Implicit Method Research Articles

Efficient magnetohydrodynamic modelling of the time-evolving corona by COCONUT

Magnetohydrodynamic (MHD) solar corona models are critical in the Sun-to-Earth modelling chain and are the most complex and computationally intensive component. Compared to quasi-steady-state corona models that are constrained by a time-invariant magnetogram over a Carrington rotation (CR) period, time-evolving corona models driven by time-varying photospheric magnetograms are more realistic and can maintain more useful information to accurately describe solar wind evolution and forecast coronal mass ejection propagation. Implicit methods have significantly improved the efficiency of quasi-steady MHD coronal modelling. However, developing efficient time-evolving corona models to improve space weather forecasting is also important. This paper aims to demonstrate that time-evolving corona simulations can be performed efficiently and accurately using an implicit method with relatively large time steps, thus reducing the overall computational cost. We also evaluate differences between coronal structures captured by time-evolving and quasi-steady simulations over a CR period during solar minimum. We extended the quasi-steady COCONUT model, a global MHD corona model that uses implicit methods to select large time steps, into a time-evolving corona model. Specifically, we used a series of hourly updated photospheric magnetograms to drive the evolution of coronal structures from the solar surface to $25; R_s$ during two CRs around the 2019 eclipse in an inertial coordinate system. At each time step, the inner-boundary magnetic field was temporal-interpolated and updated from adjacent observation-based magnetograms. We compare the time-evolving and quasi-steady simulations to demonstrate that the differences in these two types of coronal modelling can be obvious even for a solar minimum. The relative differences in radial velocity and density can be over $15 %$ and $25 %$ at 20$;R_s$ during one CR period. We also evaluated the impact of time steps on the simulation results. Using a time step of approximately 10 minutes balances efficiency and necessary numerical stability and accuracy for time-evolving corona simulations around solar minima. The chosen 10-minute time step significantly exceeds the Courant-Friedrichs-Lewy stability condition needed for explicit corona modelling, and the time-evolving COCONUT can thus simulate the coronal evolution during a full CR within only 9 hours (using 1080 CPU cores for 1.5M grid cells). The simulation results demonstrate that time-evolving MHD coronal simulations can be performed efficiently and accurately using an implicit method, offering a more realistic alternative to quasi-steady-state simulations. The fully implicit time-evolving corona model thus promises to simulate the time-evolving corona accurately in practical space weather forecasting.

Mixed atomistic-implicit quantum/classical approach to molecular nanoplasmonics.

A multiscale quantum mechanical (QM)/classical approach is presented that is able to model the optical properties of complex nanostructures composed of a molecular system adsorbed on metal nanoparticles. The latter is described by a combined atomistic-continuum model, where the core is described using the implicit boundary element method (BEM) and the surface retains a fully atomistic picture and is treated employing the frequency-dependent fluctuating charge and fluctuating dipole (ωFQFμ) approach. The integrated QM/ωFQFμ-BEM model is numerically compared with state-of-the-art fully atomistic approaches, and the quality of the continuum/core partition is evaluated. The method is then extended to compute surface-enhanced Raman scattering within a time-dependent density functional theory framework.

Higher-order accurate mass lumping for explicit isogeometric methods based on approximate dual basis functions

Abstract This paper introduces a mathematical framework for explicit structural dynamics, employing approximate dual functionals and row-sum mass lumping. We demonstrate that the Petrov–Galerkin method developed in our previous work—utilizing row-sum mass lumping—can be interpreted as a Galerkin method with a customized higher-order accurate mass matrix. Unlike prior work, our method correctly incorporates Dirichlet boundary conditions, while preserving optimal spatial accuracy. The mathematical analysis is substantiated by spectral analysis, two-dimensional linear benchmarks illustrating robustness under mesh distortion and a three-dimensional geometrically non-linear forced vibration analysis. The obtained results reveal that our approach achieves accuracy and robustness comparable to a traditional Galerkin method employing the consistent mass formulation, while retaining the explicit nature of the lumped mass formulation.

