Mesh-based Algorithm Research Articles

Ncorpi[formula omitted]N : A [formula omitted] software for N-body integration in collisional and fragmenting systems

NcorpiON is a general purpose N-body software initially developed for the time-efficient integration of collisional and fragmenting systems of planetesimals or moonlets orbiting a central mass. It features a fragmentation model, based on crater scaling and ejecta models, able to realistically simulate a violent impact.The user of NcorpiON can choose between four different built-in modules to compute self-gravity and detect collisions. One of these makes use of a mesh-based algorithm to treat mutual interactions in O(N) time. Another module, much more efficient than the standard Barnes–Hut tree code, is a O(N) tree-based algorithm called FalcON. It relies on fast multipole expansion for gravity computation and we adapted it to collision detection as well. Computational time is reduced by building the tree structure using a three-dimensional Hilbert curve. For the same precision in mutual gravity computation, NcorpiON is found to be up to 25 times faster than the famous software REBOUND.NcorpiON is written entirely in the C language and only needs a C compiler to run. A python add-on, that requires only basic python libraries, produces animations of the simulations from the output files. NcorpiON can communicate with REBOUND’s webGL viewer via MPI for 3D visualization. The name NcorpiON, reminding of a scorpion, comes from the French N-corps, meaning N-body, and from the mathematical notation O(N), due to the running time of the software being almost linear in the total number N of bodies. NcorpiON detects collisions and computes mutual gravity faster than REBOUND, and unlike other N-body integrators, it can resolve a collision by fragmentation. The fast multipole expansions are implemented up to order eight to allow for a high precision in mutual gravity computation.

Gradient enhanced physics-informed neural network for iterative form-finding of tensile membrane structures by potential energy minimization

Tensile membrane structures (TMS) are overwhelmingly popular as practical design solutions for large roofing structures. The TMS designer, however, has to perform a “form-finding” as the stable configuration of TMS are not known beforehand. Although many form-finding approaches are currently available, most suffer from various implementation complications, particularly with regards to convergence issues stemming from improper hyper-parameter selection, mesh distortion and the choice of initial reference configuration. In this study, a new iterative form-finding methodology is proposed and implemented by the direct minimization of a potential energy functional. A mesh-free approach based on gradient enhanced physics-informed neural network (gPINN) is employed, which expands the applicability to most common TMS types while eliminating the aforementioned issues faced by traditional mesh-based algorithms. Furthermore, a new method for selecting the initial reference configuration using transfinite interpolation is proposed that is significantly better suited to form-finding than conventional approaches. Additionally, approximate distance functions are employed to impose exact boundary conditions. Extensive numerical case studies on frame- and cable-supported TMS, along with multi-dimensional parametric variations, show the efficacy and robustness of the proposed form-finding framework.

Research Progress of SPH Simulations for Complex Multiphase Flows in Ocean Engineering

Complex multiphase flow problems in ocean engineering have long been challenging topics. Problems such as large deformations at interfaces, multi-media interfaces, and multiple physical processes are difficult to simulate. Mesh-based algorithms could have limitations in dealing with multiphase interface capture and large interface deformations. On the contrary, the Smoothed Particle Hydrodynamics (SPH) method, as a Lagrangian meshless particle method, has some merit and flexibility in capturing multiphase interfaces and dealing with large boundary deformations. In recent years, with the improvement of SPH theory and numerical models, the SPH method has made significant advances and breakthroughs in terms of theoretical completeness and computational stability, which starts to be widely used in ocean engineering problems, including multiphase flows under atmospheric pressure, high-pressure multiphase flows, phase-change multiphase flows, granular multiphase flows and so on. In this paper, we review the progress of SPH theory and models in multiphase flow simulations, discussing the problems and challenges faced by the method, prospecting to future research works, and aiming to provide a reference for subsequent research.

Volumetric Parameterization of the Placenta to a Flattened Template.

We present a volumetric mesh-based algorithm for parameterizing the placenta to a flattened template to enable effective visualization of local anatomy and function. MRI shows potential as a research tool as it provides signals directly related to placental function. However, due to the curved and highly variable in vivo shape of the placenta, interpreting and visualizing these images is difficult. We address interpretation challenges by mapping the placenta so that it resembles the familiar ex vivo shape. We formulate the parameterization as an optimization problem for mapping the placental shape represented by a volumetric mesh to a flattened template. We employ the symmetric Dirichlet energy to control local distortion throughout the volume. Local injectivity in the mapping is enforced by a constrained line search during the gradient descent optimization. We validate our method using a research study of 111 placental shapes extracted from BOLD MRI images. Our mapping achieves sub-voxel accuracy in matching the template while maintaining low distortion throughout the volume. We demonstrate how the resulting flattening of the placenta improves visualization of anatomy and function. Our code is freely available at https://github.com/mabulnaga/placenta-flattening.

