Explicit Scheme Research Articles

A Numerical Approximation of the Stochastic Ito-Volterra Integral Equation

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms and the solution are stochastic processes. Numerous studies have employed orthogonal polynomials, however most of them focus on deterministic rather than stochastic systems. This is the reason why in this study, we looked into a numerical solution for the stochastic Ito-Volterra integral equation using the explicit finite difference scheme and Bernstein polynomials as trial functions. The equidistant collocation procedure was used to calculate the unknown constant parameters in between and reach the desired approximation. The method was evaluated and contrasted with the Block Pulse method for approximate answers based on the aforementioned method, which were obtained and compared with others in the literature.

Dynamic fracture investigation of concrete by a rate-dependent explicit phase field model integrating viscoelasticity and micro-viscosity

To investigate dynamic fracture mechanisms of quasi-brittle materials, this work proposes a rate-dependent phase field model that integrates both macroscopic viscoelasticity and micro-viscosity to reflect the rate effects by free water and unhydrated inclusions. Based on the unified phase field theory, the model introduces a linear viscoelastic constitutive relation in effective stress space to consider the macro-viscosity of the bulk material. Additionally, the micro-force balance concept is utilized with the micro-viscosity to derive a parabolic phase field evolution law that accurately describes the dynamic micro-crack development. Explicit numerical solution schemes are established for the governing equations by developing VUEL and VUMAT subroutines in ABAQUS. This eliminates the convergence issue in implicit phase field modelling. Four typical benchmarks are investigated to validate the proposed model for macroscale and mesoscale heterogeneous problems. It is found that the proposed model can well capture the crack branching, delaying characteristic of micro-crack growth, and increase of macroscopic strength under higher strain rates. Using real meso‑structures from CT images, the complicated dynamic behaviour of concrete is investigated which yields deeper insight into stress wave propagation, crack evolution and load-carrying capacities.

A general class of second-order [formula omitted]-stable explicit numerical methods for stiff problems

In this paper, we propose a simple approach to the construction of a general class of L-stable explicit second-order one-step methods for solving stiff problems. These methods are nonlinear and derive from a novel approximation for the right-hand side functions of differential equations inspired by the nonstandard finite difference methodology introduced by Mickens. Through rigorous mathematical analysis, it is proved that the proposed numerical methods are not only explicit and L-stable, but also convergent of order two. Therefore, they are suitable and efficient to solve stiff problems.The proposed numerical methods generalize and improve a nonstandard explicit integration scheme for initial value problems formulated by Ramos (2007). Moreover, the present approach can be extended to construct A-stable and L-stable high-order explicit one-step methods for differential equations.Finally, the theoretical findings and advantages of the developed numerical methods are supported and illustrated by a series of numerical experiments in which stiff problems are considered.

Toward transparent taxonomy: an interactive web-tool for evaluating competing taxonomic arrangements.

Informative and consistent taxonomy above the species level is essential to communication about evolution, biodiversity and conservation, and yet the practice of taxonomy is considered opaque and subjective by non-taxonomist scientists and the public alike. While various proposals have tried to make the basis for the ranking and inclusiveness of taxa more transparent and objective, widespread adoption of these ideas has lagged. Here, we present TaxonomR, an interactive online decision-support tool to evaluate alternative taxonomic classifications. This tool implements an approach that quantifies the criteria commonly used in taxonomic treatments and allows the user to interactively manipulate weightings for different criteria to compare scores for taxonomic groupings under those weights. We use the butterfly taxon Argynnis to demonstrate how different weightings applied to common taxonomic criteria result in fundamentally different genus-level classifications that are predominantly used in different continents and geographic regions. These differences are objectively compared and quantified using TaxonomR to evaluate the kinds of criteria that have been emphasized in earlier classifications, and the nature of the support for current alternative taxonomic arrangements. The main role of TaxonomR is to make taxonomic decisions transparent via an explicit prioritization scheme. TaxonomR is not a prescriptive application. Rather, it aims to be a tool for facilitating our understanding of alternative taxonomic classifications that can, in turn, potentially support global harmony in biodiversity assessments through evidence-based discussion and community-wide resolution of historically entrenched taxonomic tensions.

