Conventional Numerical Methods Research Articles

Impedance Sensitivity Analysis Based on Discontinuous Isogeometric Boundary Element Method in Automotive Acoustics

Abstract Acoustic sensitivity analysis is an essential technique to determine the direction of structural-acoustic optimization by evaluating the gradient of the objective functions with respect to the design variables. However, acoustic sensitivity analysis with respect to acoustic impedance, which is an important parameter representing the interior absorbent material in automotive acoustics, is lacking in the study. Moreover, acoustic sensitivity analysis implemented with conventional numerical methods is time and effort-consuming in automotive acoustics, due to the large-scale mesh generation. In this work, the impedance sensitivity analysis for automotive acoustics based on the discontinuous isogeometric boundary element method is presented. The regularized boundary integral equation with impedance boundary conditions is established, then the sensitivity is derived by differentiating the boundary integral equation. The efficiency of the proposed method is improved by employing the parallel technique and generalized minimal residual solver. A long duct example with an analytical solution validates the accuracy of the proposed method, and an automotive passenger compartment subjecting to impedance boundary conditions illustrates that the computing time of the proposed method is one order of magnitude less than the conventional method. This work presents an easily implementable and efficient tool to investigate acoustic sensitivity with respect to impedance, showing great potential in the application of automotive acoustics.

A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods

To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equation is solved at each time step usually in physical space using iterative solvers, and the resulting pressure gradient is then applied to make the velocity field divergence-free. It is generally accepted that this pressure-correction stage is the most time-consuming part of the flow solver and any meaningful acceleration would contribute significantly to the overall computational efficiency. The objective of the present work was to develop a fast hybrid pressure-correction algorithm for numerical simulation of incompressible flows around obstacles in the context of projection methods. The key idea is to adopt different numerical methods/discretisations in the sub-steps of projection methods. Here, a classical second-order time-marching projection method, which consists of two sub-steps, was chosen for the purposes of demonstration. In the first sub-step, the momentum equations were discretised on unstructured grids and solved by conventional numerical methods, here a meshless method. In the second sub-step (pressure-correction), the proposed algorithm adopts a double-discretisation system and combines the weighted least-squares approximation with the essence of immersed boundary methods. Such a design allowed us to develop an FFT-based solver to speed up the solution of the pressure Poisson equation for flow cases with obstacles, while keeping the implementation of the boundary conditions for the momentum equations as easy as conventional numerical methods do with unstructured grids. The numerical experiments of five test cases were performed to verify and validate the proposed hybrid algorithm and evaluate its computational performance. The results showed that the new FFT-based hybrid algorithm works and is robust, and it was significantly faster than the multigrid-based reference method. The hybrid algorithm opens an avenue for the development of next-generation high-performance parallel computational fluid dynamics solvers for incompressible flows.

Modeling Methodology Based on Fast and Refined Neural Networks for Non-Isolated DC–DC Converters With Configurable Parameter Settings

Compared with conventional physics-based methods, e.g., analytical modeling and numerical modeling, data-driven methods can extract input-to-output relationships from the data without much prior knowledge of the physical system, thus showing great potential in modeling power electronics (PE) converters with complex switching behaviors and configurable parameter settings. Previous data-driven PE circuit modeling approaches are mostly based on sequential neural networks, and their execution speed suffers from large sequential lengths due to a high sampling rate for high modeling accuracy. Moreover, modeling of refined singular ripples is missing and configurable parameter settings are not available in these data-driven modeling approaches. To address the above-mentioned issues, this paper proposes a hybrid physics-informed machine learning (ML) method to model the non-isolated DC-DC converters. The approach empirically decomposes the output signals into transient large signals and periodic small signals. For transient large signals, a fully-connected neural network (NN) is used to map circuit parameters with system characteristics, such that configurable circuit parameter settings are allowed. For periodic signals, a long short-time memory (LSTM) network together with convolutional neural network (CNN) is used to accelerate the simulation by predicting signal features in the compressed latent space. A buck converter with configurable parameter settings is modeled by the proposed hybrid physics-informed ML method. Periodic ripples are successfully generated, while execution speed is about 10 times faster than that of conventional numerical methods.

