Boundary Formulation Research Articles

Face Boundary Formulation for Harmonic Models: Face Image Resembling.

This paper is devoted to numerical algorithms based on harmonic transformations with two goals: (1) face boundary formulation by blending techniques based on the known characteristic nodes and (2) some challenging examples of face resembling. The formulation of the face boundary is imperative for face recognition, transformation, and combination. Mapping between the source and target face boundaries with constituent pixels is explored by two approaches: cubic spline interpolation and ordinary differential equation (ODE) using Hermite interpolation. The ODE approach is more flexible and suitable for handling different boundary conditions, such as the clamped and simple support conditions. The intrinsic relations between the cubic spline and ODE methods are explored for different face boundaries, and their combinations are developed. Face combination and resembling are performed by employing blending curves for generating the face boundary, and face images are converted by numerical methods for harmonic models, such as the finite difference method (FDM), the finite element method (FEM) and the finite volume method (FVM) for harmonic models, and the splitting-integrating method (SIM) for the resampling of constituent pixels. For the second goal, the age effects of facial appearance are explored to discover that different ages of face images can be produced by integrating the photos and images of the old and the young. Then, the following challenging task is targeted. Based on the photos and images of parents and their children, can we obtain an integrated image to resemble his/her current image as closely as possible? Amazing examples of face combination and resembling are reported in this paper to give a positive answer. Furthermore, an optimal combination of face images of parents and their children in the least-squares sense is introduced to greatly facilitate face resembling. Face combination and resembling may also be used for plastic surgery, finding missing children, and identifying criminals. The boundary and numerical techniques of face images in this paper can be used not only for pattern recognition but also for face morphing, morphing attack detection (MAD), and computer animation as Sora to greatly enhance further developments in AI.

The Dynamic Response of an Arch Dam During a Recorded Low-Intensity Earthquake

The dynamic behavior of a concrete arch dam, the Baixo Sabor dam, built in Portugal, is investigated. A numerical model was developed to represent the dam, foundation, and reservoir system. This model was calibrated and validated through comparison with experimental data from forced vibration tests and ambient vibration monitoring. Recently, a low-intensity earthquake occurred in the region and the dam response was recorded by a seismic monitoring system. The previously calibrated numerical model was used to analyze the dynamic response of the dam under this seismic input, employing a dynamic boundary formulation that takes into account the wave propagation in the rock mass, preventing wave reflections. The results obtained show generally good agreement with the experimental measurements at the dam crest and abutments. The analysis methodology and the main issues involved in the modelling of arch dams under seismic action are discussed.

MFS-DBF: A trustworthy multichannel feature sieve and decision boundary formulation system for Obstructive Sleep Apnea detection

The fine identification of sleep apnea events is instrumental in Obstructive Sleep Apnea (OSA) diagnosis. The development of sleep apnea event detection algorithms based on polysomnography is becoming a research hotspot in medical signal processing. In this paper, we propose an Inverse-Projection based Visualization System (IPVS) for sleep apnea event detection algorithms. The IPVS consists of a feature dimensionality reduction module and a feature reconstruction module. First, features of blood oxygen saturation and nasal airflow are extracted and used as input data for event analysis. Then, visual analysis is conducted on the feature distribution for apnea events. Next, dimensionality reduction and reconstruction methods are combined to achieve the dynamic visualization of sleep apnea event feature sets and the visual analysis of classifier decision boundaries. Moreover, the decision-making consistency is explored for various sleep apnea event detection classifiers, which provides researchers and users with an intuitive understanding of the detection algorithm. We applied the IPVS to an OSA detection algorithm with an accuracy of 84% and a diagnostic accuracy of 92% on a publicly available dataset. The experimental results show that the consistency between our visualization results and prior medical knowledge provides strong evidence for the practicality of the proposed system. For clinical practice, the IPVS can guide users to focus on samples with higher uncertainty presented by the OSA detection algorithm, reducing the workload and improving the efficiency of clinical diagnosis, which in turn increases the value of trust.