MPM vs. CEL: Numerical modelling of penetration processes

MPM vs. CEL: Numerical modelling of penetration processes

MATHEMATICAL MODELING OF ACOUSTIC PROPOGATION THROUGH AURALIZATION TECHNIQUES INSIDE ENCLOSERS WITH VARIATION OF BOUNDARY CONDITIONS

Registration of acoustic properties and auralization of enclosed spaces is becoming increasingly important. In today's world, when designing or renovating historic buildings such as opera houses, churches and concert halls, it is important to simulate sound propagation in order to preserve the original acoustic properties. In our article, we consider the process of propagation of a sound wave in an internal three-dimensional non-stationary area, namely, the modeling of acoustics in a concert hall. To do this, according to the given input parameters, initial and boundary conditions, the distribution function of sound pressure in a given area over a period of time was determined. In the course of calculations, we use a computing platform to implement the finite element method, as well as the finite difference method using an explicit scheme as an example. On the basis of numerical results, we draw conclusions about the effectiveness of closed space auralization methods, and also describe aspects of optimization and use of methods.

A new explicit numerical scheme for enhancement of heat transfer in Sakiadis flow of micro polar fluid using electric field

This article suggests a fourth-order numerical approach for solving ordinary differential equations (ODEs) that are both linear and nonlinear. The suggested scheme is an explicit predictor-corrector scheme. For linear ODE, the proposed numerical scheme's stability area is discovered. The proposed strategy yields the same stability region as the traditional fourth-order Runge-Kutta method. In addition, partial differential equations (PDEs) are used to develop the mathematical model for the flow of non-Newtonian micro-polar fluid over the sheet and heat and mass transit using electric field effects. These PDEs are further transformed into dimensionless boundary value problems. Boundary value problems are resolved using the proposed shooting-based scheme. The findings show that increasing values of ion kinetic work and Joule heating parameters cause the temperature profile to climb. The results produced by the suggested strategy are compared to those discovered through earlier studies. The results of this study could serve as a starting point for future fluid-flow investigations in a secure industrial environment.

CMW-Net: Learning a Class-Aware Sample Weighting Mapping for Robust Deep Learning.

Modern deep neural networks can easily overfit to biased training data containing corrupted labels or class imbalance. Sample re-weighting methods are popularly used to alleviate this data bias issue. Most current methods, however, require to manually pre-specify the weighting schemes relying on the characteristics of the investigated problem and training data. This makes them fairly hard to be generally applied in practical scenarios, due to their significant complexities and inter-class variations of data bias. To address this issue, we propose a meta-model capable of adaptively learning an explicit weighting scheme directly from data. Specifically, by seeing each training class as a separate learning task, our method aims to extract an explicit weighting function with sample loss and task/class feature as input, and sample weight as output, expecting to impose adaptively varying weighting schemes to different sample classes based on their own intrinsic bias characteristics. Extensive experiments substantiate the capability of our method on achieving proper weighting schemes in various data bias cases, like class imbalance, feature-independent and dependent label noises, and more complicated bias scenarios beyond conventional cases. Besides, the task-transferability of the learned weighting scheme is also substantiated, by readily deploying the weighting function learned on relatively smaller-scale CIFAR-10 dataset on much larger-scale full WebVision dataset. The general availability of our method for multiple robust deep learning issues, including partial-label learning, semi-supervised learning and selective classification, has also been validated. Code for reproducing our experiments is available at https://github.com/xjtushujun/CMW-Net.

Blockchain Disaster Management for Humanitarian Logistic as Post-Disaster Response Measures

Indonesia has a high risk of earthquake and tsunami disasters because there's many tectonic plates meet. This also causes Indonesia to have many geological changes compared to other countries. Therefore, an explicit scheme to provide information related to disasters, like an information system in post-disaster management is important. The purpose of this research is to provide transparent information regarding the data on the goods needed and the data on goods to be distributed to ensure the amount used and not used, so that victims affected by disasters can be handled quickly and appropriately. The method used in this research is a literature review. The results of this study indicate the existence of a Blockchain Disaster Management Information System as a form of a new scheme in the post-disaster management process and is an upgraded form of information system that has been developed previously. This scheme uses the blockchain concept to provide transparency and data immutability. This scheme coordinates with various institutions such as BPBD (Regional Disaster Management Agency), BNPB (National Disaster Management Agency), BASARNAS (National Search and Rescue Agency), PMI (Indonesian Red Cross Society), the nearest hospital, and other related institutions. © 2023 Universitas Pendidikan Indonesia

