An adaptive finite-difference method for seismic traveltime modeling based on 3D eikonal equation

3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.

Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

Coupled-generalized nonlinear Schr¨odinger equations solved by adaptive step-size methods in interaction picture

We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(RK4IP-CQE), and the other is the local error adaptive step-control method(RK4IP-LEM). The methods are developed in the vector form of fourthorder Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.

A novel adaptive harmonic balance method with an asymptotic harmonic selection

The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.

Phase-field modeling of dendritic growth under forced flow based on adaptive finite element method

A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.

Design and analysis of an advanced thermal management system for the solar close observations and proximity experiments spacecraft

In this paper,the mission and the thermal environment of the Solar Close Observations and Proximity Experiments(SCOPE)spacecraft are analyzed,and an advanced thermal management system(ATMS)is designed for it.The relationship and functions of the integrated database,the intelligent thermal control system and the efficient liquid cooling system in the ATMS are elaborated upon.For the complex thermal field regulation system and extreme space thermal environment,a modular simulation and thermal field planning method are proposed,and the feasibility of the planning algorithm is verified by numerical simulation.A solar array liquid cooling system is developed,and the system simulation results indicate that the temperatures of the solar arrays meet the requirements as the spacecraft flies by perihelion and aphelion.The advanced thermal management study supports the development of the SCOPE program and provides a reference for the thermal management in other deep-space exploration programs.

Study on damage mechanism and damage distribution of the rear plate under impact of debris cloud

The debris cloud generated by the hypervelocity impact(HVI)of orbiting space debris directly threatens the spacecraft.A full understanding of the damage mechanism of rear plate is useful for the optimal design of protective structures.In this study,the hypervelocity yaw impact of a cylindrical aluminum projectile on a double-layer aluminum plate is simulated by the FE-SPH adaptive method,and the damage process of the rear plate under the impact of the debris cloud is analyzed based on the debris cloud structure.The damage process can be divided into the main impact stage of the debris cloud and the structural response of the rear plate.The main impact stage lasts a short time and is the basis of the rear plate damage.In the stage of structure response,the continuous deformation and inertial motion of the rear plate dominate the perforation of the rear plate.We further analyze the damage mechanism and damage distribution characteristics of the rear plate in detail.Moreover,the connection between velocity space and position space of the debris cloud is established,which promotes the general analysis of the damage law of debris cloud.Based on the relationship,the features of typical damage areas are identified by the localized fine analysis.Both the cumulative effect and structural response cause the perforation of rear plate;in the non-perforated area,cratering by the impact of hazardous fragments is the main damage mode of the rear plate.

A New Efcient Explicit Deferred Correction Framework:Analysis and Applications to Hyperbolic PDEs and Adaptivity

The deferred correction(DeC)is an iterative procedure,characterized by increasing the accuracy at each iteration,which can be used to design numerical methods for systems of ODEs.The main advantage of such framework is the automatic way of getting arbitrarily high order methods,which can be put in the Runge-Kutta(RK)form.The drawback is the larger computational cost with respect to the most used RK methods.To reduce such cost,in an explicit setting,we propose an efcient modifcation:we introduce interpolation processes between the DeC iterations,decreasing the computational cost associated to the low order ones.We provide the Butcher tableaux of the new modifed methods and we study their stability,showing that in some cases the computational advantage does not afect the stability.The fexibility of the novel modifcation allows nontrivial applications to PDEs and construction of adaptive methods.The good performances of the introduced methods are broadly tested on several benchmarks both in ODE and PDE contexts.

