Search Results (56)

Environmental policies and intermittent renewable energy (RE) drive large-scale hydrogen production towards hybrid supply configurations, combining collocated RE units and the electricity market (EM). This links the power and hydrogen sectors through EM/hydrogen prices, dispatch, and hydrogen demand profiles. In a hybrid configuration, the strategic role of RE in the EM enhances these links by creating profit opportunities. This work develops a bi-level model, optimizing electrolyzer size and location, operational decisions and RES bidding strategies, while explicitly modeling EM clearing. In the upper-level, an EM player, owning strategically bidding RE assets, evaluates expanding into the use of electrolyzers that act as price-takers. The lower-level problem clears the EM. The proposed framework is applied to an IEEE 24-node test system. The results show how EM conditions determine investments for different hydrogen price cases. It is revealed that differentiated electricity sourcing across electrolyzers and efficiency-preserving dispatch impact operational decisions, leading to revenue improvements. Moreover, renewable capacity withholding is used to avoid zero EM prices and mitigate the economic impact of unmet hydrogen demand when RE availability is limited and electrolyzer participation in the EM is restricted. Time-window-constrained hydrogen demand mitigates unutilized RE by 39% compared to that for hourly demand. Full article

A new generalization of the Logarithmic mean function and Euler’s Beta k-Logarithm function is proposed using the Mittag–Leffler k-function. We study their analytical properties, including functional relations, symmetry relation, inequalities, summation representations, and integral representations. Mellin transformations are established, and a generalized k-Beta Logarithmic distribution is presented along with its probabilistic applications. Furthermore, we introduce a novel k-Beta Logarithmic fractional derivative operator of Caputo type and develop a Legendre spectral collocation method with Chebyshev–Gauss–Lobatto nodes for the numerical solution of associated fractional differential equations. Rigorous error analysis in the weighted $L^2$-norm is provided, establishing algebraic convergence for finite-regularity solutions and exponential convergence for analytic solutions. Numerical experiments confirm the theoretical convergence rates and demonstrate the efficiency and spectral accuracy of the proposed scheme. Full article

This research paper investigates the solution of diffusion equations characterized by Third-Kind (Robin) boundary conditions within n-dimensional complex domains. The analysis is conducted in the $L_2$ Hilbert space, which facilitates the substantiation of both the existence and uniqueness of solutions through variational methods. Analytical solutions are derived for multidimensional domains by employing the Fourier method and spectral analysis techniques. Complementing this theoretical framework, a high-accuracy numerical approach based on the Associated Legendre Polynomials Collocation Spectral Method (ALP-CSM) with Chebyshev–Gauss–Lobatto nodes is developed. Rigorous convergence analysis confirms spectral accuracy, with numerical examples in one, two, and three dimensions demonstrating error decay from $\mathcal{O}\left({10}^{-3}\right)$ to machine precision $\mathcal{O}\left({10}^{-15}\right)$. The mathematical impact of Third-Kind boundary conditions on the diffusion rate and the steady state of the system is demonstrated. The obtained results provide a robust tool for modeling physical processes, particularly in systems involving heat exchange on the surfaces of complex-structured domains, offering both theoretical insight and computational efficiency. Full article

This work investigates the influence of center positioning in Radial Basis Function (RBF) collocation methods for solving two-dimensional structural problems. The study enforces equilibrium using the indefinite equations approach and evaluates different center distributions to assess their impact on solution accuracy and stability. The numerical results are compared against Finite Element Method (FEM) solutions to determine the effectiveness of the tested approaches. The findings provide insights into optimal node placement strategies, improving the reliability and applicability of RBF collocation methods in structural analysis. Full article

