Quintic Research Articles

Controllable and abundant soliton states from an all-fiber laser based on a ZrGeTe4 saturable absorber

With many applications increasing expectations for the tunability of coherent pulses, the demand for tunable soliton fiber lasers (TSFLs) is growing. Two-dimensional ternary zirconium germanium telluride (ZrGeTe4) nanomaterials provide an opportunity to obtain high-performance TSFLs. In this research, we developed a TSFL with ZrGeTe4-based saturable absorber (SA). Employing a strategy of constant pump power, tunable soliton states were acquired. The 1st to 5th order harmonic mode-locking were obtained sequentially. The shortest pulse able to obtain was 1.05 ps. Furthermore, the soliton molecule was also obtained. The results suggest that ZrGeTe4-SA may provide an effective route for photonics research.

Selection of effective combination of time and frequency features using PSO-based technique for monitoring oil pipelines

Pipeline installation is a time-consuming and expensive process in the oil sector. Because of this, a pipe is often utilized to carry diverse petroleum products; hence, it is crucial to use a precise and dependable control system to identify the kind and quantity of oil products being transported. This study attempts to identify four petroleum products by using an X-ray tube-based system, feature extraction in the frequency and temporal domains, and feature selection using Particle Swarm Optimization (PSO) in conjunction with a Group Method of Data Handling (GMDH) neural network. A sodium iodide detector, a test pipe that simulates petroleum compounds, and an X-ray source make up the implemented system. The detector's output signals were transmitted to the frequency domain, where the amplitudes of the top five dominant frequencies could be determined. Furthermore, the received signals were analyzed to extract five temporal characteristics-MSR, 4th order moment, skewness, WL, and kurtosis. The PSO system takes into account the extracted time and frequency features as input in order to introduce the optimal combination. Four different GMDH neural networks were constructed, and the chosen characteristics were used as inputs for those networks. Finding the volume ratio of each product was the responsibility of each neural network. The four designed neural networks were able to predict the amount of ethylene glycol, crude oil, gasoil, and gasoline with RMSE of 0.26, 0.17, 0.19, and 0.23, respectively. One compelling argument for using the proposed approach in the oil industry is that it can calculate the volume ratio of products with a root mean square error of no more than 0.26. The adoption of a feature selection method to choose the best ones is credited with this remarkable degree of precision. By providing appropriate inputs to neural networks, the control system has significantly outperformed its predecessors in terms of precision and efficiency.

Lithofacies, stratigraphy and depositional history of Middle Muschelkalk evaporites (Zeglingen Formation) in northern Switzerland

In northern Switzerland, Middle Muschelkalk evaporites (Zeglingen Formation) were deposited under arid conditions in the southernmost part of the epicontinental Central European Basin during times of reduced inflow of sea water from the Tethyan realm. Because of their marginal position in the basin, direct and detailed correlation of Muschelkalk sediments of northern Switzerland with equivalent strata in interior parts of the basin is not straightforward. Based on detailed sedimentological logging of 640 m of drill cores from ten wells in northern Switzerland, 22 lithofacies and 10 lithofacies associations were distinguished for the Middle Muschelkalk evaporites. High-resolution regional correlations of gamma-ray logs record substantial thickness variation of the evaporites. Locally, dissolution was recognized by visual core examination that could be dated to Middle Triassic times and that was likely related to subsurface fluid flow along deeper seated faults. In combination with the regional thickness variation, the dissolution phenomena suggest a tectonically active depositional setting in the Middle Triassic. Middle Muschelkalk evaporites consist of nine types of mainly auto-cyclic shallowing- or brining-upward mini-cycles which form a correlatable succession of five distinct 4th order cycle-sets. Despite the tectonically active depositional environment, most lithofacies encountered appear to have nearly flat bounding surfaces. Thus, marine transgressions flooded wide areas nearly simultaneously. The corresponding deposits serve as reference levels to tie the peripheral facies of northern Switzerland into the supra-regional context.