Stochastic Process-Based Inversion of Electromagnetic Data for Hydrocarbon Resistivity Estimation in Seabed Logging

This work proposes a stochastic process-based inversion to estimate hydrocarbon resistivity based on multifrequency electromagnetic (EM) data. Currently, mesh-based algorithms are used for processing the EM responses which cause high time-consuming and unable to quantify uncertainty. Gaussian process (GP) is utilized as the alternative forward modeling approach to evaluate the EM profiles with uncertainty quantification. For the optimization, gradient descent is used to find the optimum by minimizing its loss function. The prior EM profiles are evaluated using finite element (FE) through computer simulation technology (CST) software. For validation purposes, mean squared deviation and its root between EM profiles evaluated by the GP and FE at the unobserved resistivities are computed. Time taken for the GP and CST to evaluate the EM profiles is compared, and absolute error between the estimate and its simulation input is also computed. All the resulting deviations were significantly small, and the GP took lesser time to evaluate the EM profiles compared to the software. The observational datasets also lied within the 95% confidence interval (CI) where the resistivity inputs were estimated by the proposed inversion. This indicates the stochastic process-based inversion can effectively estimate the hydrocarbon resistivity in the seabed logging.

A Novel Methodology for Hydrocarbon Depth Prediction in Seabed Logging: Gaussian Process-Based Inverse Modeling of Electromagnetic Data

Seabed logging (SBL) is an application of electromagnetic (EM) waves for detecting potential marine hydrocarbon-saturated reservoirs reliant on a source–receiver system. One of the concerns in modeling and inversion of the EM data is associated with the need for realistic representation of complex geo-electrical models. Concurrently, the corresponding algorithms of forward modeling should be robustly efficient with low computational effort for repeated use of the inversion. This work proposes a new inversion methodology which consists of two frameworks, namely Gaussian process (GP), which allows a greater flexibility in modeling a variety of EM responses, and gradient descent (GD) for finding the best minimizer (i.e., hydrocarbon depth). Computer simulation technology (CST), which uses finite element (FE), was exploited to generate prior EM responses for the GP to evaluate EM profiles at “untried” depths. Then, GD was used to minimize the mean squared error (MSE) where GP acts as its forward model. Acquiring EM responses using mesh-based algorithms is a time-consuming task. Thus, this work compared the time taken by the CST and GP in evaluating the EM profiles. For the accuracy and performance, the GP model was compared with EM responses modeled by the FE, and percentage error between the estimate and “untried” computer input was calculated. The results indicate that GP-based inverse modeling can efficiently predict the hydrocarbon depth in the SBL.

Toward the Assessment of Intrinsic Geometry of Implicit Brain MRI Manifolds

Principal and Gaussian curvatures are commonly used intrinsic metrics for geometric morphometrics analysis: to assess morphometric changes in brain geometry (developmental neuroimaging studies), to quantify shape deformation (organ motion assessment), or to analyze shape variability across subjects in musculoskeletal studies (statistical shape analysis of bones). However, most of existing algorithms for estimating curvatures act on explicit surfaces (triangle meshes), making them time consuming and sensitive to parameterization and neighborhood size. In this paper, we present a suite of fast and parameterization-free algorithms to estimate second order morphometric parameters given an implicit representation for the surface and without any loss of accuracy. We first show results for direct comparisons of our algorithms with a suite of popular algorithms for estimating curvatures of surfaces represented by triangular meshes. Then, in the context of brain imaging, methods were validated against developmental brain MRI data in which surface based analysis has very often failed. We also provided a modified version of the algorithm that can deal with a Freesurfer output surface mesh, and which was evaluated using an adult brain with more complicated folding patterns. Our algorithm provided a more realistic measures of intrinsic curvature for the white matter (mostly ranged between ±0.07 mm−2) which confirms its robustness. As compared to mesh-based algorithms, our algorithm reduces computation times from a few minutes to only a few seconds, showing a decrease by a factor of up to 7.