Numerical Study on Hydrodynamic Performance and Vortex Dynamics of Multiple Cylinders Under Forced Vibration at Low Reynolds Number

Flow around clustered cylinders is widely encountered in engineering applications such as wind energy systems, pipeline transport, and marine engineering. To investigate the hydrodynamic performance and vortex dynamics of multiple cylinders under forced vibration at low Reynolds numbers, with a focus on understanding the interference characteristics in various configurations, this study is based on a self-developed radial basis function iso-surface ghost cell computing platform, which improves the implicit iso-surface interface representation method to track the moving boundaries of multiple cylinders, and employs a self-constructed CPU/GPU heterogeneous parallel acceleration technique for efficient numerical simulations. This study systematically investigates the interference characteristics of multiple cylinder configurations across various parameter domains, including spacing ratios, geometric arrangements, and oscillation modes. A quantitative analysis of key parameters, such as aerodynamic coefficients, dimensionless frequency characteristics, and vorticity field evolution, is performed. This study reveals that, for a dual-cylinder system, there exists a critical gap ratio between X/D = 2.5 and 3, which leads to an increase in the lift and drag coefficients of both cylinders, a reduction in the vortex shedding periodicity, and a disruption of the wake structure. For a three-cylinder system, the lift and drag coefficients of the two upstream cylinders decrease with increasing spacing. On the other hand, this increased spacing results in a rise in the drag of the downstream cylinder. In the case of a four-cylinder system, the drag coefficients of the cylinders located on either side of the flow direction are relatively high. A significant increase in the lift coefficient occurs when the spacing ratio is less than 2.0, while the drag coefficient of the downstream cylinder is minimized. The findings establish a comprehensive theoretical framework for the optimal configuration design and structural optimization of multicylinder systems, while also providing practical guidelines for engineering applications.

A Fully Explicit–Explicit Staggered Algorithm for the Dynamic Response of Fluid-Saturated Porous Media

The analysis of the dynamic response of fluid-saturated porous media under stress waves is of great practical value in the fields of geotechnical engineering, geophysics, earthquake engineering and marine engineering. In this research, a new fully explicit finite element algorithm for solving the coupled soil-pore fluid dynamic problem is developed based on the u–p formulation. The proposed method is a staggered algorithm that is realized with the central difference method used to solve the displacement u and the improved Euler method used to solve the fluid pressure p, it has a second-order theoretical accuracy since both the central difference method and the improved Euler method are second-order methods. The correctness and efficiency of the proposed method are investigated through two numerical examples. The computational results of the one-dimensional soil column model shows that the numerical solution of the proposed algorithm agree well with the theoretical analytical solution. The differences of the computational accuracy and efficiency between the proposed method and the other existing methods are also discussed in the numerical examples, and the results show that the proposed explicit method is higher in calculation efficiency than the implicit algorithm, and its accuracy is higher than that of the existing first-order explicit method.

Implicit Central Difference Approximations of Averaged Dynamics of Highly Oscillatory Systems With Applications to Direct Optimal Control

ABSTRACTTrajectory optimization of highly oscillatory systems can require huge computational efforts if the horizon of the problem is much larger than the duration of a single cycle. To alleviate this effort, stroboscopic averaging methods can be used, which utilize local single‐cycle simulations of the oscillatory dynamics to then approximate the average dynamics of the system and integrate them with integration steps much larger than a single cycle. Targeting especially the field of direct optimal control, where, after discretization, the simulation of the dynamics is often included implicitly in the equality constraints of the nonlinear programming problem, we introduce an implicit central difference scheme for the approximation of the average dynamics. In the introduced implicit central difference methods, we solve a nonlinear system of equations that connects single‐cycle simulations of the oscillatory dynamics in order to approximate the average dynamics from a linear combination of points in state‐space. We derive the accuracy order for this generalized ‐point central difference approximation of the average dynamics and confirm the claims in numerical experiments. Compared to existing explicit approaches, the introduced methods are up to twice as efficient while maintaining the same level of accuracy.