Autonomous ship navigation with an enhanced safety collision avoidance technique

The motion of an autonomous ship is different from that of ground and aerial robots due to its maneuvering and environmental constraints. As a result, many techniques have been introduced for autonomous ship path planning. This paper presents a novel technique for global and local navigation planning of autonomous ships under complex static and dynamic constraints. Our technique, termed safety-enhanced path planning (SPP), has been developed to avoid potential collisions with underwater obstacles near seaside areas. SPP pre-processes the map to preserve the shape of visible obstacles and mark a safety-outline around the shores. Subsequently, an offset safety line (OSL) is drawn about the original shore to protect the ship when passing close to threat-defined offshore areas. The global path is produced with an enhanced A* multi-directional algorithm, considering the kinematic constraint of the ship. To ensure optimal path quality, the global path is further refined with a smoothing filter to improve consistency and smoothness. Additionally, local navigation is introduced to help the autonomous ship avoid collisions with other obstacle ships. Local offset trajectories are produced with 4th and 5th degree polynomials along longitudinal and lateral coordinates in time t. Distance closest point approach (DCPA) is utilized for early obstacle prediction to help the ship maneuver in complex dynamic obstacle avoidance scenarios. The trajectory set is filtered with an efficient cost policy to obtain the best trajectory for dynamic collision avoidance. We conduct simulations in MATLAB and compared with other maritime path planning methods to verify the effectiveness of our approach.

Optical soliton perturbation of the quintic Gerdjikov-Ivanov model

This aim of this paper is revealing the optical soliton solutions of the perturbed quintic Gerdjikov-Ivanov equation, which models optical soliton transmission in the photonic crystal fibers and optical fibers. With the aid of the new Kudryashov scheme, we successful achieved the bright and dark solitons and we simulated their graphical presentation.

MHD rotating flow over a stretching surface: The role of viscosity and aggregation of nanoparticles

The magnetohydrodynamic (MHD) rotating flow that occurs across a stretching surface has numerous practical applications in a variety of domains. These fields include astronomy, engineering, the material sciences, and space exploration. The combined examination of magnetohydrodynamics rotating flow across a stretching surface, taking into consideration fluctuating viscosity and nanoparticle aggregation, has significant ramifications across several different domains. It is essential for both the growth of technology and the attainment of deeper insights into the complicated fluid dynamics to maintain research in this field. Given the aforementioned motivation, the principal aim of this study is to examine the effects of variable viscosity on the bidirectional rotating magnetohydrodynamic flow over a stretching surface. Aggregation effects on nanoparticles are used in the analysis. Titania (TiO2) is taken nanoparticle and ethylene glycol as base fluid. The nonlinear ordinary differential equations and the boundary conditions that correspond to them can be transformed into a dimensionless form by using a technique called similarity transformation. To get a numerical solution to the transformed equation, the Runge-Kutta 4th order (RK-4) method is utilized, and this is done in conjunction with the shooting method. The impact of various leading variables on dimensionless velocity, the coefficients of temperature, skin friction and local Nusselt number are graphically represented. Velocity profiles in both direction increases with increasing values of φ. The Nusselt number increases with increasing values of the radiation and temperature ratio parameters. When a 1 % volume fraction of nanoparticles is introduced, the Nusselt number exhibits a 0.174 % increase for the aggregation model compared to the regular fluid in the absence of radiation effects. When the aggregation model is used with a 1 % volume fraction of nanoparticles, the skin friction increases by 0.1153 % in the x direction and by 0.1165 % in the y direction compared to the regular fluid. Tables show the variation in Nusselt numbers, as well as a comparison of the effects of nanoparticle's aggregation model without and with radiation. Moreover, the numerical results obtained were compared with previously published data, demonstrating a satisfactory agreement. We firmly believe that this finding will have extensive implications for engineering and various industries.

4th-Order-SENS: A Software Module for Efficient and Exact 4th-Order Sensitivity Analysis of Neutron Transport

This work presents a software module called 4th-Order-SENS, which enables the efficient computation of exactly obtained expressions for all sensitivities, up to and including the 4th order, of a functional of the particle flux (e.g., the leakage of particles out of a body) with respect to nuclear parameters (total, scattering, and fission cross sections; nu, chi, sources; and number densities) for systems modeled by the neutron transport equation. The 4th-Order-SENS module implements the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Linear Systems (nth-CASAM-L), which is the only practically implementable methodology for obtaining the exact expressions of arbitrarily high-order sensitivities of model responses to model parameters, for response-coupled forward/adjoint large-scale linear systems. In addition to presenting the equations that are solved to obtain the 1st-order through 4th-order sensitivities, this work also describes the components of the module 4th-Order-SENS, including the user interface, input file, output files, and several independent code verification capabilities using symmetries and/or finite-difference formulas. The 4th-Order-SENS module is written in Python and Fortran and runs on Linux platforms. Several illustrative applications involving fixed-source problems in one-dimensional spherical and slab geometries are also presented.