Ground-Level Mapping and Navigating for Agriculture Based on IoT and Computer Vision

Autonomous agricultural systems are a promising solution to bridge the gap between labor shortage for agriculture tasks and the continuing needs for increasing productivity in agriculture. Automated mapping and navigation system will be a cornerstone of most autonomous agricultural system. Accordingly, we propose a ground-level mapping and navigating system based on computer vision technology (Mesh Simultaneous Localization and Mapping algorithm, Mesh-SLAM) and Internet of Things (IoT), to generate a 3D farm map on both the edge side and cloud. The innovation of this system includes three layers as sub-systems that are 1) ground-level robot vehicles’ layer for conducting frames collection only with a monocular camera, 2) edge node layer for image feature data edge computing and communication, and 3) cloud layer for general management and deep computing. High efficiency and speed of mapping stage are enabled by making the robot vehicles directly stream continuous frames to their corresponding edge node. Then each edge node, that coordinate a certain range of robots, applies a new Mesh-SLAM frame by frame, whose core is reconstructing the features map by a mesh-based algorithm with scalable units and reduce the feature data size by a filtering algorithm. Additionally, the cloud-computing allows comprehensive arrangement and heavily deep computing. The system is scalable to larger-scale fields and more complex environment by taking advantage of dynamically distributing the computation power to edges. Our evaluation indicates that: 1) this Mesh-SLAM algorithm outperforms in mapping and localization precision, accuracy, and yield prediction error (resolution at centimeter); and 2) The scalability and flexibility of the IoT architecture make the system modularized, easy adding/removing new functional modules or IoT sensors. We conclude the trade-off between cost and performance widely augments the feasibility and practical implementation of this system in real farms.

Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints

We introduce the algorithm SHEBO (surrogate optimization of problems with hidden constraints and expensive black-box objectives), an efficient optimization algorithm that employs surrogate models to solve computationally expensive black-box simulation optimization problems that have hidden constraints. Hidden constraints are encountered when the objective function evaluation does not return a value for a parameter vector. These constraints are often encountered in optimization problems in which the objective function is computed by a black-box simulation code. SHEBO uses a combination of local and global search strategies together with an evaluability prediction function and a dynamically adjusted evaluability threshold to iteratively select new sample points. We compare the performance of our algorithm with that of the mesh-based algorithms mesh adaptive direct search (MADS, NOMAD [nonlinear optimization by mesh adaptive direct search] implementation) and implicit filtering and SNOBFIT (stable noisy optimization by branch and fit), which assigns artificial function values to points that violate the hidden constraints. Our numerical experiments for a large set of test problems with 2–30 dimensions and a 31-dimensional real-world application problem arising in combustion simulation show that SHEBO is an efficient solver that outperforms the other methods for many test problems.

Efficient scheduling of power communication resources based on fuzzy weighted constraint equalisation

Resources in the power communication system are affected by crosstalk between power grid subnets during scheduling, resulting in a poor equalisation of resource allocation. In order to improve equalisation allocation of resources in the power communication system, an efficient scheduling method of power communication system resources based on fuzzy weighted constraint equalisation is proposed. In this method, the nonlinear time series analysis method is used to construct an information flow model of power communication system resource data and the channel equalisation control is carried out in transmission links of the power communication system; the fuzzy weighted constraint equalisation method is used to implement adaptive baud-spaced equalisation handling during resource scheduling and the fuzzy mesh-based clustering algorithm is used to carry out pairing of classification attribute weights of power resources, so as to achieve efficient clustering of resources and to improve the link equalisation in resource scheduling. Simulation results show that with this method, the average data recall rate during resource scheduling reaches about 90% and the equalisation curve changes very smoothly, which fully indicates that with this method, the data recall rate and scheduling efficiency are high and the equalisation capability of communication channels is strong.

Placental Flattening via Volumetric Parameterization.

We present a volumetric mesh-based algorithm for flattening the placenta to a canonical template to enable effective visualization of local anatomy and function. Monitoring placental function in vivo promises to support pregnancy assessment and to improve care outcomes. We aim to alleviate visualization and interpretation challenges presented by the shape of the placenta when it is attached to the curved uterine wall. To do so, we flatten the volumetric mesh that captures placental shape to resemble the well-studied ex vivo shape. We formulate our method as a map from the in vivo shape to a flattened template that minimizes the symmetric Dirichlet energy to control distortion throughout the volume. Local injectivity is enforced via constrained line search during gradient descent. We evaluate the proposed method on 28 placenta shapes extracted from MRI images in a clinical study of placental function. We achieve sub-voxel accuracy in mapping the boundary of the placenta to the template while successfully controlling distortion throughout the volume. We illustrate how the resulting mapping of the placenta enhances visualization of placental anatomy and function. Our implementation is freely available at https://github.com/mabulnaga/placenta-flattening.