Response Prediction for Linear and Nonlinear Structures Based on Data-Driven Deep Learning

Dynamic analysis of structures is very important for structural design and health monitoring. Conventional numerical or experimental methods often suffer from the great challenges of analyzing the responses of linear and nonlinear structures, such as high cost, poor accuracy, and low efficiency. In this study, the recurrent neural network (RNN) and long short-term memory (LSTM) models were used to predict the responses of structures with or without nonlinear components. The time series k-means (TSkmeans) algorithm was used to divide label data into different clusters to enhance the generalization of the models. The models were trained with different cluster acceleration records and the corresponding structural responses obtained by numerical methods, and then predicted the responses of nonlinear and linear structures under different seismic waves. The results showed that the two deep learning models had a good ability to predict the time history response of a linear system. The RNN and LSTM models could roughly predict the response trend of nonlinear structures, but the RNN model could not reproduce the response details of nonlinear structures (high-frequency characteristics and peak values).

Stable recursive auxiliary field quantum Monte Carlo algorithm in the canonical ensemble: Applications to thermometry and the Hubbard model.

Many experimentally accessible, finite-sized interacting quantum systems are most appropriately described by the canonical ensemble of statistical mechanics. Conventional numerical simulation methods either approximate them as being coupled to a particle bath or use projective algorithms which may suffer from nonoptimal scaling with system size or large algorithmic prefactors. In this paper, we introduce a highly stable, recursive auxiliary field quantum Monte Carlo approach that can directly simulate systems in the canonical ensemble. We apply the method to the fermion Hubbard model in one and two spatial dimensions in a regime known to exhibit a significant "sign" problem and find improved performance over existing approaches including rapid convergence to ground-state expectation values. The effects of excitations above the ground state are quantified using an estimator-agnostic approach including studying the temperature dependence of the purity and overlap fidelity of the canonical and grand canonical density matrices. As an important application, we show that thermometry approaches often exploited in ultracold atoms that employ an analysis of the velocity distribution in the grand canonical ensemble may be subject to errors leading to an underestimation of extracted temperatures with respect to the Fermi temperature.

Numerical simulation analysis of the rolling process based on the particle swarm hybrid algorithm

ABSTRACT It is very complicated to study the three-dimensional deformation of metal during rolling. The conventional finite element numerical analysis method generally adopts a fixed algorithm to calculate the whole rolling process. This method consumes huge computing power and sacrifices some computing accuracy. In this paper, according to the characteristics of different rolling stages, on the basis of considering the degree of metal deformation, a particle swarm hybrid algorithm with adaptive weight-learning factor is proposed.The Zoutendijk algorithm, Rosen algorithm, Wolfe algorithm and particle swarm hybrid algorithm are used to numerically simulate the rolling transverse thickness distribution. The accuracy of the rolling model and the particle swarm hybrid algorithm are verified. The influence of work roll edge contact and asymmetric roll bending on the deformation of rolling metal is analysed based on particle swarm mixing algorithm.

Radial basis function based finite element method: Formulation and applications

In the study, a method is proposed and developed for solid analysis that is a hybrid of the radial basis function and the finite element method (RBF-FEM). Based on the finite nodes, the method employs the radial basis functions to produce the shape functions with simplicity, especially when increasing the element node number. The formulation and applications of the method in the analysis of solids are examined. Several numerical examples are carried out to analyze the convergence, accuracy, and computational time cost. Its comeouts are then compared with that by the finite element method. The study also shows the factors that affect the accuracy of the method, such as the radial basis function types, radial basis function shape parameter, node number, and node position in an element. It is shown that the method quickly produces better results with large-node-number elements (seven and eight nodes) in comparison to the conventional numerical method. Discussion on the method and the extensibility of the approach are addressed in the conclusion.