Analysis of Nonlinear Flow and Heat Transfer Issues in Nanofluid by Using RK-4th Order Method

Nanofluids, composed of a base fluid with dispersed nanoparticles, have gained significant attention due to their unique thermal and flow characteristics. Understanding the nonlinear flow and heat transfer phenomena in nanofluids is crucial for optimizing their performance in engineering applications. In this study, we propose using the Runge-Kutta 4th order (RK-4) numerical method to analyze these issues. The RK-4 method is known for its accuracy and efficiency in solving ordinary differential equations. By applying this method to the governing equations of fluid flow and heat transfer, we can accurately capture the nonlinear behavior of nanofluids. We investigate various nonlinear phenomena, such as boundary layer separation, flow instability, and heat transfer enhancement, considering factors like nanoparticle concentration, size, shape, fluid properties, Reynolds number, and temperature gradient. The RK-4 method provides accurate solutions, revealing critical parameters that affect flow and heat transfer behavior. Comparisons with experimental data and other numerical methods validate the approach, demonstrating its reliability. Parametric studies are conducted to optimize nanofluid characteristics for improved heat transfer and fluid flow. This research enhances our understanding of nonlinear flow and heat transfer in nanofluids and enables efficient numerical analysis, opening new avenues for improving nanofluid-based systems.

Mathematical study of viscoelastic polymer during roll-over-web coating

Roll-coating, also known as roll-to-roll coating or web coating is a continuous and high-speed method used in various industrial applications to apply a thin and uniform layer of material onto a substrate. This process is commonly employed in industries such as electronics, photovoltaic, printing, packaging, and other fields where precise and consistent coating is essential. Here we present an asymptotic analysis of forward roll coating over a rigid substrate for low Weissenberg number viscoelastic fluids. The analysis uses lubrication theory coupled with regular perturbation theory assuming a simplified Phan-Thien-Tanner (SPPT) constitutive equation and small values of the extensibility parameter ε. The analytical expressions of velocity fields, pressure gradient and pressure fields are obtained while the load carrying force, and power input are estimated by numerical solutions (4th order Runge-Kutta). Increases in both Wi and ε increases the pressure gradient in the nip region and increases in viscoelasticity reduce the overall force on the roll. Further, SPTT model predicts 14% lower pressure for [Formula: see text] in the nip region when compared to Newtonian model.

Transient magnetized Soret effect on dissipative couple stress convection flow past a cylinder

The current article aims to reveal the thermal characteristics of dissipative magnetized chemically reactive unsteady couple stress convection along a cylinder with radiation, heat source/sink, and Soret influences. Governing partial differential equations (PDEs) are produced based on considered physical situation and geometry. Resultant Navier–Stokes equations (NS-E) are highly non-linear, coupled in nature. Analytical techniques fail to find the solutions of these resultant NS-equations. The discretized algebraic NS equations are solved by applying Crank–Nicolson numerical scheme through pentadiagonal and tridiagonal algorithms. Also, the flow of couple stress fluid with physical effects gives a 4th order PDE which needs pentadiagonal algorithm to solve it. Implementing this algorithm numerically is challenging and it is worthy to investigate to analyze the flow behavior. Hence, the simulated couple stress fluid velocity, energy, and mass diffusion profiles including engineering quantities of interest in the boundary layer region are discussed for different parametric values. Contemporary exploration illustrates that magnifying the buoyancy ratio parameter enhances the velocity field. Thermal field elevated for higher values of energy source/sink number. Also, contour plots of velocity, temperature, and mass diffusion profiles have been drawn in the vicinity of a cylinder. In addition, the range of control parameters performed in this study are = 0.00.6, = 0.2 0.8, = 0.00.3, = 0.10.4, and = 1.04.0. Finally, investigated dimensionless outcomes are verified with available solutions and got good agreement.

Bio-Convective Hartmann Flow of Couple Stress Hybrid Nanofluid Between Two Dilating Parallel Walls with Heat and Mass Transfer

The study of bio-convective flow of hybrid nanofluid attracted many researchers because of tremendous applications in the fields of biofuel biotechnology, enzyme-based biosensors and biomedical science. The present work addresses a comparative study of CuO/Al2O3-water and CuO-water nanoparticles on heat and mass transfer characteristics of the squeezing flow of MHD couple stress fluid between two parallel plates by suspending motile micro-organisms. An approximated numerical technique (Shooting method along with Runge-Kutta 4th order scheme) have been employed to analyse the system of coupled nonlinear ordinary differential equations. The above numerical investigations were carried out for various governing parameters such as couple stress parameter, Hartmann number, bioconvection Peclet number, squeezing parameter etc. The effects of these physical parameters are illustrated graphically over velocity components, temperature distribution, diffusion of concentration and density of motile microorganisms. In addition to this the numerical values of skin friction, the local Nusselt number and local Sherwood number are tabulated at the upper plate for CuO-water and CuO–Al2O3-water at the expanding and squeezing cases. The numerical results for temperature profiles are in good consistency with earlier research.

