Grid Points In Space Research Articles

Two fast finite difference methods for a class of variable-coefficient fractional diffusion equations with time delay

This paper introduces the fast Crank–Nicolson (CN) and compact difference schemes for solving the one- and two-dimensional fractional diffusion equations with time delay. The CN method is employed for temporal discretization, while the fractional centered difference (FCD) formula discretizes the Riesz space derivative. Additionally, a novel fourth-order scheme is developed using compact difference operators to improve accuracy. The convergence and stability of these schemes are rigorously proven. The discretized systems combining Toeplitz-like structures can be effectively solved by Krylov subspace solvers with suitable preconditioners. Each time level of these methods requires a computational complexity of O(plogp) per iteration and a memory of O(p), where p represents the total number of grid points in space. Numerical examples are given to illustrate both the theoretical results and the computational efficiency of the fast algorithm.

Scheme using a finite‐volume method for local horizontal derivatives in the spectral model: The non‐hydrostatic case

AbstractIn a typical non‐hydrostatic spectral dynamic numerical weather prediction (NWP) kernel, all forecast variables are transformed between grid point and spectral spaces to compute their gradients and solve the implicit problem. This kernel requires numerous spectral transformations, which depend heavily on extensive global communication and significantly hinder parallel computing efficiency. This paper introduces an innovative non‐hydrostatic spectral kernel that incorporates a finite‐volume method within the spectral framework. We have developed a horizontal divergence (D)‐based structure equation, allowing direct computation of most prognostic variables and their horizontal gradients at grid point space. By doing so, the need for spectral transformations is substantially decreased. Our experiments demonstrate that this new approach reduces the cost of spectral transformations by up to 40%, enhancing the overall model efficiency by 15%–22%. Additionally, a series of tests confirmed the accuracy and stability of this new solver.

Optimizing Interpolation Methods and Point Distances for Accurate Earthquake Hazard Mapping

Earthquake hazard mapping assesses and visualizes seismic hazards in a region using data from specific points. Conducting a seismic hazard analysis for each point is essential, while continuous assessment for all points is impractical. The practical approach involves identifying hazards at specific points and utilizing interpolation for the rest. This method considers grid point spacing and chooses the right interpolation technique for estimating hazards at other points. This article examines different point distances and interpolation methods through a case study. To gauge accuracy, it tests 15 point distances and employs two interpolation methods, inverse distance weighted and ordinary kriging. Point distances are chosen as a percentage of longitude and latitude, ranging from 0.02 to 0.3. A baseline distance of 0.02 is set, and other distances and interpolation methods are compared with it. Five statistical indicators assess the methods. Ordinary kriging interpolation shows greater accuracy. With error rates and hazard map similarities in mind, a distance of 0.14 points seems optimal, balancing computational time and accuracy needs. Based on the research findings, this approach offers a cost-effective method for creating seismic hazard maps. It enables informed risk assessments for structures spanning various geographic areas, like linear infrastructures.

A Block Hybrid Method with Equally Spaced Grid Points for Third-Order Initial Value Problems

In this paper, we extend the block hybrid method with equally spaced intra-step points to solve linear and nonlinear third-order initial value problems. The proposed block hybrid method uses a simple iteration scheme to linearize the equations. Numerical experimentation demonstrates that equally spaced grid points for the block hybrid method enhance its speed of convergence and accuracy compared to other conventional block hybrid methods in the literature. This improvement is attributed to the linearization process, which avoids the use of derivatives. Further, the block hybrid method is consistent, stable, and gives rapid convergence to the solutions. We show that the simple iteration method, when combined with the block hybrid method, exhibits impressive convergence characteristics while preserving computational efficiency. In this study, we also implement the proposed method to solve the nonlinear Jerk equation, producing comparable results with other methods used in the literature.

Nonparametric Copula Density Estimation Methodologies

This paper proposes several methodologies whose objective consists of securing copula density estimates. More specifically, this aim will be achieved by differentiating bivariate least-squares polynomials fitted to Deheuvels’ empirical copulas, by making use of Bernstein’s approximating polynomials of appropriately selected orders; by differentiating linearized distribution functions evaluated at optimally spaced grid points; and by implementing the kernel density estimation technique in conjunction with a repositioning of the pseudo-observations and a certain criterion for determining suitable bandwidths. Smoother representations of such density estimates can further be secured by approximating them by means of moment-based bivariate polynomials. The various copula density estimation techniques being advocated herein are successfully applied to an actual dataset as well as a random sample generated from a known distribution.