Uniqueness of Finite Element Limit Analysis solutions based on weak form lower and upper bound methods

Finite Element Limit Analysis (FELA) is increasingly used for calculating the ultimate bearing capacity of structures made of ductile materials. Within FELA for reinforced concrete structures the elements have been based on rigorous lower bound or boundary mixed formulations. The lower bound element formulation may be overly constrained for certain meshes and the dual displacement interpretation may contain spurious modes, moreover the boundary mixed element formulation has an internal equilibrium node with no associated displacement field. Here a consistent and general weak formulation based on virtual work is presented specifically for both the lower and the upper bound problem, and it is shown that they are each others dual ensuring uniqueness of the optimal solution. As a consequence there is no difference between the solutions based on the weak upper and lower bound methods. Here a plane element is presented, with a linear stress variation and a quadratic displacement field, optionally including a concentrated bar element with a linear variation of the normal force. These elements are applied in a verification example and two reinforced concrete examples where they show very good results for both load level, stress distribution and collapse mechanism even for coarse meshes.

Dirichlet and Neumann boundary conditions for a lattice Boltzmann scheme for linear elastic solids on arbitrary domains

We propose novel, second-order accurate boundary formulations of Dirichlet and Neumann boundary conditions for arbitrary curved boundaries, within the scope of our recently introduced lattice Boltzmann method for linear elasticity. The proposed methodology systematically constructs and analyzes the boundary formulations on the basis of the asymptotic expansion technique; thus, it is expected to be of general applicability to boundary conditions for lattice Boltzmann formulations, well beyond the focus of this paper. For Dirichlet boundary conditions, a modified version of the bounce-back method is developed, whereas the Neumann boundary conditions are based on a novel generalized ansatz proposed in this work. The Neumann boundary formulation requires information from one additional neighbor node, for which a finite difference algorithm is introduced that enables the handling of very general boundary geometries. The theoretical derivations are verified by convergence studies using manufactured solutions, as well as by comparison with the analytical solution of the classical plate with hole problem.

Boundary and bulk notions of transport in the AdS3/CFT2 correspondence

We construct operators in holographic two-dimensional conformal field theory, which act locally in the code subspace as arbitrary bulk spacelike vector fields. Key to the construction is an interplay between parallel transport in the bulk spacetime and in kinematic space. We outline challenges, which arise when the same construction is extended to timelike vector fields. We also sketch several applications, including boundary formulations of the bulk Riemann tensor, dreibein, and spin connection, as well as an application to holographic complexity.

Application of a microplane damage model for concrete to an isogeometric scaled boundary formulation for 3D solids

AbstractMicroplane models have the advantage of describing damage‐induced anisotropy, which is common in quasi‐brittle materials such as concrete, in a simple and straightforward way. Over the past decades, various microplane models have been formulated to describe different loading cases and phenomena in concrete structures. They include pure damage and pure plasticity based microplane models or a combination of these two approaches. In this work, as a first step, a microplane damage model, which is derived from the principle of energy equivalence, is applied in the framework of an isogeometric 3D solid in boundary representation. Isogeometric analysis has the advantage that it can represent exactly complex geometries, which can influence the correct description of damage evolution. In addition, the use of a boundary representation in combination with NURBS and B‐splines is in accordance with the modeling technique common in CAD and allows for a straightforward application of the design model to the analysis process. The boundary is described using bi‐variate NURBS while the interior of the solid is approximated using uni‐variate B‐splines. The combination of isogeometric analysis with a model that can capture the finely distributed cracking of the concrete matrix represents a modeling strategy that can effectively support the development of thin‐walled shell structures made of textile‐reinforced concrete. Several examples are studied in order to investigate the ability of the microplane damage model to correctly describe quasi‐brittle fracture in this kind of non‐standard discretization formulation. Furthermore, a comparison to the standard finite element method is conducted.

A Numerical Procedure for Shakedown Analysis of Thick Cylindrical Vessels with Crossholes under Dual Cyclic Loadings.

A modified numerical procedure for the shakedown analysis of structures under dual cyclic loadings, based on the Abdalla method, is proposed in this paper. Based on the proposed numerical procedure, the shakedown analysis of the thick cylindrical vessels with crossholes (TCVCs) under cyclic internal pressure and cyclic thermal loading was carried out. The effects of material parameters (elastic modulus and thermal expansion coefficient) and crosshole radius on the elastic shakedown limit of TCVCs are discussed and, finally, normalized and formularized. Furthermore, the obtained shakedown limit boundary formulation is compared with FEA results and is verified to evaluate the shakedown behavior of TCVCs under cyclic internal pressure and cyclic thermal loading.