Tuning the flexural frequency of overhang-/T-shaped microcantilevers for high harmonics

High-harmonic (HH) frequencies in microcantilevers impose several applications in precision detection thanks to the higher sensitivity of the higher modes in comparison to the fundamental modes. In this study, we showed that by tuning the cantilever length by changing the clamped position, the dimensional ratio of the overhang to the main cantilever part is altered and the HHs could be effectively obtained. Multiple HH frequencies have been achieved, from the 4th to 8th order of the second and from the 11th to 26th order of the third-mechanical mode versus the first mode, and these orders are much higher if higher modes are used. The analytical calculation is in agreement with available results of other groups. HH behavior when the cantilever interacts with the sample is also examined and is strongly dependent on the overhang parameters. These results could guide the experimentalist in the tuning and controlling of the HHs in detecting objects.

Design of a High Speed Electro-optic Q-switch Circuit for Aerospace Applications

In order to meet the requirements of high amplitude and high speed of electro-optic Q-switch voltage, a high speed electro-optic Q-switch circuit for aerospace applications is designed. According to the principle of Marx generator, the circuit uses a high speed driving chip to drive the switching transistor to conduct. The charge of the primary energy storage capacitor of the pulse transformer is quickly released, and the secondary induced voltage drives the switches of the Marx generator to open quickly and synchronously. By utilizing the fast and synchronous opening of MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor), cascaded discharge is carried out on the energy storage capacitors of the 8th order Marx generator circuit, thereby outputting high voltage pulse signal. The experimental results show that the Marx generator has maximum boost output range of 4000V and high voltage pulse rise time of less than 30ns. Compared to traditional pulse transformer control methods, the Q-switch voltage rise time is reduced by nearly 40ns. The internal components of circuit meet the requirements of multiple indicators such as anti-irradiation space environment, and have the characteristic of short output high voltage rise time, which can provide high speed and high voltage driving pulses for the electro-optic Q-switch crystal inside the laser cavity.

Changes in the Thermal and Stress-Strain State of the HPC Rotor of a Powerful NPP Turbine after the Blades Damage

In practice, during the operation of steam turbines, accidental damage to the blades of the rotors and stators of powerful steam turbines occurs. The main causes of emergency stops of steam turbines were vibration fatigue of the blades material, erosive damage to the blades body, and resonance problems during the power equipment operation. Based on this study, the assessment of changes in the thermal and stress-strain state of power equipment elements, which at nuclear power plants significantly affect the continued operation of the turbine after its damage, are quite relevant. Changes in the thermal and stress-strain state, which may occur after damage to the rotor of high-pressure cylinder (HPC rotor) of the K-1000-60/3000 turbine power unit of the LMZ in the station conditions, have been considered and analyzed and will provide an opportunity to assess the individual resource and continue the power unit operation. In the calculated assessment of changes in the thermal and stress-strain state of the HPC rotor, taking into account the data of the technical audit regarding damage, a geometric model of the rotor was created. Studies were conducted for three options of designs: the original option (five stages of the HPC rotor), the option without the blades of the last stage and the option without the fifth stage (with four first stages). For the project design, when working at the nominal parameters of the steam, the most stressed areas are the unloading holes of the 5th stage (σi=202.8 MPa), axial hole of the rotor in the area of the 5th stage (σi=195.2 MPa), as well as the 5th-degree welding fillet from the side of the end seals (σi=200.3 MPa) and unloading holes of the 4th and 3rd stages with a stress intensity of about 170–185 MPa. The high values of the stress intensity in the area of the 5th stage can be explained by the significant concentration of the mass of both the stage itself and its blades, which provoke significant centrifugal forces when working at the nominal rotation frequency. For a HPC rotor without blades of the 5th stage, there is a shift of the maximum stress intensity to the area of the unloading holes of the 4th and 3rd stages, as well as the axial hole of the shaft under the same stages. The maximum stress value is σi max=184.8 MPa. At the same time, the intensity of stresses in the area of unloading holes of the 5th degree decreased almost by half, to the level of 124 MPa.