A virtual sensing method based on plane-wave assumptions for active noise control headrests

Active noise control (ANC) headrests have been studied to suppress cabin noise and achieve a comfortable sound environment in public transportation mobility. To improve the suppression performance at the ear, this system requires virtual sensing technology to estimate sound pressure at the ear from microphone observations on the headrest. In this study, we propose a virtual sensing method for ANC headrests based on the assumption that noise arrives as plane-wave. The proposed method assumes that the cross-correlation between the observed signals of two adjacent microphones located on a grid point in space is constant and independent of absolute position. Based on this assumption, the cross-correlation estimated from observations between two microphones far from the ear is used to predict the noise propagation from the microphones near the ear to the ear. When noise reaches the ear first, the estimated cross-correlation becomes non-causal. To address this issue, we propose a method for predicting noise at the ear that involved removing pure delays in the impulse response of primary path estimated from observations of a reference microphone placed near the noise source and a microphone placed far from the ear. The effectiveness of the proposed method is demonstrated by computer simulation.

Local Refinement and Adaptive Strategy for a System of Free Boundary Power Options with High Order Compact Differencing

In this research, we propose fourth-order non-uniform Hermitian differencing with a fifth-order adaptive time integration method for pricing system of free boundary exotic power put options consisting of the option value, delta sensitivity, and gamma. The main objective for implementing the above scheme is to carefully account for the irregularity in the locality of the left corner point after fixing the free boundary. Specifically and mainly, we stretch the performance of our proposed method threefold. First, we exploit the non-uniform fourth-order Hermitian scheme to locally concentrate space grid points arbitrarily close to the left boundary. Secondly, we further leverage the adaptive nature of the embedded time integration method, which allows optimal selection of a time step based on the space grid point distribution and regional variation. Thirdly, we introduce a fourth-order combined Hermitian scheme, which requires fewer grid points for computing the near boundary point of the delta sensitivity and gamma. Another novelty is how we approximate the optimal exercise boundary and its derivative using a fifth-order Robin boundary scheme and fourth-order combined Hermitian scheme. Our proposed method consistently achieves reasonable accuracy with very coarse grids and little runtime across the numerical experiments. We further compare the results with existing methods and the ones we obtained from the uniform space grid.

USING PINN TO SOLVE EQUATIONS OF EQUIDISTRIBUTIONAL METHOD FOR CONSTRUCTING 2D STRUCTURED ADAPTED NUMERICAL GRIDS

The Equidistributional method is a popular technique for constructing numerical grids in engineering and scientific simulations. It is based on the principle of equidistribution, which requires evenly spaced grid points to reduce numerical errors. However, traditional Equidistributional methods can become inefficient and inaccurate for complex geometries and boundary conditions. In this paper, we present a new approach for solving the Equidistributional method's equations using physics-informed neural networks (PINN). PINN is a type of machine learning algorithm that has been shown to be effective for solving partial differential equations (PDEs). Our findings suggest that the use of PINN has the potential to significantly enhance the performance of the Equidistributional method for constructing 2D structured adapted numerical grids.         TRANSLATE with x English Arabic Hebrew Polish Bulgarian Hindi Portuguese Catalan Hmong Daw Romanian Chinese Simplified Hungarian Russian Chinese Traditional Indonesian Slovak Czech Italian Slovenian Danish Japanese Spanish Dutch Klingon Swedish English Korean Thai Estonian Latvian Turkish Finnish Lithuanian Ukrainian French Malay Urdu German Maltese Vietnamese Greek Norwegian Welsh Haitian Creole Persian   //   TRANSLATE with COPY THE URL BELOW Back EMBED THE SNIPPET BELOW IN YOUR SITE Enable collaborative features and customize widget: Bing Webmaster Portal Back //     Язык этой страницы: Английский   Перевести на Русский         Азербайджанский Албанский Амхарский Английский Арабский Армянский Африкаанс Бенгальский Бирманский Болгарский Валлийский Венгерский Вьетнамский Греческий Гуджарати Датский Иврит Индонезийский Исландский Испанский Итальянский Казахский Каннада Каталанский Китайский (традиционный) Китайский (упрощенный) Корейский Креольский (гаити) Курманджи Кхмерский Лаосский Латышский Литовский Малагасийский Малайский Малаялам Мальтийский Маори Маратхи Немецкий Непальский Нидерландский Норвежский Панджаби Персидский Польский Португальский Пушту Румынский Русский Самоанский Словацкий Словенский Тайский Тамильский Телугу Турецкий Украинский Урду Финский Французский Хинди Хорватский Чешский Шведский Эстонский Японский   Всегда переводить Английский на РусскийPRO Никогда не переводить Английский Никогда не переводить jpcsip.kaznu.kz

