Space-time Method Research Articles

Space–Time Analysis of Refueling Patterns of Alternative Fuel Vehicles Using GPS Trajectory Data and Machine Learning

ABSTRACTThe urgency to combat climate change has led countries worldwide to embrace clean energy solutions across various sectors, including transportation, to reduce greenhouse gas emissions. This shift is evident in the growing popularity and adoption of alternative fuel vehicles (AFVs), such as natural gas vehicles and electric vehicles. AFVs have significantly lower carbon footprints compared to conventional petrol‐powered vehicles with internal combustion engines. Consequently, there arises a need to gain a deeper understanding of AFV refueling demand to optimize the distribution of refueling stations. To address this, our research proposes an innovative space–time method that integrates GPS trajectory data with the support vector machine technique to accurately identify and analyze patterns in AFV refueling behavior. The results highlight distinct space–time patterns, notably the clustering of refueling activities in areas like Shuiguohu, Shouyilu, Houhu, Hanshuiqiao, Zhoutou, and Yongfeng around noon, influenced by taxi drivers' breaks. This underscores the importance of increasing staff levels at refueling stations in these areas during peak refueling periods, forming alliances with local eateries, and coordinating taxi shift hours to evenly distribute refueling demand throughout the day, ultimately reducing congestion during peak refueling periods in these areas. The proposed method by this research is applicable to urban contexts worldwide and equips policymakers and planners with a powerful tool for effective planning of future AFV refueling stations.

Space–Time Methods Based on Isogeometric Analysis for Time-fractional Schrödinger Equation

Space–Time Methods Based on Isogeometric Analysis for Time-fractional Schrödinger Equation

Space–time method for analyzing transient heat conduction in functionally graded materials

In this study, a novel approach is presented for simulating transient heat conduction in functionally graded materials (FGM) with varying material properties only in the z direction. The proposed collocation method employs a meshless localized space–time radial basis function (LSTRBF), which yields a linear sparse matrix system, offering advantages over the global method in terms of scalability and suitability for multidimensional problems. Additionally, a novel shape parameter strategy, known as variable leave-one-out cross-validation (LOOCV), is introduced to enhance accuracy while overcoming conventional LOOCV limitations. Four benchmark numerical examples are utilized to demonstrate the simplicity, efficiency, accuracy, and stability of the method. Overall, the proposed LSTRBF method presents a promising alternative for efficiently and accurately simulating transient heat conduction in FGMs.

Towards a spatio‐temporal multicriteria evaluation method: A suitability analysis of residential units in a 3D urban environment

AbstractSpatial multi‐criteria evaluation (MCE) techniques aid urban planning management by analyzing decision problem alternatives for solutions to help inform decision‐making. However, there is a lack of such methods that incorporate the temporal dimension, an important factor when analyzing the dynamic urban landscape and decisions surrounding its changes. A novel spatio‐temporal MCE approach is proposed that operates in three‐dimensional (3D) space and time to identify changing suitability values of decision alternatives. This space–time method is implemented to evaluate the suitability of residential units over a 15‐year period in part of downtown City of Vancouver, Canada. The results indicate that the majority of units exhibit a decrease in suitability with time due to depreciation and reduction of assets like view and privacy from the construction of new buildings. The proposed method can be used by urban planners and developers to assist in long‐term assessments of proposed development scenarios and their impact on existing urban infrastructure.

High-order spline upwind for space–time Isogeometric Analysis

We propose an innovative isogeometric space–time method for the heat equation, with smooth splines approximation in both space and time. To enhance the stability of the method we add a stabilizing term, based on a linear combination of high-order artificial diffusions. This term is designed in order to make the linear system lower block-triangular, that is, lower triangular with respect to time. In order to keep optimal accuracy, the stabilization terms are further weighted in terms of the residual. Through a series of numerical experiments, we validate the method’s capability, showcasing its stability and accuracy.

A space–time variational method for optimal control problems: well-posedness, stability and numerical solution

We consider an optimal control problem constrained by a parabolic partial differential equation with Robin boundary conditions. We use a space–time variational formulation in Lebesgue–Bochner spaces yielding a boundedly invertible solution operator. The abstract formulation of the optimal control problem yields the Lagrange function and Karush–Kuhn–Tucker conditions in a natural manner. This results in space–time variational formulations of the adjoint and gradient equation in Lebesgue–Bochner spaces, which are proven to be boundedly invertible. Necessary and sufficient optimality conditions are formulated and the optimality system is shown to be boundedly invertible. Next, we introduce a conforming uniformly stable simultaneous space–time (tensorproduct) discretization of the optimality system in these Lebesgue–Bochner spaces. Using finite elements of appropriate orders in space and time for trial and test spaces, this setting is known to be equivalent to a Crank–Nicolson time-stepping scheme for parabolic problems. Comparisons with existing methods are detailed. We show numerical comparisons with time-stepping methods. The space–time method shows good stability properties and requires fewer degrees of freedom in time to reach the same accuracy.