Phase-field modeling of solid-state sintering with interfacial anisotropy

Sintered structures observed in experiments can consist of faceted crystal grains. To predict the formation of such structures, a new phase-field (PF) model of solid-state sintering that can analyze morphological changes and microstructural evolutions considering the strong interface anisotropies of sintered particles was developed in this study. The developed PF model treats the crystal grain orientation-dependent surface and misorientation-dependent grain boundary anisotropies. Furthermore, this model employs quaternions to calculate the particle rotation, eliminating complicated calculations involved in analyzing the crystal orientation in three-dimensional (3D) simulations. The morphological change in a sintered particle and the grain boundary formulation at triple junctions simulated using the developed model were validated by comparing them with theoretical solutions. The neck growth and densification rates were investigated by performing 3D simulations using two particles with interface anisotropies. The simulation results revealed that neck growth and densification are affected by surface energy and mobility anisotropies. A 3D PF simulation using 200 particles demonstrated that the developed PF model can potentially reproduce sintered structures with faceted particles observed in experiments. The PF model provides a promising simulation for predicting the microstructural evolution of actual materials during solid-state sintering.

Free boundary formulations for two extended Blasius problems

In this paper, we have defined the free boundary formulation for two extended Blasius problems. These problems are of interest in boundary layer theory and are deduced from the governing partial differential equations by using appropriate similarity variables. The computed results, for the so-called missing initial condition, are favorably compared with recent results available in the literature.

Water detection framework for industrial electric arc furnaces: Boundary modelling and formulation

AbstractThis paper describes the development of a boundary model for the off‐gas water vapour in an industrial steelmaking electric arc furnace (EAF). The solution addresses the mechanistic components of a complete EAF water detection framework. The boundary model has been implemented on an industrial alternating current (AC) EAF. The model specifies upper and lower limits in real‐time of the expected EAF off‐gas water vapour leaving the furnace, and it provides a valuable on‐line monitoring tool to the operator on what boundary to expect for the off‐gas water vapour in different circumstances. An essential data required for the framework is the EAF off‐gas composition. So, in this work, an off‐gas analyzer with a human machine interface (HMI) and a supervisory control and data acquisition (SCADA) system was installed in the first step. Then, in order to evaluate the developed water leak detection framework and verify the obtained results, industrial trials were designed in which a certain amount of water was intentionally added into the furnace by increasing the electrode spray water flow rate. Moreover, we have shown how the presented framework can be used to appropriately adjust the alarm setting values in control/emergency shutdown systems of industrial EAF to enhance the safety and availability of the plant.

LaBCof: Lattice Boltzmann boundary condition framework

The boundary condition is one of the most challenging aspects of lattice Boltzmann simulations. One of the reasons that make it difficult to implement a new boundary condition is the dependency of formulation on the orientation of the boundary nodes. So, any boundary condition formulation should be derived, implemented, and verified in terms of the boundary orientation. In this study a new framework for the implementation of boundary conditions in the lattice Boltzmann method has been developed. The main goal of this framework is to implement a boundary condition for one side/corner of a domain which can then be applied to any other side/corner. Since implementing a boundary condition depends on the orientation of the boundary nodes, using this framework makes it easier to implement any set of boundary conditions. The framework is developed in C++ using object-oriented programming. It is then verified by implementing some common boundary conditions in LBM. This framework can be used for any kind of data structure of lattice Boltzmann code.

Communication-, Computation-, and Control-Enabled UAV Mobile Communication Networks

Unmanned-aerial-vehicles (UAVs)-enabled mobile-edge computing (MEC) networks have shown a huge advantage in providing on-demand communication and computation service for the ground users. To reap the benefit of these integrated networks, reducing their energy consumption becomes a key issue, since both UAVs and ground users are energy-limited devices. To address this problem, this article attempts to provide a novel method that optimizes communication, computation, and control (3C), i.e., user association, computational task offloading, and UAVs flight control, to reduce the communication and computation energy consumption. Specifically, in order to find out the appropriate deployment positions for UAV MEC servers to provide on-demand communication and computation service, we propose the concept of the virtual force field (VFF) based on the user statistical distribution model and then devise a coordinated flight control algorithm for UAV MEC servers. After that, the user association and computational task offloading are optimized alternately. Utilizing the optimal transport theory (OTT), we derive the boundary formulation of the optimal user association and develop an iterative algorithm to approach the optimal association boundary. Then, given the user association, the optimal computational task offloading scheme is investigated. The convergence of the proposed iterative algorithm and the alternating optimization algorithm is proved. The complexity of the 3C optimization method is also analyzed. Simulation results demonstrate that the proposed designs considerably outperform the similar existing algorithm. Comparisons with the benchmark scheme show that the proposed scheme can reduce about 88% energy consumption and also improve energy efficiency performance greatly under the same simulation setups.