Elastic Alignment of Triangular Surface Meshes

A novel region-based approach is proposed to find a thin plate spline map between a pair of deformable 3D objects represented by triangular surface meshes. The proposed method works without landmark extraction and feature correspondences. The aligning transformation is simply found by solving a system of integral equations. Each equation is generated by integrating a non-linear function over the object domains. We derive recursive formulas for the efficient computation of these integrals for open and closed surface meshes. Based on a series of comparative tests on a large synthetic dataset, our triangular mesh-based algorithm outperforms state of the art methods both in terms of computing time and accuracy. The applicability of the proposed approach has been demonstrated on the registration of 3D lung CT volumes, brain surfaces and 3D human faces.

A Review of Color Image Vectorization Techniques

Digital image processing of gray scale or color images has become an important research and investigation tool in many areas of science and engineering. As the resolution of output devices has risen over the past 20 decades, the demand of high resolution contents has also increased. However, most images are stored in raster format. This format represents images on the computer screen using a rectangular grid of pixels, arranged in rows and columns and the images have a fixed resolution; once the image has been defined at a specific resolution, it cannot be scaled further. Therefore, the image is degraded when enlarged or scaled down which is a major problem in computer graphics, vision, and imaging. Since images with higher pixel density are enviable in many applications, there is an increasing demand to acquire high resolution raster images from low resolution. Raster images are resolution independent therefore; there is a need to convert raster images to vector. Vector graphics use geometrical primitives to express a raster image. These primitives are more compact, editable, scalable, resolution independent and also smaller in file size. Several vectorization algorithms have been developed for the last three decades. This paper presents a review of three categories of raster to vector algorithms, triangulation, mesh-based and parametric patches and algorithms developed using these techniques by various academic authors. Our findings reveal that important algorithms for converting raster images into vector have been developed. However, some of these algorithms perform better than others. Some deficiencies in the algorithms are caused by many possible outlines that can be obtained from the same bitmap image and the technique used by authors. The techniques are powerful but they also have some limitations when representing pixels. Most of the methods produce acceptable results for non-photorealistic images but some are worse or the same as the problem since they blur the image as well especially in photorealistic images. Further research should focus on how to use techniques discussed in this paper to develop a raster to vector algorithm that can convert photorealistic images to vector without compromising image quality.

Evaluation of mesh- and binary-based contour propagation methods in 4D thoracic radiotherapy treatments using patient 4D CT images

Based on four dimensional (4D) computed tomography (CT) images, mesh- and binary-based contour propagation algorithms for 4D thoracic radiotherapy treatments were evaluated. Gross tumor volumes (GTVs), lungs, hearts and spinal cords on the CT images at the end-exhale and end-inhale phases for six patients were delineated by the physician. All volumes of interest (VOIs) were automatically propagated from the end-exhale phase to the end-inhale phase using two propagation methods. The propagated VOIs were quantitatively compared with the VOIs contoured at the end-inhale phase by the physician using Dice Similarity Coefficient (DSC), Mean Slicewise Hausdorff Distance (MSHD), Center Of Mass (COM) displacement and volume difference. A two-sided Student’s t test was implemented to examine the significance of the differences between the results obtained from the two algorithms. For GTVs, statistically significant differences between the two algorithms were not observed. For all the other VOIs, the mesh-based method showed higher mean DSCs for the heart, left lung, right lung and spinal cord, lower mean MSHD for the spinal cord, lower mean COM displacement for the heart, and lower mean volume differences for the left lung, right lung and spinal cord with statistically significant differences than the binary-based method. The running time for propagation was approximately 3s and 3min for the mesh- and binary-based methods, respectively. Collectively, the mesh-based algorithm provides superiorities in running time and reliability for contour propagation in 4D radiotherapy.

HYBRID LATTICE BOLTZMANN METHOD FOR THE SIMULATION OF BLENDING PROCESS IN STATIC MIXERS

A lattice Boltzmann method is proposed to simulate the blending of two fluids in static, laminar mixers. The method uses a mesh-based algorithm to solve for the fluid flow, and a meshless technique to trace the interface between the blended fluids. This hybrid approach is highly accurate, because the position of the interface can be traced beyond the resolution of the grid. The numerical diffusion is negligible in this model, and it is possible to reproduce mixing patterns that contain more than one hundred striations with high fidelity. The implementation of this method in the massively parallel library Palabos is presented, and simulation results are compared with experimental data to emphasize the accuracy of the results.