Bottlenose dolphins share fish farm areas while maintaining sexual segregation: Investigating group memberships through spatially and temporally explicit parameters

Abstract Group membership is a key attribute of animal societies and central to the study of social structure in several taxa. However, social structure analyses are sensitive to the way data are collected and associations defined. In this study, a time–space method was used to investigate the social structure of common bottlenose dolphins Tursiops truncatus observed and photographed across 7 years in the semi‐enclosed Gulf of Corinth, Greece. Instead of adopting traditional group definitions, individuals were considered as being members of the same group if photographed within a specific time and space window. This approach can be applied post hoc across studies and can offer advantages under challenging sampling conditions (e.g. when dealing with groups spread over vast areas or when group membership is otherwise hard to assess). Dolphins were mostly found around coastal cage aquaculture facilities farming European sea bass Dicentrarchus labrax and gilthead seabream Sparus aurata. Dolphins formed clusters largely or entirely composed of individuals of the same sex, suggestive of sex‐based homophily. Habitat partitioning was not detected: there was substantial spatial overlap among dolphin clusters, with all individuals using a relatively small area in the northern portion of the Gulf, where most of the productive fish farms were located. Associations between females were stronger than those between males, and daughters tended to stay in the group of their mothers. Sex‐based social clustering may allow females and calves to limit interactions with potentially aggressive males, while individuals of both sexes benefit from prey concentrated around fish farms. Adaptation to foraging around farms can result in trade‐offs between the costs and benefits of nourishment and social interaction. This may have both positive or negative effects on the animals that should be considered in the context of ensuring their favourable conservation status.

Method for reconstruction of axisymmetric capillary wave surface topography using inverse ray-tracing of refracted laser sheet

Capillary waves can be used to measure the fundamental fluid properties such as surface tension as well as, potentially, the viscosity of Newtonian fluids. This requires the measurement of various wave parameters, mainly wavelength, amplitude, and decay coefficient. However, the different scales of magnitudes make it a challenging task. Optical methods are well suited to analyze such problems due to their non-intrusive nature and high dynamic measurement resolution in both space and time. These methods are further categorized as point methods for a single probe measurement and space–time methods for transient measurement of the complete surface. Dynamic space–time methods are preferred despite the associated complex post-processing since they enable reconstruction of the wave surface. Some existing methods are discussed, and an improved method is then proposed to actually solve the associated inverse optics problem. In the method, an axisymmetric wave surface is re-constructed by analyzing the refracted laser sheet. The assumptions, simplifications, and constraints are taken to be compatible with experimental aspects for future validation. It is derived using the fundamental concepts in physics and the only major assumption of the axisymmetric nature of wave surface. The method exploits the underlying symmetry in the topography, making it more versatile, and suited for linear and non-linear capillary waves and waves with planar wavefront. The impact of parameters on the final result is determined through numerical simulations. Very low error (average and maximum) values are observed between reference and reconstructed topography for damped and undamped wave surfaces with a wide range of curvatures. Optimum values of critical parameters and associated reasoning are presented.

Two space–time methods for solving Burgers’ equation

Burgers’ equation is a kind of quasi-linear important partial differential equation appeared in many fields. The nonlinear term contained in this equation results in difficulty in finding its high precision numerical solution. Most existed research focused on one-dimensional and two-dimensional Burgers’ systems. Seldom research studied the three-dimensional Burgers’ problem. In this paper, two space–time methods based on the polynomial particular solutions (ST-MPPS) and the polynomial used as basis functions directly, have been proposed to solve three-dimensional Burgers’ equation at different final time with different Reynolds numbers. The numerical examples show that the greatest attraction of the ST-MPPS is its high precision and robustness. When using the space–time polynomial functions method, some interesting phenomenon appears with the Reynolds number increasing.

Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems

<p style='text-indent:20px;'>We consider a hyperbolic system of partial differential equations on a bounded interval coupled with ordinary differential equations on both ends. The evolution is governed by linear balance laws, which we treat with semigroup and time-space methods. Our goal is to establish the exponential stability in the natural state space by utilizing the stability with respect to the first-order energy of the system. Derivation of a priori estimates plays a crucial role in obtaining energy and dissipation functionals. The theory is then applied to specific physical models.</p>

Localized space–time method of fundamental solutions for three-dimensional transient diffusion problem

Localized space–time method of fundamental solutions for three-dimensional transient diffusion problem

Multilevel space–time block diagonal preconditioners for parabolic problems

We present and investigate two new robust space–time preconditioned GMRES methods for solving linear system of equations arising from the discretization of parabolic equations. With these methods, a block diagonal linear system instead of a block lower bidiagonal linear system will be solved in each space–time subdomain. It shows that this technique can reduce the cost of the computation and memory overhead. We develop an optimal convergence theory which shows that convergence rate is bounded independently of the spatial mesh sizes, the time step size, the number of subdomains, the number of levels and the window size. Some numerical results are reported to confirm the theory in terms of optimality and scalability. Moreover, numerical comparisons with space–time additive Schwarz algorithm are also given to show the actual competitiveness our proposed space–time methods.

A Posteriori Error Analysis for Implicit\u2013Explicit hp-Discontinuous Galerkin Timestepping Methods for Semilinear Parabolic Problems

A posteriori error estimates in the L_infty (mathcal {H})- and L_2(mathcal {V})-norms are derived for fully-discrete space–time methods discretising semilinear parabolic problems; here mathcal {V}hookrightarrow mathcal {H}hookrightarrow mathcal {V}^* denotes a Gelfand triple for an evolution partial differential equation problem. In particular, an implicit–explicit variable order (hp-version) discontinuous Galerkin timestepping scheme is employed, in conjunction with conforming finite element discretisation in space. The nonlinear reaction is treated explicitly, while the linear spatial operator is treated implicitly, allowing for time-marching without the need to solve a nonlinear system per timestep. The main tool in obtaining these error estimates is a recent space–time reconstruction proposed in Georgoulis et al. (A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems, Submitted for publication) for linear parabolic problems, which is now extended to semilinear problems via a non-standard continuation argument. Some numerical investigations are also included highlighting the optimality of the proposed a posteriori bounds.

WHITE STAG model: wise human interaction tracking and estimation (WHITE) using spatio-temporal and angular-geometric (STAG) descriptors

To understand human to human dealing accurately, human interaction recognition (HIR) systems require robust feature extraction and selection methods based on vision sensors. In this paper, we have proposed WHITE STAG model to wisely track human interactions using space time methods as well as shape based angular-geometric sequential approaches over full-body silhouettes and skeleton joints, respectively. After feature extraction, feature space is reduced by employing codebook generation and linear discriminant analysis (LDA). Finally, kernel sliding perceptron is used to recognize multiple classes of human interactions. The proposed WHITE STAG model is validated using two publicly available RGB datasets and one self-annotated intensity interactive dataset as novelty. For evaluation, four experiments are performed using leave-one-out and cross validation testing schemes. Our WHITE STAG model and kernel sliding perceptron outperformed the existing well known statistical state-of-the-art methods by achieving a weighted average recognition rate of 87.48% over UT-Interaction, 87.5% over BIT-Interaction and 85.7% over proposed IM-IntensityInteractive7 datasets. The proposed system should be applicable to various multimedia contents and security applications such as surveillance systems, video based learning, medical futurists, service cobots, and interactive gaming.

Space–time polynomial particular solutions method for solving time-dependent problems

A new space–time method, utilizing polynomials as the basis function, has been developed for solving time-dependent problems. Our proposed method does not have stability issues, nor does it require any parameters as were needed in the space–time radial basis function method, such as, the shape parameter, or those for the nodes distribution. In this article, various linear and nonlinear numerical examples on irregular and regular space domains are considered by the new space–time method. The results obtained demonstrate that our proposed method is stable and highly accuracy.

Space–time Galerkin methods for simulation of laser heating using the generalized nonlinear model

The generalized thermal model is a thermodynamically consistent extension of the classical Fourier’s law for describing thermal energy transportation which is very relevant to applications involving very small length, time scales and/or at extremely low temperatures. Under such conditions, thermal propagation has been observed to manifest as waves, a phenomenon widely referred to as second sound effect. However, this is in contrast to the paradoxical prediction of the Fourier’s model that thermal disturbances propagate with infinite speed. In this work, we review the nonlinear model based on the theory of Green and Naghdi for thermal conduction in rigid bodies and present its implementation within a class of space–time methods. The unconditional stability of the time-discontinuous Galerkin method without restriction over the grid structure of the space–time domain is proved. We also perform a number of numerical experiments to study the convergence properties and analyze the thermal response of materials under short-pulsed laser heating in two space dimensions.