Generalized and efficient wall boundary condition treatment in GPU-accelerated smoothed particle hydrodynamics

This paper presents a generalized and efficient wall boundary treatment in the smoothed particle hydrodynamics (SPH) method for 3-D complex and arbitrary geometries with single- and multi-phase flows to be executed on graphics processing units (GPUs). Using a force balance between the wall and fluid particles with a novel penalty method, a pressure boundary condition is applied on the wall dummy particles which effectively prevents non-physical particle penetration into the wall also in highly violent impacts and multi-phase flows with high density ratios. A new density reinitialization scheme is also presented to enhance the accuracy and robustness. The proposed method is simple in comparison with previous wall boundary formulations on GPUs and enforces no additional memory caching and thus is well suited for massively parallel architecture of GPUs. The method is validated in various test cases involving inviscid violent single- and multi-phase flows, demonstrating very good robustness, accuracy and performance. The new wall boundary treatment is able to improve the high accuracy of its previous version by Adami et al. [1] also in 3-D and multi-phase problems, while it is efficiently executable on GPUs. Therefore, the method can be a reliable solution for the long-lasting wall boundary condition challenge in SPH for a broad range of problems.

De-homogenization of optimal 2D topologies for multiple loading cases

This work presents an extension of the highly efficient de-homogenization method for obtaining high-resolution, near-optimal 2D topologies optimized for minimum compliance subjected to multiple load cases. We perform a homogenization-based topology optimization based on stiffness optimal Rank-N microstructure parameterizations to obtain stiffness optimal multi-scale designs on relatively coarse grids. To avoid relatively thin microstructure features, we regularize the design by introducing a material indicator field which results in well-defined widths and structural boundaries. In order to avoid singularities from the multiple load case problem, the orientations of the microstructures are further regularized. Subsequently, we derive a single-scale interpretation of stiffness optimal multi-scale designs on a fine grid using de-homogenization. The single-scale interpretation can be derived without costly postprocessing analysis on the fine grid, as an implicit boundary formulation is used.The effect of starting guesses is discussed, as they are non-trivial for Rank-N microstructures. Different numerical examples verify the performance of the inexpensive high-resolution solutions, both in comparison to the Rank-N based homogenization solutions, to equivalent density-based large-scale solutions, as well as to strict isotropic microstructure solutions. Depending on starting guesses, the approach consistently delivers structural performance values within a few percent of density-based large-scale solutions with a CPU time reduction factor of more than 300. Finally, we confirm that isotropic as well as orthogonal Rank-2 microstructure models are inferior to stiffness optimal anisotropic microstructure models for minimum compliance problems subjected to multiple load cases.

Security Region of Integrated Heat and Electricity System Considering Thermal Dynamics

The broad development of integrated heat and electricity systems (IHES) improved the energy utilization efficiency, but it also increased the risk of cascaded accidents and the difficulty of operation. The security region that defines the permitted operation range is efficient for the planning and control of IHESs, while the accurate formulation of security region boundary renders its applications. To address this problem, this article first proposes a novel equivalent thermal model (ETM) to build the direct connection between the operations states and the control variables in the heating system. The ETM directly characterizes the network response to the inputs and accurately describes the dynamic process in the heat system. On this basis, the method to construct the security region for IHES is presented considering the thermal dynamics, where the critical boundary is formulated with a set of accurate hyperplanes. To describe the thermal dynamics, numerical simulations from different aspects verify the effectiveness of the ETM. The results of security region indicate that the thermal dynamics influence the operation security and renewable penetration in the power system significantly.