OpenMP Fortran programs for solving the time-dependent dipolar Gross-Pitaevskii equation

OpenMP Fortran programs for solving the time-dependent dipolar Gross-Pitaevskii equation

Identification of transtensional and transpressional features in the Sea of Marmara using onshore-offshore seismic and geodetic data

The scope of the study is to determine transtensional and transpressional features along the North Anatolian Fault beneath the Sea of Marmara, using seismic and geodetic data. For this purpose, focal mechanisms of small size NAF earthquakes, recorded by broadband stations and OBSs, have been derived and used as a tool to identify the transtensional and transpressional features. The focal mechanisms of: (1) small to moderate size events are obtained by the CMT inversion technique of Kuge (2003), using onshore waveform data from 2002?2015, (2) micro-earthquakes are obtained using the technique of Horiuchi (2015), using offshore waveform data recorded by 15 OBS stations from 2015?2016. Furthermore, published GPS velocities are used to determine the style of faulting and strain rates. The geodetic horizontal crustal strain rates are determined at equally spaced grid points by interpolating northing and easting components of the 112 GPS vectors from 1994?2013. The results indicate that extensional and strike-slip style deformation dominates the region, while contractional features are rare. Significant extension is observed in Çınarcık Basin and the area between Marmara Island and Central Basin. Yalova-Çınarcık region shows predominantly N-S extension while the Çınarcık Basin events show NE-SW extension. Compressional or transpressional features are derived to the west of Marmara Island and Ganos and in the Central segment extending from Central Basin toward Çınarcık Basin. The GPS strain rate results point out the highest values, 24 × 10?8/year, in Çınarcık Basin, while the lowest values, 11 × 10?8/year, are observed in Central Marmara. The highest strain rates in both edges of the fault segment in Çınarcık Basin can be indicative of a steadily creeping fault segment. In turn, lower strain rates in the Central Marmara region suggest that this segment of the NAF is locked.

Numerical and experimental evaluation of low-intensity transcranial focused ultrasound wave propagation using human skulls for brain neuromodulation.

Low-intensity transcranial focused ultrasound (tFUS) has gained considerable attention as a promising noninvasive neuromodulatory technique for human brains. However, the complex morphology of the skull hinders scholars from precisely predicting the acoustic energy transmitted and the region of the brain impacted during the sonication. This is due to the fact that different ultrasound frequencies and skull morphology variations greatly affect wave propagation through the skull. Although the acoustic properties of human skull have been studied for tFUS applications, such as tumor ablation using a multielement phased array, there is no consensus about how to choose a single-element focused ultrasound (FUS) transducer with a suitable frequency for neuromodulation. There are interests in exploring the magnitude and dimension of tFUS beam through human parietal bone for modulating specific brain lobes. Herein, we aim to investigate the wave propagation of tFUS on human skulls to understand and address the concerns above. Both experimental measurements and numerical modeling were conducted to investigate the transmission efficiency and beam pattern of tFUS on five human skulls (C3 and C4 regions) using single-element FUS transducers with six different frequencies (150-1500kHz). The degassed skull was placed in a water tank, and a calibrated hydrophone was utilized to measure acoustic pressure past it. The cranial computed tomography scan data of each skull were obtained to derive a high-resolution acoustic model (grid point spacing: 0.25mm) in simulations. Meanwhile, we modified the power-law exponent of acoustic attenuation coefficient to validate numerical modeling and enabled it to be served as a prediction tool, based on the experimental measurements. The transmission efficiency and -6dB beamwidth were evaluated and compared for various frequencies. An exponential decrease in transmission efficiency and a logarithmic decrease of -6dB beamwidth with an increase in ultrasound frequency were observed. It is found that a >750kHz ultrasound leads to a relatively lower tFUS transmission efficiency (<5%), whereas a <350kHz ultrasound contributes to a relatively broader beamwidth (>5mm). Based on these observations, we further analyzed the dependence of tFUS wave propagation on FUS transducer aperture size. We successfully studied tFUS wave propagation through human skulls at different frequencies experimentally and numerically. The findings have important implications to predict tFUS wave propagation for ultrasound neuromodulation in clinical applications, and guide researchers to develop advanced ultrasound transducers as neural interfaces.