Application of Symmetric Explicit Symplectic Integrators in Non-Rotating Konoplya and Zhidenko Black Hole Spacetime

In this study, we construct symmetric explicit symplectic schemes for the non-rotating Konoplya and Zhidenko black hole spacetime that effectively maintain the stability of energy errors and solve the tangent vectors from the equations of motion and the variational equations of the system. The fast Lyapunov indicators and Poincaré section are calculated to verify the effectiveness of the smaller alignment index. Meanwhile, different algorithms are used to separately calculate the equations of motion and variation equations, resulting in correspondingly smaller alignment indexes. The numerical results indicate that the smaller alignment index obtained by using a global symplectic algorithm is the fastest method for distinguishing between regular and chaotic cases. The smaller alignment index is used to study the effects of parameters on the dynamic transition from order to chaos. If initial conditions and other parameters are appropriately chosen, we observe that an increase in energy E or the deformation parameter η can easily lead to chaos. Similarly, chaos easily occurs when the angular momentum L is small enough or the magnetic parameter Q stays within a suitable range. By varying the initial conditions of the particles, a distribution plot of the smaller alignment in the X–Z plane of the black hole is obtained. It is found that the particle orbits exhibit a remarkably rich structure. Researching the motion of charged particles around a black hole contributes to our understanding of the mechanisms behind black hole accretion and provides valuable insights into the initial formation process of an accretion disk.

CHARACTERISTIC METHOD FOR SOLVING FILTRATION PROBLEM

During construction, a liquid solution of a grout or waterproof filler is pumped into porous rock to improve its properties. The filtration of a suspension moving at a variable speed in a porous medium is simulated. A one-dimensional problem of filtration in a homogeneous porous medium with a curvilinear concentration front of suspended and retained particles is considered. For the numerical solution of the problem by the method of finite differences, the method of characteristics is used. The transition to characteristic variables allows one to straighten the front and construct a discrete grid with a constant step. When calculating the solution using an explicit difference scheme, additional points are used that do not coincide with the grid nodes. A detailed description of the algorithm for calculating a solution at the grid nodes and an example of a numerical solution of the problem are given.

Theta method applied to two-energy groups point kinetics equations

The point kinetics equations with two-energy groups and multi-group of delayed neutrons are a system of stiff linear/nonlinear ordinary differential equations strongly coupled, which is used to simulate the dynamics system of a homogeneous nuclear reactor by determining the population of neutrons and precursor groups. The matrix form of the mathematical model is solved by the theta method where the matrix inverse is calculated analytically. Numerical results are obtained through iterative schemes to approximate analytical solutions. The stiffness condition of the system of equations can cause instability in the solutions of explicit iterative schemes commonly employed so far. In this work, an implicit iterative scheme is used to approximate numerical solutions to the homogeneous nuclear reactor with one and six groups of delayed neutrons. The results are discussed and compared on light of literature reports. Unprecedented comparisons with experimental data from an AGN-201 nuclear reactor are also discussed. For the case studies, the theta method exhibits accurate and computationally efficient results.

A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations

We present a new exactly divergence-free and well-balanced hybrid finite volume/finite element scheme for the numerical solution of the incompressible viscous and resistive magnetohydrodynamics (MHD) equations on staggered unstructured mixed-element meshes in two and three space dimensions. The equations are split into several subsystems, each of which is then discretized with a particular scheme that allows to preserve some fundamental structural features of the underlying governing PDE system also at the discrete level. The pressure is defined on the vertices of the primary mesh, while the velocity field and the normal components of the magnetic field are defined on an edge-based/face-based dual mesh in two and three space dimensions, respectively. This allows to account for the divergence-free conditions of the velocity field and of the magnetic field in a rather natural manner. The non-linear convective and the viscous terms in the momentum equation are solved at the aid of an explicit finite volume scheme, while the magnetic field is evolved in an exactly divergence-free manner via an explicit finite volume method based on a discrete form of the Stokes law in the edges/faces of each primary element. The latter method is stabilized by the proper choice of the numerical resistivity in the computation of the electric field in the vertices/edges of the 2D/3D elements. To achieve higher order of accuracy, a piecewise linear polynomial is reconstructed for the magnetic field, which is guaranteed to be exactly divergence-free via a constrained L2 projection. Finally, the pressure subsystem is solved implicitly at the aid of a classical continuous finite element method in the vertices of the primary mesh and making use of the staggered arrangement of the velocity, which is typical for incompressible Navier-Stokes solvers. In order to maintain non-trivial stationary equilibrium solutions of the governing PDE system exactly, which are assumed to be known a priori, each step of the new algorithm takes the known equilibrium solution explicitly into account so that the method becomes exactly well-balanced. We show numerous test cases in two and three space dimensions in order to validate our new method carefully against known exact and numerical reference solutions. In particular, this paper includes a very thorough study of the lid-driven MHD cavity problem in the presence of different magnetic fields and the obtained numerical solutions are provided as free supplementary electronic material to allow other research groups to reproduce our results and to compare with our data. We finally present long-time simulations of Soloviev equilibrium solutions in several simplified 3D tokamak configurations, showing that the new well-balanced scheme introduced in this paper is able to maintain stationary equilibria exactly over very long integration times even on very coarse unstructured meshes that, in general, do not need to be aligned with the magnetic field.

