memory. The experimental evaluation indicates that the high quality and performance attributes of this method see substantial improvement over existing state-of-the-art unstructured grid technology currently incorporated in several commercial systems. The proposed mesh generator will be part of an Extreme-Scale Anisotropic Mesh Generation Environment to meet industries expectations and NASA\u27s CFD visio

Micro Synthetic Jets as Effective Actuator

Synthetic jets have previously been studied as actuators for external macroflow control and recently been proposed for internal microflow applications. Despite the wide variety of the potential applications of synthetic jet actuators, the majority of the studies have been done at macro scales. Furthermore, there has not been any design methodology that addresses the effectiveness of the micro synthetic jet actuators. Bearing these needs in mind, a micro synthetic jet configuration is considered in a microscale environment where Kn number is less than 0.1 and more than 0.001. Flowfields are simulated by solving the compressible Navier-Stokes equations. The wall boundary conditions have been modified to accommodate the slip velocity and the temperature jump conditions encountered for this specific range of the Knudsen numbers. The membrane motion is modeled in a realistic manner as a moving boundary in order to accurately compute the flow inside the actuator cavity. Due to lack of experimental studies on micro synthetic jets, validation of the current method is accomplished in two steps. In the first step, capabilities of the methodology are tested successfully by computing flowfields inside a microchannel, microfilter, and micro backward facing step. In the second step, a realistic modeling of a synthetic jet in macro flow conditions is validated with experimental results. As the main contribution of this study, a detailed parametric study is presented that covers a large design space of synthetic jet actuation and design variables. In this study, both the synthetic jets in quiescent environment and in cross flow conditions are considered. The design variables for the parametric study are the membrane oscillation frequency, the membrane oscillation amplitude, the orifice width, the orifice height, the cavity height, and the cavity width. Studying the characteristic length allows an understanding of a synthetic jet for different Knudsen and Reynolds numbers. The momentum flux, jet velocity, vortex formation and shedding, the area and the circulation of the vortex, are the metrics considered to determine the effectiveness of a synthetic jet. The final phase of the present study is on developing and demonstrating a design optimization methodology. This is accomplished in two steps. First, each design variable is considered one at a time as and other design variables are kept constant. This approach yields an effective actuator when considering the possibility of the limits on any design variable to be constant. As compared to the baseline case, the optimization studies yield 2%, 15%, 15%, 200% increase in actuation efficiency when the single-variable is the orifice width, the orifice height, the cavity height, or the frequency, respectively. Then a multi variable optimization is performed to obtain the synthetic jet configuration that yields the best efficiency. This study includes shape optimization using shape parameters and Bezier polynomials. As compared to the baseline case, the shape optimization using shape parameters results in a 170% increase in the actuation efficiency while the shape optimization with Bezier polynomials results in more than 10 times increase

A Comparison of Optimization Software for Mesh Shape-Quality Improvement Problems

Simplicial mesh shape-quality can be improved by optimizing an objective function based on tetrahedral shape measures. If the objective function is formulated in terms of all elements in a given mesh rather than a local patch, one is confronted with a large-scale, nonlinear, constrained numerical optimization problem. We investigate the use of six general-purpose state-of-the-art solvers and two custom-developed methods to solve the resulting largescale problem. The performance of each method is evaluated in terms of robustness, time to solution, convergence properties, and sealability on several two- and three-dimensional test cases