An iterative dynamic chemical stiffness removal method for reacting flow simulations

An iterative dynamic chemical stiffness removal method (IDCSR) based on quasi-steady-state approximation (QSSA) is proposed. The IDCSR method is built on a previously developed non-iterative method which has proved to work well for small timestep sizes. A novel iterative procedure is designed in IDCSR to enable explicit time integration of stiff chemistry at relatively large timestep sizes relevant to practical reacting flow simulations. The effectiveness of the iterative procedure is first demonstrated with a toy problem and homogeneous auto-ignition with fixed integration step sizes, showing that larger timestep sizes can be allowed for explicit time integration using IDCSR compared with the previous non-iterative method. IDCSR is then compared with existing explicit chemistry solvers for simulations of homogeneous auto-ignition and shows similar or lower computational cost but significantly higher accuracy across a wide range of timestep sizes. IDCSR is further combined with an automatic adaptive time-stepping scheme for simulations of 0-D homogeneous auto-ignition and a 2-D laminar lifted n-dodecane jet flame. For the 0-D auto-ignition simulations, IDCSR is shown to reduce both the error (by 43%–90%) and computational cost (by 6–15 times) compared with existing explicit solvers, while achieving speed-up factors of up to 400 compared with VODE for a wide range of timestep sizes and reaction mechanisms. For the 2-D jet flame simulations, speed-up factors of 15 and 31 for chemistry integration, and 5 and 9 for overall simulation, are achieved by IDCSR compared with CVODE with and without analytic Jacobian, respectively.

A Generalized Single‐Step Multi‐Stage Time Integration Formulation and Novel Designs With Improved Stability and Accuracy

ABSTRACTThis paper focuses upon the single‐step multi‐stage time integration methods for second‐order time‐dependent systems. Firstly, a new and novel generalization of the Runge‐Kutta (RK) and Runge‐Kutta‐Nyström (RKN) methods is proposed, featuring an advanced Butcher table for designing new and optimal algorithms. It encompasses not only the classical multi‐stage methods as subsets, but also introduces novel designs with enhanced accuracy, stability, and numerical dissipation/dispersion properties. Secondly, to sharpen the focus on the present developments, several existing multi‐stage explicit time integration methods (which are of interest and the focus of this paper) are revisited within the proposed unified mathematical framework, such that it highlights the differences, advantages, and disadvantages of various existing methods. Thirdly, the consistency analysis is rigorously demonstrated using both single‐step and multi‐step local truncation errors, addressing the order reduction problem observed in existing methods when applied to nonlinear dynamics problems. Finally, two sets of single‐step, two‐stage, third‐order time‐accurate schemes with controllable numerical dissipation/dispersion at the bifurcation point are presented. In contrast to existing methods, these newly proposed schemes preserve third‐order time accuracy in nonlinear dynamics applications and exhibit improved stability in cases involving physical damping. Numerical examples are demonstrated to verify the theoretical analysis and the superior performance of the proposed schemes compared to existing methods.

Evidence syntheses in educational technology research: What is not published in English is not visible? A tertiary mapping review

AbstractEvidence syntheses, such as systematic reviews, aim to summarise the current state of research in a field, often using the publication language of a study as a criterion for inclusion or exclusion. However, this has serious implications for capturing evidence from a wider range of geographical areas, and the potential for linguistic bias. In order to explore this issue, a trilingual tertiary mapping review of 446 evidence syntheses within the field of educational technology (EdTech) and published in English, Spanish and German was undertaken, analysing the frequency of multi‐ and monolingual evidence syntheses, reasons for language choice by research teams, and the composition of research teams in multi‐ and monolingual evidence syntheses. Items were included if they were a form of evidence synthesis with an explicit method section, indexed within ERIC, Scopus, Web of Science, Dialnet, FIS‐Bildung, or Google Scholar, education‐related, and published between 1983 and May 2022. The results showed that only eight languages were considered in published syntheses, only five languages were used to construct search strings, most evidence syntheses included research published in English without explaining why, and multilingual research team composition did not predict multilingual evidence syntheses. The findings suggest the need to address publication languages not only as a formal criterion but as an integral aspect of methodological approach, influencing the content and scope of syntheses in educational research.

Error analysis for the implicit boundary integral method

The implicit boundary integral method (IBIM) provides a framework to construct quadrature rules on regular lattices for integrals over irregular domain boundaries. This work provides a systematic error analysis for IBIMs on uniform Cartesian grids for boundaries with different degrees of regularity. First, it is shown that the quadrature error gains an additional order of d-12 from the curvature for a strongly convex smooth boundary due to the “randomness” in the signed distances. This gain is discounted for degenerated convex surfaces. Then the extension of error estimate to general boundaries under some special circumstances is considered, including how quadrature error depends on the boundary’s local geometry relative to the underlying grid. Bounds on the variance of the quadrature error under random shifts and rotations of the lattices are also derived.