Microrotating chemically reactive hybrid nanomaterial in a high porous medium influenced by Cattaneo-Christov double diffusion and non-linear slip

ABSTRACT A simultaneous heat and mass transfer due to microrotating Darcy-Forchheimer flow of hybrid nanofluid over a moving thin needle is investigated. Darcy-Forchheimer medium accommodating hybrid nanofluid flow yields greater heat transfer rate, thereby leading to greater mass transfer rate over thin needle in industrial applications such as blood flow problems, aerodynamics, transportation, coating of wires, lubrication, and geothermal power generation. The thermophoresis and Brownian motion phenomena are introduced to enrich thermal treatment. Heat and mass transfer are accompanied by Cattaneo-Christov heat and mass flux. The hybrid nanofluid is radiative and dissipative in nature. Arrhenius pre-exponential factor law is introduced. Entropy generation analysis is carried out. The 4th order Runge-Kutta method along with shooting technique is devised to get requisite numerical solution of the transformed non-dimensional system of equations. Darcy-Forchheimer effect to simultaneous heat and mass transfer of microrotating hybrid nanofluid flow over thin needle subject to non-linear slip is the novelty of present study which is beyond of previous investigations. Rise in Forchheimer number (strengthening Darcy Forchheimer medium) leads to surface viscous drag decreases by 11.11% for hybrid nanofluid and 10.78% for pure nanofluid indicating the control of momentum transfer, thereby regulating heat transfer rate effectively.

A low-complexity multi-channel active noise control system using local secondary path estimation and clustered control strategy for vehicle interior engine noise

Conventional multi-channel active noise control (ANC) system based on the adaptive notch filtered-x least mean square algorithm is typically used for active control of vehicle interior engine noise with prominent harmonic characteristics. However, due to the large estimated secondary path length and the centralized control strategy, the system has high computational complexity and fragile stability. To alleviate this problem, an efficient multi-channel ANC system using the local secondary path (LSP) estimation and clustered control strategy is proposed in this paper. Based on the modified LSP estimation method, the system may utilize a set of low-order but accurate LSP models to simplify the convolution operations of reference filtering. Besides, the proposed clustered control strategy combines the advantages of centralized and decentralized control strategies, and thus the system not only enjoys good noise attenuation performance and stability, but also its computational burden is further greatly reduced. Numerical simulations are performed to evaluate the noise attenuation performance and frequency mismatch effect of the proposed multi-channel ANC system. In addition, a series of real vehicle ANC experiments are conducted. The results show that, under stationary work conditions, the interior overall, 2nd order, 4th order, 6th order engine noises may be attenuated by 12.91 dB(A), 32.98 dB(A), 15.34 dB(A) and 8.74 dB(A), respectively, and under nonstationary work conditions, the maximum overall noise reductions at the four error microphones may reach 6.40 dB(A), 6.14 dB(A), 12.48 dB(A) and 11.07 dB(A), respectively. This fully confirms the effectiveness of the proposed multi-channel ANC system in real-world applications.

Bjorken Sum Rule with Analytic Coupling at Low Q2 Values

The experimental data obtained for the polarized Bjorken sum rule Gamma _{1}^{{p - n}}({{Q}^{2}}) for small values of Q2 are approximated by the predictions obtained in the framework of analytic QCD up to the fifth order perturbation theory, whose coupling constant does not contain the Landau pole. We found an excellent agreement between the experimental data and the predictions of analytic QCD, as well as a strong difference between these data and the results obtained in the framework of perturbative QCD.

Fully-discrete spatial eigenanalysis of discontinuous spectral element methods: Insights into well-resolved and under-resolved vortical flows