An Efficient and Accurate Approach to Electrical Boundary Layer Nanofluid Flow Simulation: A Use of Artificial Intelligence

Engineering and technological research groups are becoming interested in neural network techniques to improve productivity, business strategies, and societal development. In this paper, an explicit numerical scheme is given for both linear and nonlinear differential equations. The scheme is correct to second order. Additionally, the scheme’s consistency and stability are guaranteed. Backpropagation of Levenberg–Marquardt, the effect of including an induced magnetic field in a mathematical model for electrical boundary layer nanofluid flow on a flat plate, is quantitatively investigated using artificial neural networks. Later, the model is reduced into a set of boundary value problems, which are then resolved using the suggested scheme and a shooting strategy. The outcomes are also contrasted with earlier studies and the MATLAB solver bvp4c for validation purposes. In addition, neural networking is also employed for mapping input to outputs for velocity, temperature, and concentration profiles. These results prove that artificial neural networks can make precise forecasts and optimizations. Using a neural network to optimize the fluid flow in an electrical boundary layer while subjected to an induced magnetic field is a promising application of the suggested computational scheme. Fluid dynamics benefits greatly from combining numerical methods and artificial neural networks, which could lead to new developments in various fields. Results from this study may aid in optimizing fluid systems, leading to greater productivity and effectiveness in numerous technical fields.

Near-field seismoacoustic wave scattering due to an irregular interface: a unified framework

SUMMARY Near-field seismoacoustic scattering must be considered across various domains, including marine seismic exploration, ocean acoustics and marine seismic engineering. This is a complex process due to the fluid–solid interaction between seawater and the seabed, particularly when the seabed is saturated with fluid. The interaction between sea fluid, saturated porous seabed and solid bedrock must also be considered. In this study, seawater and dry bedrock are treated as generalized saturated porous media with porosity of one and zero, respectively. The coupling between seawater, saturated seabed and dry bedrock can be analysed within a unified framework of generalized saturated porous media. Therefore, we proposed an efficient, unified method to address the challenges posed by near-field seismoacoustic scattering. This method comprises free field wave motion computation, which is used to provide input for scattering analysis. It also introduces a unified computational framework for modelling the wave propagation in the water-saturated seabed-bedrock system, and local transmitting boundary are used to account for the effect of an infinite domain. First, the differential equation of the generalized saturated porous media is discretized using lumped mass-based FEM, and the ordinary differential equation is integrated in time using an explicit scheme. Then, the equations for the motion of the nodes on the interface between two generalized saturated porous media with various porosity are derived. These equations are suitable for special cases such as fluid–solid interface, fluid-saturated porous media interface and saturated porous media-solid interface. To demonstrate the validity and feasibility of the proposed approach, a 1-D problem is considered, and the obtained response is verified using an analytical solution. Then, we compute the cases of a vertically incident plane P wave onto a 2-D basin-like fluid–solid structure, and compared the synthetic seismograms with results reported by other researchers. In this study, the findings of our proposed approach satisfy the continuity requirements at the interface and are consistent with those obtained using the reflection/transmission matrix method. Additionally, a 3-D site with basin-like terrain was analysed. The proposed approach treats the fluid, saturated porous media and solid in a unified framework, and has high efficiency due to lumped mass matrix-based explicit finite element and local transmitting artificial boundary. Furthermore, our approach can be easily implemented in parallel, making it suitable for solving large-scale seismoacoustic scattering problems.