Solving redundant inverse kinematics of CMOR based on chaos-driven particle swarm optimization algorithm

The China Fusion Engineering Test Reactor (CFETR) multipurpose overload robot (CMOR) is used to maintain the vacuum chamber inner components damaged by heat loads, electromagnetic fields, and nuclear radiation. The CMOR is a redundant robot whose configuration does not meet the condition of the Pieper criterion. Redundant kinematic problems can only be solved by numerical methods, not analytical methods. Conventional numerical iterative methods include considerable computational load, accumulated errors, and the Jacobian matrix's singularity. To solve redundant inverse kinematics efficiently, we compared the behaviors of 25 versions of particle swarm optimization (PSO) algorithms with 12 one-dimensional chaotic maps under unimodal and multimodal test functions. Moreover, we selected three chaos-driven PSO algorithms with optimal convergence performance to address CMOR inverse kinematics. The experimental results indicated that chaos-driven PSO algorithms have higher computational efficiency and can effectively improve the speed and accuracy of algorithm convergence. This proposed algorithm delivers a novel and efficient method for inverse kinematics of redundant robots based on chaotic maps.

Improved numerical scheme for the generalized Kuramoto model

We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the generalized Kuramoto model corresponds to particles on the unit sphere undergoing rigid body rotations with position-dependent angular velocities. We demonstrate that our improved scheme is able to reproduce known analytic results and capture the expected behavior of the three-dimensional oscillators in various cases. On the other hand, we find that the conventional numerical method, which amounts to a direct numerical integration with the constraint that forces the particles to be on the unit sphere at each time step, may result in inaccurate and misleading behavior especially in the long time limit. We analyze in detail the origin of the discrepancy between the two methods and present the effectiveness of our method in studying the limit cycle of the Kuramoto oscillators.

Homotopy analysis of mixed convection flow of a magnetized viscoelastic nanofluid from a stretching surface in non-Darcy porous media with revised Fourier and Fickian approaches

This article addresses theoretically the mixed convection hydromagnetic flow of electrically conducting viscoelastic nanofluid from a vertical permeable stretching sheet in a non-Darcy porous medium with Cattaneo–Christov double-diffusion model to evaluate the heat transfer phenomena in steady boundary layer flow on a stretchable surface. In this regard, thermal and solutal hyperbolic wave relaxation effects are included for non-Fourier and non-Fickian models. Heat absorption is also included in the analysis. The Buongiorno two-component nanoscale model is adopted for simulating Brownian motion and thermophoretic body force effects. A non-Darcy drag force model is employed for the porous medium and the Reiner–Rivlin second-grade model for non-Newtonian characteristics. Via appropriate dimensionless similarity variables, the nonlinear dimensional partial differential conservation equations for momentum, energy and concentration with associated boundary conditions are rendered into a nonlinear dimensionless ordinary differential boundary value problem. The homotopy analysis method (HAM) is utilized to solve the boundary value problem and the impact of emerging parameters including thermal relaxation parameters, non-Newtonian material parameter, Darcy permeability parameter, porous inertial parameter and Hartmann magnetic number on the momentum, heat and mass transfer characteristics are visualized graphically and in tables. A 30th-order approximation for HAM is shown to produce sufficient accuracy for the velocity and temperature fields and a 40th-order estimates is adequate for the concentration field. It is observed that increasing the magnitude of thermal and solutal relaxation parameters has the opposite effect on the thermal and concentration distributions. The novelty of the work is the simultaneous inclusion of multiple effects (non-Fourier and non-Fickian thermal relaxation hyperbolic wave models, non-Darcy drag effects and heat generation/absorption) which are relevant to rheological nanomaterials processing and also the deployment of homotopy analysis as an alternative to conventional numerical methods such as finite differences, finite elements and MATLAB solvers. The study is relevant to the manufacture of electro-conductive polymers (ECPs) and smart (functional) magnetic nano-liquids.