Overlapping Grid-Based Optimized Single-Step Hybrid Block Method for Solving First-Order Initial Value Problems

This study presents a new variant of the hybrid block methods (HBMs) for solving initial value problems (IVPs). The overlapping hybrid block technique is developed by changing each integrating block of the HBM to incorporate the penultimate intra-step point of the previous block. In this paper, we present preliminary results obtained by applying the overlapping HBM to IVPs of the first order, utilizing equally spaced grid points and optimal points that maximize the local truncation errors of the main formulas at the intersection of each integration block. It is proven that the novel method reduces the local truncation error by at least one order of the integration step size, O(h). In order to demonstrate the superiority of the suggested method, numerical experimentation results were compared to the corresponding HBM based on the standard non-overlapping grid. It is established that the proposed method is more accurate than HBM versions of the same order that have been published in the literature.

Statistical post-processing of reanalysis wind speeds at hub heights using a diagnostic wind model and neural networks

Abstract. The correct representation of wind speeds at hub height (e.g., 100 m above ground) is becoming more and more important with respect to the expansion of renewable energy. In this study, a post-processing of the wind speed of the regional reanalysis COSMO-REA6 in Central Europe is performed based on a combined physical and statistical approach. The physical basis is provided by downscaling wind speeds with the help of a diagnostic wind model, which reduces the horizontal grid point spacing by a factor of 8 compared to COSMO-REA6 and considers different vertical atmospheric stabilities. In the second step, a statistical correction is performed using a neural network, as well as a generalized linear model based on different variables of the reanalysis. Although only a few measurements by masts or lidars are available at hub height, an improvement of the wind speed in the root-mean-squared error of almost 30 % can be achieved. A final comparison with radiosonde observations confirms the added value of combining the physical and statistical approaches in post-processing the wind speed.

Dendrite-resolved, full-melt-pool phase-field simulations to reveal non-steady-state effects and to test an approximate model

We study the epitaxial, columnar growth of (multiply oriented) dendrites/cells for a spot melt in a polycrystalline Al–Cu substrate using two-dimensional, phase-field, direct numerical simulations (DNS) at the full-melt-pool scale. Our main objective is to compare the expensive DNS model to a much cheaper but approximate “line” model in which a single-crystal phase-field simulation is confined to a narrow rectangular geometry. To perform this comparison, we develop algorithms that automatically extract quantities of interest (QoIs) from both DNS and line models. These QoIs allow us to quantitatively assess the assumptions in the line model and help us analyze its discrepancy with the DNS model. We consider four sets of heat source parameters, mimicking welding and additive manufacturing conditions, that create a combination shallow and deep melt pools. Our largest DNS simulation used 16K × 14K grid points in space. Our main findings can be summarized as follows. Under AM conditions, the QoIs of line models are in excellent agreement with the full DNS results for both shallow and deep melt pools. Under welding conditions, the primary spacing of the DNS model is smaller than the prediction of line model. We identify a geometric crowding effect that accounts for the discrepancies between the DNS and line models. We propose two potential mechanisms that determine the response of the microstructure to geometric crowding.