The minimum fuel transfer problem in low-thrust trajectory optimization remains a major challenge and is typically addressed using bang-bang control. A novel methodology integrating Adaptive Multiresolution Collocation (AMRC) and Sequential Convex Programming (SCP) to solve the minimum-fuel low-thrust trajectory optimization problem is proposed. First, the approach employs the cubic spline wavelet-like transform for mesh refinement, where wavelet coefficients serve as error indicators to dynamically concentrate nodes in regions of rapid state variation. Then, the nonlinear programming problem is convexified via control variable relaxation and small-perturbation linearization, reformulated as a second-order cone programming (SOCP) problem, and efficiently solved using convex optimization tools. Subsequently, progressive selection of the location points ensures rapid and accurate convergence to the optimal trajectory. Finally, numerical simulations of Earth–Mars and Earth–Venus transfer validate the effectiveness and accuracy of the AMRC-based method. Compared with conventional approaches, the proposed method achieves comparable optimality while markedly improving computational efficiency, precisely localizing switching times, and improving numerical precision, requiring only 29.7% of the nodes and 14.7% of the computation time of uniform-grid convex optimization, achieving fuel-optimal deviations within 0.07% of the indirect method and demonstrating accuracy improvements of 2–3 orders of magnitude over GPOPS. Full article

Pedestrian inertial navigation is a pivotal technology for achieving seamless indoor and outdoor positioning. Traditional methods based on the Extended Kalman Filter (EKF) suffer from cumulative errors induced by inertial measurement unit (IMU) noise, which severely degrade the accuracy of pedestrian trajectory estimation over long durations. To address this critical limitation, a post-processing trajectory optimization approach for pedestrian inertial navigation based on the Birkhoff pseudospectral method is proposed in this paper. Leveraging the initial attitude and position estimates derived from the Zero-Velocity Update (ZUPT) technique and the EKF framework, the proposed method first parameterizes continuous-time acceleration measurements by adopting Chebyshev nodes as collocation points, and then formulates and solves the trajectory optimization problem via a Birkhoff pseudospectral framework, which effectively suppresses noise interference from the IMU accelerometer. Simulation experiments validate the superior noise suppression capability of the proposed algorithm. Furthermore, physical experiments conducted with a foot-mounted IMU demonstrate that the final position error is reduced by approximately 90% in comparison with the traditional EKF-based method. Full article

Direct collocation transcription is a dominant technique for solving complex optimal control problems, converting continuous dynamics into large-scale, sparse nonlinear programming problems. The computational efficiency of this approach is fundamentally limited by the evaluation of first- and second-order derivatives required by modern optimization algorithms. While general-purpose automatic differentiation tools exist, they often fail to fully exploit the repetitive substructure inherent in trajectory discretization. This paper presents a vectorized, sparse, second-order forward automatic differentiation framework specifically tailored for direct collocation methods. By explicitly distinguishing between scalar and vector nodes within the expression graph, the proposed method leverages the independence of mesh point evaluations to enable Single Instruction, Multiple Data (SIMD) execution and optimize memory access patterns. This structure-aware approach ensures linear time complexity with respect to the number of discretization nodes while maintaining the flexibility to handle complex dependencies. The methodology is implemented in the open-source software package pockit and is validated through three distinct engineering case studies: the aggressive stabilization of a nano-quadrotor, the powered descent guidance of a reusable launch vehicle, and a low-thrust heliocentric orbital transfer. These applications demonstrate the framework’s capability to deliver high-performance derivative computation for large-scale, nonlinear dynamical systems. Full article

In this study, a finite-volume computational fluid dynamics (CFD) technique for application on skewed meshes using staggered pressure nodes is proposed. The method is based on the derivation of a momentum equation for the cell face velocities from appropriately discretised momentum equations in the two cells surrounding the cell face with the driving pressure difference pertaining to the staggered adjacent nodes. In this way, a staggered mesh-like method is obtained that would prevent the occurrence of oscillatory behaviour in pressure or velocity fields. The cell-face velocities are then forced to obey continuity via an equation for pressure akin to other standard CFD schemes. This article describes the formulation of the cell-face momentum equation as well as the way the nodal velocity is reconstructed from the surrounding cell-face velocities. The method is demonstrated to recover the advantages of the PISO solution algorithm that were diminished in implementations in collocated schemes. It is also validated on a reference two-dimensional, steady viscous flow case on both rectangular and skewed meshes to verify its accuracy. It is then applied to the case of an unsteady vortex-shedding flow past a square obstacle, on both rectangular and skewed meshes, and the results are compared with a solution obtained from a collocated method as well as with an experimental value of the Strouhal number. Full article