Digital twin for natural gas infrastructure operation and management via streaming dynamic mode decomposition with control

The gradual energy consumption increments and demand patterns diversification require an advanced operational protocol for natural gas infrastructure. However, conventional numerical methods suffer from low reliability and practicality due to the lack of usage of data that possess coherent physics in the system. The requirements to address this issue are system identification of data sequence and continuous modification to capture the changes of various environmental variables. Thus, we present the first data-driven digital twin model based on dynamic mode decomposition (DMD), which is well-suited for processing nonlinear, high-dimensional sequential data. It predicts pipeline flows and operating costs from measured data. Additionally, it adapts to changes in physical characteristics in pipelines. The proposed model was tested on real pipelines with a length of 5,000 km and demonstrated high accuracy, with a maximum error less than 0.2 MPa, and efficient computation, with a cost less than 2 s for 240 h. The proposed method constructs a reliable digital twin because it has the potential to be aware of the latent behavior of coherent physics in pipelines. The resulting digital twin forecast future status accurately and, based on this, may help establish advanced operating strategies in terms of safety and cost efficiency.

Preparing valence-bond-solid states on noisy intermediate-scale quantum computers

Quantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on a gate-based quantum computer a general class of quantum spin wave functions, the so-called valence-bond-solid (VBS) states, that are important for two reasons. First, VBS states are the exact ground states of a class of interacting quantum spin models introduced by Affleck, Kennedy, Lieb, and Tasaki (AKLT). Second, the two-dimensional VBS states are universal resource states for measurement-based quantum computing. We find that schemes to prepare VBS states based on their tensor-network representations yield quantum circuits that are too deep to be within reach of noisy intermediate-scale quantum (NISQ) computers. We then apply the general nondeterministic method herein proposed to the preparation of the spin-1 and spin-$3/2$ VBS states, the ground states of the AKLT models defined in one dimension and in the honeycomb lattice, respectively. Shallow quantum circuits of depth independent of the lattice size are explicitly derived for both cases, making use of optimization schemes that outperform standard basis gate decomposition methods. The probabilistic nature of the proposed routine translates into an average number of repetitions to successfully prepare the VBS state that scales exponentially with the number of lattice sites $N$. However, two strategies to quadratically reduce this repetition overhead for any bipartite lattice are devised. Our approach should permit to use NISQ processors to explore the AKLT model and variants thereof, outperforming conventional numerical methods in the near future.

Cosmology-informed neural networks to solve the background dynamics of the Universe

The field of machine learning has drawn increasing interest from various other fields due to the success of its methods at solving a plethora of different problems. An application of these has been to train artificial neural networks to solve differential equations without the need of a numerical solver. This particular application offers an alternative to conventional numerical methods, with advantages such as lower memory required to store solutions, parallelization, and, in some cases, a lower overall computational cost than its numerical counterparts. In this work, we train artificial neural networks to represent a bundle of solutions of the differential equations that govern the background dynamics of the Universe for four different models. The models we have chosen are $\Lambda \mathrm{CDM}$, the Chevallier-Polarski-Linder parametric dark energy model, a quintessence model with an exponential potential, and the Hu-Sawicki $f(R)$ model. We use the solutions that the networks provide to perform statistical analyses to estimate the values of each model's parameters with observational data; namely, estimates of the Hubble parameter from cosmic chronometers, type Ia supernovae data from the Pantheon compilation, and measurements from baryon acoustic oscillations. The results we obtain for all models match similar estimations done in the literature using numerical solvers. In addition, we estimate the error of the solutions that the trained networks provide by comparing them with the analytical solution when there is one, or to a high-precision numerical solution when there is not. Through these estimations we find that the error of the solutions is at most $\sim1\%$ in the region of the parameter space that concerns the $95\%$ confidence regions that we find using the data, for all models and all statistical analyses performed in this work.