Molecular docking studies of Amidoxime-containing heterocyclic compounds from Zinc database against homology modelled PfADSL

Malaria remains one of the most infectious life-threatening diseases in the world. The lingering effect of drug resistance by malarial parasites, especially Plasmodium falciparum, has made it essential for the continuous search for novel antimalarial drugs that can act on new protein targets and through new modes of action. Amidoxime functional groups have, in recent years, shown to be good incorporations in heterocyclic backbones due to their vast biological activities. Hence, the antimalarial activities of some amidoxime-containing heterocyclic compounds have been predicted using molecular docking studies to determine the binding affinities and the inhibition constants of the compounds. The amidoxime-containing compounds were downloaded from the ZINC database and docked, using Auto Dock vina, against the active sites of homology modelled Plasmodium falciparumadenylosuccinate lyase (PfADSL) as obtained from the SWISS-MoDeL. The grid box was constructed using 80, 80, and 80, pointing in x, y, and z directions, respectively, with a grid point spacing of 0.375 A. The post-docking analysis, which entails determining the hydrogen bond formed and the bond length between the compounds and the protein target, was carried out using AutoDockTools, LigPlot and PyMOLmolecular viewer. The docking studies showed that the compounds possess binding affinities ranging from -8.6 to- 5.7 kcal/mol, with ZINC2268942 having the lowest binding affinity. The presence of the amidoxime-functional group on the best hit contributed significantly to the hydrogen bonds formed between the compound and the binding sites of PfADSL,which were observed atThr 124D, Ser 125D, Thr 172C, His 173C, Gln 250D, and Ser 299A. The results obtained from the molecular docking studies will be helpful in the development of a potential antimalarial drug that can target PfADSL after careful experimental validation of the target, then in vitro and in vivo screening.

Evaluation and optimisation of the I/O scalability for the next generation of Earth system models: IFS CY43R3 and XIOS 2.0 integration as a case study

Abstract. Earth system models have considerably increased their spatial resolution to solve more complex problems and achieve more realistic solutions. However, this generates an enormous amount of model data which requires proper management. Some Earth system models use inefficient sequential input/output (I/O) schemes that do not scale well when many parallel resources are used. In order to address this issue, the most commonly adopted approach is to use scalable parallel I/O solutions that offer both computational performance and efficiency. In this paper we analyse the I/O process of the European Centre for Medium-Range Weather Forecasts (ECMWF) operational Integrated Forecasting System (IFS) CY43R3. IFS can use two different output schemes: a parallel I/O server developed by Météo-France used operationally and an obsolete sequential I/O scheme. The latter is the only scheme that is being exposed by the OpenIFS variant of IFS. “Downstream” Earth system models that have adopted older versions of an IFS derivative as a component – such as the EC-Earth 3 climate model – also face a bottleneck due to the limited I/O capabilities and performance of the sequential output scheme. Moreover, it is often desirable to produce grid-point-space Network Common Data Format (NetCDF) files instead of the IFS native spectral and grid-point output fields in General Regularly-distributed Information in Binary form (GRIB), which requires the development of model-specific post-processing tools. We present the integration of the XML Input/Output Server (XIOS) 2.0 into IFS CY43R3. XIOS is an asynchronous Message Passing Interface (MPI) I/O server that offers features especially targeted at climate models: NetCDF output files, inline diagnostics, regridding, and, when properly configured, the capability to produce CMOR-compliant data. We therefore expect our work to reduce the computational cost of data-intensive (high-resolution) climate runs, thereby shortening the critical path of EC-Earth 4 experiments. The performance evaluation suggests that the use of XIOS 2.0 in IFS CY43R3 to output data achieves an adequate performance as well, outperforming the sequential I/O scheme. Furthermore, when we also take into account the post-processing task, which is needed to convert GRIB files to NetCDF files and also transform IFS spectral output fields to grid-point space, our integration not only surpasses the sequential output scheme but also the operational IFS I/O server.

A Fast Preconditioned Semi-Implicit Difference Scheme for Strongly Nonlinear Space-Fractional Diffusion Equations

In this paper, we propose a semi-implicit difference scheme for solving one-dimensional nonlinear space-fractional diffusion equations. The method is first-order accurate in time and second-order accurate in space. It uses a fractional central difference formula and the backward Euler method to approximate its space and time derivatives, respectively. Stability and convergence properties of the proposed scheme are proved with the help of a discrete Grönwall inequality. Moreover, we extend the method to the solution of two-dimensional nonlinear models. A fast matrix-free implementation based on preconditioned Krylov subspace methods is presented for solving the discretized linear systems. The resulting fast preconditioned semi-implicit difference scheme reduces the memory requirement of conventional semi-implicit difference schemes from O(Ns2) to O(Ns) and the computational complexity from O(Ns3) to O(NslogNs) in each iterative step, where Ns is the number of space grid points. Experiments with two numerical examples are shown to support the theoretical findings and to illustrate the efficiency of our proposed method.