This study employs the fourth-order phase-field method (PFM) to investigate crack propagation. The PFM incurs significant computational costs due to its need for a highly dense node arrangement for accurate crack propagation. This study proposes an adaptive loading step size strategy combined with a scattered node (SCN_var) arrangement with variable spacings. The mechanical and phase-field models are solved using the strong-form meshless local radial basis function collocation method in a staggered approach. The method’s performance is evaluated based on accuracy and computational cost, using regular nodes (RGN) and scattered nodes (SCN_uni) with uniform spacing, as well as SCN_var with variable node spacing. Two benchmark tests are used to analyze the proposed method: a symmetric double-notch tension and a single-edge notch shear test. The analysis shows that the adaptive step size strategy improves numerical stability while the SCN_var significantly reduces computational cost. Using SCN_var, the CPU time is decreased by about thirty times compared to uniform nodes in the tensile case and by approximately three times in the shear case, without sacrificing accuracy. This confirms that directing computational resources to critical regions can significantly reduce CPU time, suggesting that adaptive node redistribution could further enhance computational performance. Full article

Microwave Radiation Imagers (MWRIs) onboard the FY-3B, FY-3C, and FY-3D satellites are the primary sensors for sea surface temperature (SST) observation. Benefiting from the resolution of several key calibration issues in brightness temperature products, MWRI SST records spanning more than a decade have been reprocessed. In this study, these reprocessed SST products are evaluated using direct comparison and the extended triple collocation (ETC) method, along with additional error analyses. Compared with iQuam SST, the reprocessed MWRI SST products from the three satellites show total root mean square errors (RMSEs) of 0.80–0.82 °C and total biases of −0.12 °C to 0.00 °C. ETC analyses based on MWRI, ERA5, and Argo SSTs indicate random errors of 0.76–0.78 °C. Furthermore, the reprocessed MWRI SST products demonstrate temporal stability and exhibit minimal crosstalk effects from sea surface wind speed, columnar water vapor, and columnar cloud liquid water in SST retrievals. Compared with previous versions, the reprocessed products show significant improvements, with consistent performance across FY-3B, FY-3C, and FY-3D. However, differences in SST observations due to the varying local times of the ascending nodes among the three satellites should be corrected in practical applications. Full article

Accurate prediction of photovoltaic performance hinges on resolving the electron density in the P-region and the hole density in the N-region. Motivated by this need, we present a comprehensive assessment of a meshless global radial basis function (RBF) collocation strategy for the steady current continuity equation, covering a one-dimensional two-region P–N junction and a two-dimensional single-region problem. The study employs Gaussian (GA) and generalized multiquadric (GMQ) bases, systematically varying shape parameter and node density, and presents a detailed performance analysis of the meshless method. Results map the accuracy–stability–computation-time landscape: GA achieves faster convergence but over a narrower stability window, whereas GMQ exhibits greater robustness to shape-parameter variation. We identify stability plateaus that preserve accuracy without severe ill-conditioning and quantify the runtime growth inherent to dense global collocation. A utopia-point multi-objective optimization balances error and computation time to yield practical node-count guidance; for the two-dimensional case with equal weighting, an optimum of 19 intervals per side emerges, largely insensitive to the RBF choice. Collectively, the results establish global RBF collocation as a meshless, accurate, and systematically optimizable alternative to conventional mesh-based solvers for high-fidelity carrier-density prediction in P-N junctions, thereby enabling more reliable performance analysis and design of photovoltaic devices. Full article