Simulation of 2D wedge impacts on water using the SPH–ALE method

Prediction of the forces on pitching boat hulls is a subtle issue, since the underlying phenomena are highly dynamic and unsteady. The solution of a full 3D model of the hull is possible, but comes with a high computational cost; alternatively, it might be simpler to assume the hull as consecutive 2D slices. The traditional CFD approach, with mesh-based algorithms, introduces additional complexity due to mesh motion and interface tracking. By adopting a Lagrangian point of view, the computational algorithm would be substantially simpler, since free surface and moving geometries would be handled easily. In the current work, the smoothed particle hydrodynamics meshless method is used within an arbitrary Lagrangian–Eulerian framework (SPH–ALE), in order to predict the force and motion of a wedge during high-velocity water entry. Various impacts have been simulated, using wedges of different shapes and masses. Two methods of particle refinement have also been examined, in order to increase the accuracy near the point of impact. Results of the method are compared with experimental and numerical results from literature, showing good agreement.

103 浮体式多自由度波力発電装置の粒子法を用いた挙動解析(OS9 オーガナイズドセッション《計算力学と数値シミュレーション》)

Recently, environment problems due to the use of fossil fuel, such as global warming, climate change, air pollution, acid rain and many others, are becoming serious. To solve the problem, alternative renewable energy is required. In this paper, we focuses on the effective use of ocean power and have developed a compact, low-cost but flexible floating buoy to generate electric power from ocean wave. In order to optimize the design, we perform fluid-structure interaction analyses to consider the buoy motion without experiments. However, it was difficult to achieve the optimization for the commercial code, ANSYS, because there are many restrictions in ANSYS due to its mesh-based algorithm. Therefore, we originally develop a particle(SPH)-based analysis code.

An effective limiting algorithm for particle-based numerical simulations of compressible flows

Eulerian computational fluid dynamics (CFD) and Lagrangian computational structural dynamics (CSD) are used extensively in the aerospace industry. Combined mesh-based Eulerian and particle-based Lagrangian algorithms arevery effective for modelling and simulation due to the increased efficiency of combining the two numerical simulations. However, when compressible flows are simulated using a particle-based algorithm, calculations of strong discontinuity, such as a shock wave, may become unstable. In the present study, a numerical limiter is integrated with a particle-based CFD code to remedy this instability. The limiting algorithm incorporates an ‘averaging’ technique which calculates average values using the properties of neighbouring particles (also known as material points), including mass, momentum and energy. These averaged values are then input to a min-mode limiter to eliminate numerical noise and incur dissipation in the flow in areas with steep property gradients. The results of this algorithm show very stable solutions with minimal oscillations when applied to the one-dimensional shock tube problem and an increased accuracy with reduced oscillations for a two-dimensional cylinder cross-flow problem.

メッシュ法・粒子法のハイブリッド・アプローチによる砕波・液滴飛散の数値解析(<特集>第14回動力・エネルギー技術シンポジウム)

メッシュ法・粒子法のハイブリッド・アプローチによる砕波・液滴飛散の数値解析(<特集>第14回動力・エネルギー技術シンポジウム)

ACCURATUM: improved calcium volume scoring using a mesh-based algorithm—a phantom study

To overcome the limitations of the classical volume scoring method for quantifying coronary calcifications, including accuracy, variability between examinations, and dependency on plaque density and acquisition parameters, a mesh-based volume measurement method has been developed. It was evaluated and compared with the classical volume scoring method for accuracy, i.e., the normalized volume (measured volume/ground-truthed volume), and for variability between examinations (standard deviation of accuracy). A cardiac computed-tomography (CT) phantom containing various cylindrical calcifications was scanned using different tube voltages and reconstruction kernels, at various positions and orientations on the CT table and using different slice thicknesses. Mean accuracy for all plaques was significantly higher (p < 0.0001) for the proposed method (1.220 +/- 0.507) than for the classical volume score (1.896 +/- 1.095). In contrast to the classical volume score, plaque density (p = 0.84), reconstruction kernel (p = 0.19), and tube voltage (p = 0.27) had no impact on the accuracy of the developed method. In conclusion, the method presented herein is more accurate than classical calcium scoring and is less dependent on tube voltage, reconstruction kernel, and plaque density.