Natural Frequency Analysis of Monopile Supported Offshore Wind Turbines Using Unified Beam-Column Element Model

Assessment of the natural frequency of the offshore wind turbine (OWT) system is a critical task in design to avoid resonance. The natural frequency of the monopile supported OWT may change during operation and needs to be calculated regularly. Conventional numerical methods separately model different components of the OWT system using various element types, which require tedious data manipulations and are inefficient to assess the changing natural frequency of the monopile supported OWTs. This paper develops a unified beam-column element by directly integrating the soil-pile interactions in element formulation. The proposed method is applicable for different components of the OWT system, including the rotor, the tower, the transition piece, and the monopile foundation, which enables an integrated and efficient OWT analysis by using only one type of element. The pile-soil interactions are directly considered in the element formulation. The tedious soil spring elements are avoided. Definitions and formulations of the proposed element are provided and the numerical solution procedure for the natural frequency analysis of OWTs is illustrated. The accuracy of the proposed element is validated against several closed-form solutions and the distributed spring model. The proposed method is also applied to analyze the natural frequencies of six OWTs in practice. The calculated results are consistent with the field measured data.

A Dynamic Competition Analysis of Stochastic Fractional Differential Equation Arising in Finance via Pseudospectral Method

This research focuses on the analysis of the competitive model used in the banking sector based on the stochastic fractional differential equation. For the approximate solution, a pseudospectral technique is utilized for the proposed model based on the stochastic Lotka–Volterra equation using a wide range of fractional order parameters in simulations. Conditions for stable and unstable equilibrium points are provided using the Jacobian. The Lotka–Volterra equation is unstable in the long term and can produce highly fluctuating dynamics, which is also one of the reasons that this equation is used to model the problems arising in finance, where fluctuations are important. For this reason, the conventional analytical and numerical methods are not the best choices. To overcome this difficulty, an automatic procedure is used to solve the resultant algebraic equation after the discretization of the operator. In order to fully use the properties of orthogonal polynomials, the proposed scheme is applied to the equivalent integral form of stochastic fractional differential equations under consideration. This also helps in the analysis of fractional differential equations, which mostly fall in the framework of their integrated form. We demonstrate that this fractional approach may be considered as the best tool to model such real-world data situations with very reasonable accuracy. Our numerical simulations further demonstrate that the use of the fractional Atangana–Baleanu operator approach produces results that are more precise and flexible, allowing individuals or companies to use it with confidence to model such real-world situations. It is shown that our numerical simulation results have a very good agreement with the real data, further showing the efficiency and effectiveness of our numerical scheme for the proposed model.

Under What Conditions Does Transverse Macrodispersion Exist in Groundwater Flow?

AbstractIn recent years there has been vigorous debate whether asymptotic transverse macrodispersion exists in steady three‐dimensional (3D) groundwater flows in the purely advective limit. This question is tied to the topology of 3D flow paths (termed the Lagrangian kinematics), specifically whether streamlines can undergo braiding motions or can wander freely in the transverse direction. In this study we determine which Darcy flows do admit asymptotic transverse macrodispersion for purely advective transport on the basis of the conductivity structure. We prove that porous media with smooth, locally isotropic hydraulic conductivity exhibit zero transverse macrodispersion under pure advection due to constraints on the Lagrangian kinematics of these flows, whereas either non‐smooth or locally anisotropic conductivity fields can generate transverse macrodispersion. This has implications for upscaling locally isotropic porous media to the block scale as this can result in a locally anisotropic conductivity, leading to non‐zero macrodispersion at the block scale that is spurious in that it does not arise for the fully resolved Darcy scale flow. We also show that conventional numerical methods for computation of particle trajectories do not explicitly preserve the kinematic constraints associated with locally isotropic Darcy flow, and propose a novel psuedo‐symplectic method that preserves these constraints. These results provide insights into the mechanisms that govern transverse macrodispersion in groundwater flow, and unify seemingly contradictory results in the literature in a consistent framework. These insights call into question the ability of smooth, locally isotropic conductivity fields to represent flow and transport in real heterogeneous porous media.