This study presents a comprehensive spatial eigenanalysis of fully-discrete discontinuous spectral element methods, now generalising previous spatial eigenanalysis that did not include time integration errors. The influence of discrete time integration is discussed in detail for different explicit Runge–Kutta (1st to 4th order accurate) schemes combined with either Discontinuous Galerkin (DG) or Spectral Difference (SD) methods, both here recovered from the Flux Reconstruction (FR) scheme. Selected numerical experiments using the improved SD method by Liang et al. (2009) [53,54] and Jameson (2010) [55] are performed to quantify the influence of time integration errors on actual simulations. These involve test cases of varied complexity, from one-dimensional linear advection equation studies to well-resolved and under-resolved inviscid vortical flows. When simulations are well-resolved, the overall order of accuracy of the (fully-discrete) method of choice is limited to that of the time integration scheme. Moreover, it is shown that, while both well-resolved and under-resolved simulations of linear problems correlate well with the eigenanalysis prediction of time integration errors, the correlation can be much worse for under-resolved nonlinear problems as observed via numerical experiments. In fact, in the numerical simulation of under-resolved vortical flows, the predominance of spatial errors made it practically impossible for time integration errors to be distinctly identified. As a result, the eigenanalysis predictions are expected to hold (even if partially) in direct numerical simulations of turbulence. This highlights that the interaction between space and time discretisation errors is more complex than otherwise anticipated, contributing to the current understanding about when eigenanalysis can effectively predict the behaviour of numerical errors in practical under-resolved nonlinear problems, including under-resolved turbulence computations.

Advanced sensorless nonlinear control and stability analysis of single-stage PV systems connected to the grid via a 3L-NPC inverter

This paper proposes a novel control strategy for a single-stage photovoltaic (PV) system consisting of two PV panels connected to the grid via a three-level neutral point clamped converter topology with an LCL filter. This control method is based on a developed 5th order model containing sum and difference terms of the voltages of the two input capacitors. This allows decoupling the issues of maximum power point tracking and power factor correction from the issue of balancing the power exchange generated by the panels, which facilitates control design and improves system performances. The control problem under consideration is dealt with using a non-linear controller composed of three loops: (i) an inner loop is developed, based on backstepping and Lyapunov approaches, to correct the power factor by forcing the grid current to be sinusoidal and in phase with the grid voltage; (ii) an outer loop is designed, using a filtered proportional-integral controller, to regulate the DC bus voltage to a climate-dependent reference; (iii) a balancing loop is designed, using a proportional-integral controller, to cope with the neutral point voltage balancing problem. The proposed controller also includes a state observer that provides on-line estimation of the network state variables that are not accessible to measurements. Another important aspect of this work is the development of a formal, complete and rigorous analysis in order to describe the performance and analyse the stability of the closed-loop system using various analytical tools, including averaging theory, Routh criteria and indirect Lyapunov stability. A simulation in MATLAB/SIMULINK environment shows, on the one hand, the efficiency and robustness of the proposed nonlinear controller against changing climatic conditions and, on the other hand, the superiority of this control strategy compared to the one based on a PI linear inner loop controller for the studied system with an l- filter and an LCL filter.

11-th order of accuracy for numerical solution of 3-D Poisson equation with irregular interfaces on unfitted Cartesian meshes

For the first time the optimal local truncation error method (OLTEM) with 125-point stencils and unfitted Cartesian meshes has been developed in the general 3-D case for the Poisson equation for heterogeneous materials with smooth irregular interfaces. The 125-point stencils equations that are similar to those for quadratic finite elements are used for OLTEM. The interface conditions for OLTEM are imposed as constraints at a small number of interface points and do not require the introduction of additional unknowns, i.e., the sparse structure of global discrete equations of OLTEM is the same for homogeneous and heterogeneous materials. The stencils coefficients of OLTEM are calculated by the minimization of the local truncation error of the stencil equations. These derivations include the use of the Poisson equation for the relationship between the different spatial derivatives. Such a procedure provides the maximum possible accuracy of the discrete equations of OLTEM. In contrast to known numerical techniques with quadratic elements and third order of accuracy on conforming and unfitted meshes, OLTEM with the 125-point stencils provides 11-th order of accuracy, i.e., an extremely large increase in accuracy by 8 orders for similar stencils. The numerical results show that OLTEM yields much more accurate results than high-order finite elements with much wider stencils. The increased numerical accuracy of OLTEM leads to an extremely large increase in computational efficiency.Also, a new post-processing procedure with the 125-point stencil has been developed for the calculation of the spatial derivatives of the primary function. The post-processing procedure includes the minimization of the local truncation error and the use of the Poisson equation. It is demonstrated that the use of the partial differential equation (PDE) for the 125-point stencils improves the accuracy of the spatial derivatives by 6 orders compared to post-processing without the use of PDE as in existing numerical techniques. At an accuracy of 0.1% for the spatial derivatives, OLTEM reduces the number of degrees of freedom by 900−4⋅106 times compared to quadratic finite elements. The developed post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing post-processing techniques (e.g., with finite elements).