Scientific relation extraction plays a crucial role in constructing scientific knowledge graphs that can contextually integrate knowledge from the scientific literature. However, a large majority of existing efforts do not support human guidance, which hinders refining the construction of scientific knowledge graphs and, thus, the natural cycle of scientific knowledge integration. Therefore, there is a necessity to ground the human–machine collaboration in learned mechanisms, the prerequisite of which is quantifying the contribution of candidate mechanisms. In addressing this, we introduce an efficient summation node architecture by leveraging a graph neural network (GNN) on semantic patterns among dependency graphs. Then, we quantify the potential of different semantic invariance in serving as semantic interfaces towards the flexible construction of scientific knowledge graphs. Specifically, we posit that collocation-level patterns can enhance both extraction accuracy and F1 scores. Our proposed solutions exhibit promising performances for certain relations under bi-classification configurations, facilitating the learning of more semantic invariance from the word level to the collocation level. In conclusion, we assert that the flexible and robust construction of scientific knowledge graphs in the future will necessitate continual improvements to augment learned semantic invariance. This can be achieved through the development of more integrated and extended input graphs and transformer-based GNN architectures. Full article

This paper uses the flexural vibration of cantilever beams as a benchmark problem to test mesh-free and finite element methods in structural dynamics. First, a symbolic analysis of the “kernel collocation” type mesh-free method is carried out, in which the collocation function satisfies the boundary conditions. This enables both Finite Element (FE) and mesh-free results to be compared with exact analytical ones. Thereafter, the natural frequencies and Frequency Response Function (FRF), in terms of the beam parameters, are determined and compared with the analytical results, that exist in the literature. It is shown that by adjusting the parameters of the kernel function, we can find identical peaks to those of the analytical method. The finite element method is also employed to solve this problem, and the first three natural frequencies were computed in terms of the beam parameters. When comparing the two methods, we see that by increasing the number of elements in the FEM we can always achieve better accuracy, but we will obtain twice the number of modal frequencies. However, the mesh-free method with the same number of nodes does not provide these extra frequencies. From this benchmark problem, it is concluded that the accuracy of the mesh-free methods always depends on the adjustment of the kernel function. However, the FEM is advantageous because it does not require such adjustments. Full article

In this study, we discuss the symmetries underlying Bernstein polynomial differentiation matrices, as they are used in the collocation method approach to approximate solutions of initial and boundary value problems. The symmetries are brought into connection with those of the Chebyshev pseudospectral method (Chebyshev polynomial differentiation matrices). The treatment discussed here enables a faster and more accurate generation of differentiation matrices. The results are applied in numerical solutions of several initial value problems for the partial differential equation of convection–diffusion reaction type. The method described herein demonstrates the combination of advanced numerical techniques like polynomial interpolation, stability-preserving timestepping, and transformation methods to solve a challenging nonlinear PDE efficiently. The use of Bernstein polynomials offers a high degree of accuracy for spatial discretization, and the CGL nodes improve the stability of the polynomial approximation. This analysis shows that exploiting symmetry in the differentiation matrices, combined with the wise choice of collocation nodes (CGL), leads to both accurate and efficient numerical methods for solving PDEs and accuracy that approach pseudospectral methods that use well-known orthogonal polynomials such as Chebyshev polynomials. Full article

The thermal analysis of brake discs is crucial for studying issues such as wear and cracking. This paper establishes a symmetric two-dimensional brake disc model using the barycentric rational interpolation collocation method (BRICM). The model accounts for the effects of thermal radiation and is linearized using Newton’s linear iteration method. In the spatial dimension, the two-dimensional heat conduction equation is discretized using BRICM, while in the temporal dimension, it is discretized using the finite difference method (FDM). The resulting temperature distribution of the brake disc during two consecutive braking events is consistent with experimental data. Additionally, factors affecting the accurate calculation of the temperature are examined. Compared to other models, the proposed model achieves accurate temperature distributions with fewer nodes. Furthermore, the numerical results highlight the significance of thermal radiation within the model. The results obtained using BRICM can be used to predict the two-dimensional temperature distribution of train brake discs. Full article