Damped Iterative Explicit Guidance for Multistage Rockets with Thrust Drop Faults

A damped iterative explicit guidance (DIEG) algorithm is proposed to address the problem of the insufficient convergence of classical explicit guidance methods in the event of thrust drop faults in multistage rockets. Based on the iterative guidance mode (IGM) and powered explicit guidance (PEG), this method is enhanced in three aspects: (1) an accurate transversality condition is derived and applied in the dimension-reduction framework instead of using a simplified assumption; (2) the Gauss–Legendre quadrature formula (GLQF) is adopted to increase the accuracy of the method by addressing the issue of excessive errors in calculating thrust integration using linearization methods based on a small quantity assumption under fault conditions; and (3) a damping factor for solving the time-to-go is introduced to avoid the chattering phenomenon and enhance convergence. A numerical simulation was conducted in single- and multistage mission scenarios by gradually reducing the engine thrust to compare the performance of DIEG and PEG. The results show that DIEG has a much larger convergence range than PEG and has fuel optimality similar to that of the optimization method in most fault scenarios. Finally, the robustness of DIEG under various deviations is verified through Monte Carlo simulation.

Pseudo-energy-preserving explicit Runge-Kutta methods

Using a recent characterization of energy-preserving B-series, we derive the explicit conditions on the coefficients of a Runge-Kutta method that ensure energy preservation (for Hamiltonian systems) up to a given order in the step size, which we refer to as the pseudo-energy-preserving (PEP) order. We study explicit Runge-Kutta methods with PEP order higher than their classical order. We provide examples of such methods up to PEP order six, and test them on Hamiltonian ODE and PDE systems. We find that these methods behave similarly to exactly energy-conservative methods over moderate time intervals and exhibit significantly smaller errors, relative to other Runge-Kutta methods of the same order, for moderately long-time simulations.

Finite Element Analysis of Stress Distribution in Cancellous Bone During Dental Implant Pilot Drilling

Background/Objectives: This study investigates stress distribution in cancellous bone during pilot drilling for dental implants using the Cowper–Symonds model. Understanding the biomechanical effects of drilling parameters on bone health is essential for optimizing implant stability and longevity. Methods: A finite element analysis (FEA) approach was employed to simulate the pilot drilling process in cancellous bone. A three-dimensional jawbone model was developed from CT scan data, processed using 3D Slicer, and refined with CAD tools. The drilling simulation incorporated a rigid pilot drill and flexible cancellous bone, utilizing explicit dynamic methods. Stress distribution was evaluated for drilling depths ranging from 6 mm to 16 mm, with mesh density and strain rate effects considered to ensure accuracy. Results: The results showed an increase in stress levels with drilling depth, with maximum stress recorded at 16 mm. Initial contact stress was 17.3 MPa, rising to 228.9 MPa at deeper penetration due to increased interaction between the drill and bone. Stress distribution patterns emphasized the critical role of drilling depth and design parameters in mitigating bone damage. Conclusions: This study highlights the importance of optimized drilling protocols and pilot drill design to reduce stress and preserve bone integrity. The findings provide valuable insights into improving implant procedures and demonstrate the utility of FEA as a robust tool for evaluating biomechanical impacts during implant placement. Future research should incorporate cortical bone and thermal effects for a comprehensive analysis.

KNOT OPTIMIZATION FOR BI-RESPONSE SPLINE NONPARAMETRIC REGRESSION WITH GENERALIZED CROSS-VALIDATION (GCV)

Nonparametric regression is a statistical method used to model relationships between variables without making strong assumptions about the functional form of the relationship. Nonparametric regression models are flexible and can capture complex relationships that may not be adequately represented by simple parametric forms. Spline is one of the approaches used in nonparametric regression. Splines have the disadvantage of having to use optimal nodes in the data. Therefore, this article discusses the retrieval of optimal knot points using the generalized cross-validation method in the nonparametric bi-response spline regression model. The research results showed that the generalized-cross validation method is the best method for selecting nodes from other methods such as CV, AIC, BIC, RSS, or a more explicit validation-based approach method because of the development of the Cross Validation (CV) method which automatically selects the optimal number of nodes based on the balance between bias and variance. The process of optimizing knot points with Generalized Cross Validation (GCV) on bi-response spline nonparametric regression is implemented using Python can provide optimization at optimal knot points. Based on the results of the generalized cross-validation model analysis, it is concluded that GCV can effectively optimize knot points for spline fitting, ensuring a balanced and efficient model in capturing data patterns without overfitting.