A cut finite element method for incompressible two-phase Navier–Stokes flows

We present a space–time Cut Finite Element Method (CutFEM) for the time-dependent Navier–Stokes equations involving two immiscible incompressible fluids with different viscosities, densities, and with surface tension. The numerical method is able to accurately capture the strong discontinuity in the pressure and the weak discontinuity in the velocity field across evolving interfaces without re-meshing processes or regularization of the problem. We combine the strategy proposed in P. Hansbo et al. (2014) [14] for the Stokes equations with a stationary interface and the space–time strategy presented in P. Hansbo et al. (2016) [20]. We also propose a strategy for computing high order approximations of the surface tension force by computing a stabilized mean curvature vector. The presented space–time CutFEM uses a fixed mesh but includes stabilization terms that control the condition number of the resulting system matrix independently of the position of the interface, ensure stability and a convenient implementation of the space–time method based on quadrature in time. Numerical experiments in two and three space dimensions show that the numerical method is able to accurately capture the discontinuities in the pressure and the velocity field across evolving interfaces without requiring the mesh to be conformed to the interface and with good stability properties.

Regional Climate Modelling: Methods of Obtaining the Mesoscale from High-Resolution Data

Several methods of isolating available mesoscale circulations from high-resolution data are presented. We discuss temporal and spatial filtration as the classical approach, a combined time-space method (based on two independent numerical simulations with different resolution), and a dynamic method (based on the geostrophic approach as a separation criterion between synoptic and mesoscale processes). The results demonstrate that the dynamic distinction method is the most promising one. Decomposition of the velocity field into geostrophic and ageostrophic components is performed. The research was conducted using the long-term high-resolution North Atlantic Atmospheric Downscaling (NAAD) experiment based on the Weather Research and Forecast model (WRF).

Parallel two-level space–time hybrid Schwarz method for solving linear parabolic equations

In this paper, we present a two-level space–time hybrid Schwarz preconditioner for GMRES based on the classical hybrid Schwarz method and the second-order backward differentiation formula. In the proposed method, the parabolic equations are solved in parallel on both of the space and time directions. Under some reasonable assumptions, the optimal convergence theory is developed for the proposed space–time method, i.e., the convergence rate is independent of the mesh parameters, the number of subdomains and the window size. Some numerical results are given to confirm the theory very well in terms of the convergence rate and accuracy. And the strong/weak scalability obtained with 4096 processors is also reported to show the efficiency of the proposed method.

Computer Modeling of Wind Turbines: 1. ALE-VMS and ST-VMS Aerodynamic and FSI Analysis

This is the first part of a two-part article on computer modeling of wind turbines. We describe the recent advances made by our teams in ALE-VMS and ST-VMS computational aerodynamic and fluid–structure interaction (FSI) analysis of wind turbines. The ALE-VMS method is the variational multiscale version of the Arbitrary Lagrangian–Eulerian method. The VMS components are from the residual-based VMS method. The ST-VMS method is the VMS version of the Deforming-Spatial-Domain/Stabilized Space–Time method. The ALE-VMS and ST-VMS serve as the core methods in the computations. They are complemented by special methods that include the ALE-VMS versions for stratified flows, sliding interfaces and weak enforcement of Dirichlet boundary conditions, ST Slip Interface (ST-SI) method, NURBS-based isogeometric analysis, ST/NURBS Mesh Update Method (STNMUM), Kirchhoff–Love shell modeling of wind-turbine structures, and full FSI coupling. The VMS feature of the ALE-VMS and ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow, and the moving-mesh feature of the ALE and ST frameworks enables high-resolution computation near the rotor surface. The ST framework, in a general context, provides higher-order accuracy. The ALE-VMS version for sliding interfaces and the ST-SI enable moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the sliding interface or the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-SI also enables prescribing the fluid velocity at the turbine rotor surface as weakly-enforced Dirichlet boundary condition. The STNMUM enables exact representation of the mesh rotation. The analysis cases reported include both the horizontal-axis and vertical-axis wind turbines, stratified and unstratified flows, standalone wind turbines, wind turbines with tower or support columns, aerodynamic interaction between two wind turbines, and the FSI between the aerodynamics and structural dynamics of wind turbines. Comparisons with experimental data are also included where applicable. The reported cases demonstrate the effectiveness of the ALE-VMS and ST-VMS computational analysis in wind-turbine aerodynamics and FSI.