Explicit high accuracy energy-preserving Lie-group sine pseudo-spectral methods for the coupled nonlinear Schrödinger equation

The newly developed generalized scalar auxiliary variable (GSAV) approaches are very popular methods that can be applied to construct high-accuracy energy-preserving schemes for conservative systems. However, these proposed high-order schemes are fully-implicit and have the disadvantages of huge calculating quantities and long computing time for solving nonlinear systems. Therefore, we develop in this paper explicit energy-preserving schemes to deal with the coupled nonlinear Schrödinger equation by combining the Lie-group method and GSAV approaches. The given schemes are very efficient, have high accuracy, and can inherit the modified energy of the system. Ample numerical results are presented to confirm the developed schemes' efficiency, accuracy, and conservation.

Exploiting high‐contrast Stokes preconditioners to efficiently solve incompressible fluid–structure interaction problems

AbstractIn this work, we develop a new algorithm to solve large‐scale incompressible time‐dependent fluid–structure interaction problems using a matrix‐free finite element method in arbitrary Lagrangian–Eulerian frame of reference. We derive a semi‐implicit time integration scheme which improves the geometry‐convective explicit scheme for problems involving the interaction between incompressible hyperelastic solids and incompressible fluids. The proposed algorithm relies on the reformulation of the time‐discrete problem as a generalized Stokes problem with strongly variable coefficients, for which optimal preconditioners have recently been developed. The resulting algorithm is scalable, optimal, and robust: we test our implementation on model problems that mimic classical Turek–Hron benchmarks in two and three dimensions, and investigate timing and scalability results.

A novel sequential-based hybrid approach incorporating physical modeling and deep learning for multiphase subsurface flow simulation

Multiphase subsurface flows are of great importance for both the sustainable utilization of resources and ecological protection. The simulation of multiphase flow is conventionally resolved using either physics-driven numerical discretization or data-driven machine learning strategy. Despite being perceived as distinct paradigms, their algorithmic-level synergy is expected to bring tremendous advantages. Within the implicit pressure and explicit saturation scheme, this study constructs deep learning model for pressure approximation using an ensemble of equal-probable permeability realizations and the corresponding pressure/velocity fields under randomized injection/production strategies. Specifically, this study proposes two network models, namely U-Net and Fourier Neural Operator, and empower them by physics-guided loss functions, which not only improve the training efficiency but also ensure the physical continuity of the velocity field and maintain the overall mass balance of the coupled system. Moreover, we advance the saturation front using a standard explicit solver under its strict stability condition. The results demonstrate that our hybrid approach performs strong adaptability and flexibility under different permeability and injection/production conditions enclosed in the model training set. For all test cases, we achieve less than 0.6% relative errors for both pressure and saturation solutions. More importantly, our well-trained hybrid solver only uses a fraction of second, which is several orders of magnitude faster than the traditional physics-driven numerical solvers. Our newly designed solution architecture provides a physically reliable technique for superfast multiphase subsurface flow field approximation, which is believed to be of great value for the challenging production optimization and uncertainty quantifications of subsurface resource utilizations.

Estimating water levels caused by a tropical storm along the Bangladesh coast: A numerical approach

In this study, water levels resulting from the dynamic interaction of tide and surge are estimated by solving a 2-D vertically integrated shallow water equations numerically. To solve the equations on the specific 2-D grid, the explicit Leapfrog scheme is implemented, adopting a staggered Arakawa C-grid. The domain's complex land-sea interface is approximated through the stair-step method in order to employ the finite difference technique. To incorporate the complexity of the domain with a considerably high accuracy and to reduce computational cost, one-way nested grid models are embraced. The Meghna River freshwater discharge is incorporated into the innermost child model. A stable tidal regime over the region of interest is generated by applying the four vital tidal constituents, namely M2 (principal lunar semidiurnal), S2 (principal solar semidiurnal), O1 (principal lunar diurnal) and K1 (luni-solar diurnal) in the southern open boundary of the outermost model. This previously effectuated tidal regime is used as the initial state of the sea in getting total water levels due to the dynamic interaction of tide and surge. Numerical experiments are performed with the storm AILA that hit the coast of Bangladesh on May 25, 2009. The simulated results are found to closely match observed and reported data.

Strong convergence rates of an explicit scheme for stochastic Cahn–Hilliard equation with additive noise

Strong convergence rates of an explicit scheme for stochastic Cahn–Hilliard equation with additive noise