Lyell’s Views of Translation in the Perspective of Thick Translation—Cat Country as an Example

As China’s first science fiction novel, Lao She’s satirical novel Cat Country has been welcomed by readers as soon as it was released in its first English translation. The success of this novel’s foreign translation cannot be separated from the translator William Lyell’s “thick translation”. By describing the explicit and implicit thick translation methods of Lyell’s translation of Cat Country, analyzing the translator’s thick translation skills under the characterization of thick translation, the principle of truth-seeking in translating culture, and the translation guideline of serving the readers of the translated language, the article reveals the basic rationale of the successful translation of Lyell’s translation, which will serve as a reference for the foreign translation of Chinese literature, and better serve the translation practice and theoretical construction.

Study on the transient wheel-rail rolling contact behaviour and key structural parameters of the fixed frog on tram turnout

Trains passing through the turnout experience high-frequency impacts and complex contact behaviour, increasing the likelihood of accidents. To reduce the probability of derailment, the tram turnout fixed frog is improved by optimising the depth of the flange groove to ensure a continuous rolling contact surface. This paper adopts the explicit FE method to analyze the variation pattern of the wheel-rail contact posture during tram passage, investigate the damage mechanism of this new type of structure, and explore the effects of flange groove depth and slope on the performance of vehicles passing through the turnout. The research results show that when the flange is loaded, the contact area has an irregular shape and the flange groove is subject to heavy abrasion under high stress and creep conditions. The service performance of the frog structure can be improved by reducing the flange groove slope. The results provide a theoretical basis for the maintenance and optimal design of the fixed frog.

Cross-Technology Interference-Aware Rate Adaptation in Time-Triggered Wireless Local Area Networks

The proliferation of IoT using heterogeneous wireless technologies within the unlicensed spectrum has intensified cross-technology interference (CTI) in wireless local area networks (WLANs). As WLANs increasingly adopt time-triggered transmission methods to support real-time services, this interference affects throughput, packet loss, and latency. This paper presents a CTI-aware rate adaptation framework designed to mitigate interference in WLANs without direct coordination with heterogeneous wireless devices. The framework includes a CTI identification model and CTI-aware rate selection algorithms. Leveraging short-time Fourier transform, the identification model captures the time–frequency–power characteristics of CTI signals, enabling the estimation of the average power of various heterogeneous wireless technologies employed by interfering devices. The rate selection algorithms predict CTI occurrence times and adjust the transmission rate accordingly, enhancing the performance of existing explicit and implicit interference mitigation methods. Experimental results demonstrated that the lightweight CTI identification model accurately estimated the average power of each type with an error margin of ±1.414 dBm, achieving this in under 1 ms on the target hardware. Additionally, applying the proposed framework to explicit interference mitigation enhanced goodput by 20.67%, reduced packet error rate by 2.38%, and decreased the probability of packets exceeding 1 ms latency by 0.932% compared to conventional methods.

On The Numerical Solutions of the Neutrosophic One-Dimensional Sine-Gordon System

This paper uses finite difference methods to study the numerical solution for neutrosophic Sine-Gordon system in one dimension. We use the explicit method and Crank-Nicholson method. Also, an effective comparison between the results of the two methods has been made, where we obtain the result that Crank-Nicholson method is more accurate than the explicit method, but the explicit method is easier. We also study the stability analysis for each method by using Fourier (Von-Neumann) method and get that Crank-Nicholson method is unconditionally stable while the Explicit method is stable under the condition 𝑟2≤1𝑐2 and 𝑟2≤1.

How do Spanish consumers perceive different lettuce cultivation systems? Insights from explicit and implicit methods

How do Spanish consumers perceive different lettuce cultivation systems? Insights from explicit and implicit methods

Numerical Advancements: A Duel between Euler-Maclaurin and Runge-Kutta for Initial Value Problem

This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms the Runge-Kutta method in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Runge-Kutta method. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods. In conclusion, the proposed method consistently outperforms the Runge-Kutta method experimentally in all practical problems.