Improved machine learning scoring functions for identification of Electrophorus electricus's acetylcholinesterase inhibitors.

Structure-based drug design (SBDD) is an important in silico technique, used for the identification of enzyme inhibitors. Acetylcholinesterase (AChE), obtained from Electrophorus electricus (ee), is widely used for the screening of AChE inhibitors. It shares structural homology with the AChE of human and other organisms. Till date, the three-dimensional crystal structure of enzyme from ee is not available that makes it challenging to use the SBDD approach for the identification of inhibitors. A homology model was developed for eeAChE in the present study, followed by its structural refinement through energy minimisation. The docking protocol was developed using a grid dimension of 84 × 66 × 72 and grid point spacing of 0.375 Å for eeAChE. The protocol was validated by redocking a set of co-crystallised inhibitors obtained from mouse AChE, and their interaction profiles were compared. The results indicated a poor performance of the Autodock scoring function. Hence, a batch of machine learning-based scoring functions were developed. The validation results displayed an accuracy of 81.68 ± 1.73% and 82.92 ± 3.05% for binary and multiclass classification scoring function, respectively. The regression-based scoring function produced [Formula: see text] and [Formula: see text] values of 0.94, 0.635 and 0.634, respectively.

Characteristic features of error in high-order difference calculation of 1D Poisson equation and unlimited high-accurate calculation under multi-precision calculation

In a previous paper based on the interpolation finite difference method, a calculation system was shown for calculating 1D (one-dimensional) Laplace’s equation and Poisson’s equation using high-order difference schemes. Finite difference schemes, from the usual second-order to tenth-order differences, including odd number order differences, were systematically and instantaneously derived over equally/unequally spaced grid points based on the Lagrange interpolation function. Using the direct method with the band diagonal matrix algorithm, 1D Poisson equations were numerically calculated under double precision floating arithmetic, but it became clear that high accurate calculations could not be secured in high-order differences because “digit-loss errors” caused by the finite precision of computations occurred in the calculations when using the high-order differences. The double precision calculation corresponds to 15 (significant) digit calculation. In this paper, we systematically investigate how the calculation accuracy changes by high precision calculations (30-digit, and 45-digit calculations). Under 45-digit calculation, where the digit-loss error can be almost ignored, the high-order differences enable extremely high-accurate calculations.

Potential yield simulated by global gridded crop models: using a process-based emulator to explain their differences

Abstract. How global gridded crop models (GGCMs) differ in their simulation of potential yield and reasons for those differences have never been assessed. The GGCM Intercomparison (GGCMI) offers a good framework for this assessment. Here, we built an emulator (called SMM for simple mechanistic model) of GGCMs based on generic and simplified formalism. The SMM equations describe crop phenology by a sum of growing degree days, canopy radiation absorption by the Beer–Lambert law, and its conversion into aboveground biomass by a radiation use efficiency (RUE). We fitted the parameters of this emulator against gridded aboveground maize biomass at the end of the growing season simulated by eight different GGCMs in a given year (2000). Our assumption is that the simple set of equations of SMM, after calibration, could reproduce the response of most GGCMs so that differences between GGCMs can be attributed to the parameters related to processes captured by the emulator. Despite huge differences between GGCMs, we show that if we fit both a parameter describing the thermal requirement for leaf emergence by adjusting its value to each grid-point in space, as done by GGCM modellers following the GGCMI protocol, and a GGCM-dependent globally uniform RUE, then the simple set of equations of the SMM emulator is sufficient to reproduce the spatial distribution of the original aboveground biomass simulated by most GGCMs. The grain filling is simulated in SMM by considering a fixed-in-time fraction of net primary productivity allocated to the grains (frac) once a threshold in leaves number (nthresh) is reached. Once calibrated, these two parameters allow for the capture of the relationship between potential yield and final aboveground biomass of each GGCM. It is particularly important as the divergence among GGCMs is larger for yield than for aboveground biomass. Thus, we showed that the divergence between GGCMs can be summarized by the differences in a few parameters. Our simple but mechanistic model could also be an interesting tool to test new developments in order to improve the simulation of potential yield at the global scale.