A Constant Pressure Upper Boundary Formulation for Models Employing Height-Based Vertical Coordinates

Abstract For the numerical simulation of atmospheric flows that extend as high as the thermosphere, it is more appropriate to represent the upper boundary of the model domain as a material surface at constant pressure rather than one characterized by a rigid lid. Consequently, in adapting the Model for Prediction Across Scales (MPAS) for geospace applications, a modification of the height-based vertical coordinate is presented that permits the coordinate surfaces at upper levels to transition toward a constant pressure surface at the model’s upper boundary. This modification is conceptually similar to a terrain-following coordinate at low levels, but now modifies the coordinate surfaces at upper levels to conform to a constant pressure surface at the model top. Since this surface is evolving in time, the height of the upper boundary is adaptively adjusted to follow a designated constant pressure upper surface. This is accomplished by applying the hydrostatic equation to estimate the change in height along the boundary that is consistent with the vertical pressure gradient at the model top. This alteration in the vertical coordinate requires only minor modifications and little additional computational expense to the original height-based time-invariant terrain-following vertical coordinate employed in MPAS. The viability of this modified vertical coordinate formulation has been verified in a 2D prototype of MPAS for an idealized case of upper-level diurnal heating. Significance Statement Most atmospheric numerical models that use a height-based vertical coordinate employ a rigid lid at the top of the model domain. While a rigid lid works well for applications in the troposphere and stratosphere, it is not well suited for applications extending into the thermosphere where significant vertical expansion/contraction occurs due to deep heating/cooling of the atmosphere. This paper develops and tests a simple modification to the height-based coordinate formulation that allows the height of the upper boundary to adaptively follow a constant pressure surface. This added flexibility in the treatment of the upper domain boundary for height-based models may be particularly beneficial in facilitating their transition to a deep atmosphere configuration without significant retooling of the model numerics.

Determination of Modes in the Ice–Water Bi-layer Waveguide

The seismic method on ice provides rich information and a feasible technical way for acoustic study in ice-covered water. This paper presents a method to determine the modes in ice–water bi-layer waveguides. We achieve the purpose by deducing the scaled boundary formulation for solid and fluid layers then coupling them with the coupling matrix. The wave numbers and mode shapes are compared with the results of the finite element method. It shows that the configuration for ice–water bi-layer waveguide is of high precision. In underwater acoustic applications, the depth of water is comparatively large relative to ice thickness, which addresses the additional difficulty of accuracy in high frequency. The study on convergence is carried out, and approximate formulas are addressed based on the calculated results, giving a quick insight into piratical application.

A rule-based computer support for the design of tessellation tiles

The tessellation is of repeated graphic patterns that can be applied in many visual applications. To create a graphic design of tessellation is not a simple task, which requires both visual art experience and geometric modeling. In this paper, we provide a rule-based support system to assist users, who has less experience in art, to efficiently create tessellation tiles to satisfy the user’s aesthetic perception. To this end, we propose three algorithms based on rules to solve the pattern validation problems in tessellation design, including: (1) tile boundary formulation by using the C4C4C4C4 Heesch-type isohedral tiling and Bézier curve, (2) fitting the internal design of tile into the tile boundary based on the extremal polygon containment optimization, (3) combination of tiles that satisfies symmetry or semi-symmetry. Consequently, the computer support provides automation and visualization to make users’ tessellation design more efficient and innovative.

Catalytic characterization in plasma wind tunnels under the influence of gaseous recombination

The catalytic properties of materials used in re-usable thermal protection systems (TPSs) of re-entry vehicles are mainly characterized in plasma wind tunnels. These facilities are adequate to reproduce the thermo-chemical environment found in hypersonic flights. Catalytic recombination coefficients (W) determined empirically for the TPS design process are used to validate catalytic models. Recent experiments in plasma wind tunnels present some contradictions with current catalytic models used in computational fluid dynamics simulations. This work explores the coupling between homogeneous and heterogeneous reactions and its influence on the heat flux measurements, in order to explain such contradictions. For that, three copper calorimeters (at 350 K) are inserted in probes of different sizes, and they are tested in the Plasmatron facility at the von Karman Institute under different chemical regimes, which are modified by the probe diameter. A dimensional analysis of the acquired data based on previous non-equilibrium boundary formulations shows that an empirical recombination coefficient can be falsified by the presence of homogeneous reactions. Then, in the framework for the post-flight analysis of the European Space Agency's intermediate experimental vehicle, the local heat transfer simulations methodology is applied under peak heating conditions. A new probe is designed, manufactured, and tested in the Plasmatron to measure the recombination coefficient on C/SiC under the closest flow conditions with respect to the flight.