An Uncertain Mean-AVaR Portfolio Selection via an Artificial Neural Network Scheme

This paper focuses on the computation issue of portfolio optimization with scenario-based mean-average value at Risk (AVaR) in uncertain environment. The portfolio optimization problem is designed in two cases: risk-taker and risk-averse models. The main idea is to replace the portfolio selection models with linear programming (LP) problems. Since the computing time required for solving LP greatly depends on the dimension and the structure of the problem, the conventional numerical methods are usually less effective in real-time applications. One promising approach to handle online applications is to employ recurrent neural networks based on circuit implementation. Hence, according to the convex optimization theory and some concepts of ordinary differential equations, a neural network model for solving the LP problems related to portfolio selection problems is presented. The equilibrium point of the proposed model is proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the portfolio selection problem with uncertain returns. Some illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.

Enhanced surrogate modelling of heat conduction problems using physics-informed neural network framework

Solving partial differential equations (PDEs) using deep-learning techniques provides opportunities for surrogate models that require no labelled data, e.g., CFD results, from the domain interior other than the boundary and initial conditions. We propose a new ansatz of the solution incorporated with a physics-informed neural network (PINN) for solving PDEs to impose the boundary conditions (BCs) with hard constraints. This ansatz comprises three subnetworks: a boundary function, a distance function, and a deep neural network (DNN). The new model performance is assessed thoroughly in terms of convergence speed and accuracy. To this end, we apply the PINN models to conduction heat transfer problems with different geometries and BCs. The results of 1D, 2D and 3D problems are compared with conventional numerical methods and analytical results. The results reveal that the neural networks (NNs) model with the proposed ansatz outperforms counterpart PINN models in the literature and leads to faster convergence with better accuracy, especially for higher dimensions, i.e., three-dimensional case studies.

Review of Shale Gas Transport Prediction: Basic Theory, Numerical Simulation, Application of AI Methods, and Perspectives

The gas transport mechanism in shale reservoirs is extremely complex and is a typical multiscale and multiphysics coupled transport process, considering the complex shale rock structure, wide distribution of micropores and nanopores in shale gas reservoirs, diverse gas occurrence forms, and large pore size spans. An accurate understanding of the shale gas transport process and mechanism is important for effective exploration of shale gas reservoirs. In this work, a review of the recent progress in the prediction of shale gas transport in porous media is presented. The basic theory of gas transport in nanopores is discussed. The gas transport in organic and inorganic matter and the gas adsorption effect are covered. Then, gas transport simulations with conventional multiscale numerical methods, including molecular dynamics and lattice Boltzmann simulations, are reviewed, and the multiscale modeling methods are discussed. Furthermore, the application of artificial intelligence (AI) methods in shale gas transport research is discussed. The focus is on the characterization of the shale porous geometry, including porosity, tortuosity, pore size distribution, and reconstruction of the shale porous medium. The application of AI-based methods such as neural networks and machine learning for the prediction of porous flow properties is discussed. This study intends to provide a comprehensive review of shale gas transport characteristics and to enable the accessibility of AI tools in the research of shale gas.

Coupled thermal-hydro-mechanical modeling on characteristics of excavation damage zone around deep tunnels crossing a major fault

An understanding of excavation damage zone (EDZ) is critical in safe construction of underground openings, but conventional continuum-based numerical methods such as finite element method or finite difference method have limitations in simulating crack development under coupled thermal-hydro-mechanical (THM) conditions. In this study, a numerical method of predicting EDZ subjected to coupled THM conditions is developed based on discrete element method (DEM), which can simulate propagation of newly formed cracks by adding fictitious joints. A physical model of a high temperature tunnel filled with pressurized water is first used to verify the accuracy and efficiency of the developed numerical method. Based on the case study of the Baoling Mountain tunnel of the Sichuan-Tibet railway, the effects of coupled THM conditions on characteristics of EDZ are investigated. The results show that the two EDZ indices of volume of plastic zones per length and area of cracks per length increase from M-only to THM scenarios. In addition, the shear displacements of the fault in the roof and floor of the tunnel also increase from M-only to THM scenarios. The increasing EDZ size and fault displacement in THM scenario is attributed to the higher ambient rock stress and water pressure in the fictitious joints and the fault. In high temperature regions, thermal stress increases the maximum principal stresses and induces rock damage. Effect of fault dip angle on characteristics of EDZ is also discussed.