Fusion of Convolutional Self-Attention and Cross-Dimensional Feature Transformationfor Human Posture Estimation

Human posture estimation is a prominent research topic in the fields of human-com-puter interaction,motion recognition,and other intelligent applications.However,achieving highaccuracy in key point localization,which is crucial for intelligent applications,contradicts the lowdetection accuracy of human posture detection models in practical scenarios.To address this issue,a human pose estimation network called AT-HRNet has been proposed,which combines convolu-tional self-attention and cross-dimensional feature transformation.AT-HRNet captures significantfeature information from various regions in an adaptive manner,aggregating them through convolu-tional operations within the local receptive domain.The residual structures TripNeck and Trip-Block of the high-resolution network are designed to further refine the key point locations,wherethe attention weight is adjusted by a cross-dimensional interaction to obtain more features.To vali-date the effectiveness of this network,AT-HRNet was evaluated using the COCO2017 dataset.Theresults show that AT-HRNet outperforms HRNet by improving 3.2%in mAP,4.0%in AP75,and3.9%in AP^(M).This suggests that AT-HRNet can offer more beneficial solutions for human posture estimation.

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

Adaptive element free Galerkin method applied to analysis of earthquake induced liquefaction

An automatically adaptive element free method is presented to analyze the seismic response of liquefiable soils. The method is based on the element free Galerkin method （EFGM） and the fission procedure that is part of h-refinement, indicated by error estimation. In the proposed method, a posteriori error estimate procedure that depends on the energy norm of stress and the T-Belytschko （TB） stress recovery scheme is incorporated. The effective cyclic elasto-plastic constitutive model is used to describe the nonlinear behavior of the saturated soil. The governing equations are established by u-p formulation. The proposed method can effectively avoid the volumetric locking due to large deformation that usually occurs in numerical computations using the finite element method （FEM）. The efficiency of the proposed method is demonstrated by evaluating the seismic response of an embankment and comparing it to results obtained through FEM. It is shown that the proposed method provides an accurate seismic analysis of saturated soil that includes the effects of liquefaction .

Key Techniques and Applications of Adaptive Growth Method for Stiffener Layout Design of Plates and Shells

The application of the adaptive growth method is limited because several key techniques during the design process need manual intervention of designers. Key techniques of the method including the ground structure construction and seed selection are studied, so as to make it possible to improve the effectiveness and applicability of the adaptive growth method in stiffener layout design optimization of plates and shells. Three schemes of ground structures, which are comprised by different shell elements and beam elements, are proposed. It is found that the main stiffener layouts resulted from different ground structures are almost the same, but the ground structure comprised by 8-nodes shell elements and both 3-nodes and 2-nodes beam elements can result in clearest stiffener layout, and has good adaptability and low computational cost. An automatic seed selection approach is proposed, which is based on such selection rules that the seeds should be positioned on where the structural strain energy is great for the minimum compliance problem, and satisfy the dispersancy requirement. The adaptive growth method with the suggested key techniques is integrated into an ANSYS-based program, which provides a design tool for the stiffener layout design optimization of plates and shells. Typical design examples, including plate and shell structures to achieve minimum compliance and maximum bulking stability are illustrated. In addition, as a practical mechanical structural design example, the stiffener layout of an inlet structure for a large-scale electrostatic precipitator is also demonstrated. The design results show that the adaptive growth method integrated with the suggested key techniques can effectively and flexibly deal with stiffener layout design problem for plates and shells with complex geometrical shape and loading conditions to achieve various design objectives, thus it provides a new solution method for engineering structural topology design optimization.

Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation

Recently,the simplified spherical harmonics equations(SP)model has at tracted much att entionin modeling the light propagation in small tissue ggeometriesat visible and near-infrared wave-leng ths.In this paper,we report an eficient numerical method for fluorescence moleeular tom-ography(FMT)that combines the advantage of SP model and adaptive hp finite elementmethod(hp-FEM).For purposes of comparison,hp-FEM and h-FEM are,respectively applied tothe reconstruction pro cess with diffusion approximation and SPs model.Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are designed to evaluate thereconstruction methods in terms of the location and the reconstructed fluorescent yield.Theexperimental results demonstrate that hp-FEM with SPy model,yield more accurate results thanh-FEM with difusion approximation model does.The phantom experiments show the potentialand feasibility of the proposed approach in FMT applications.

Adaptive Finite Element Method Based on Optimal Error Estimates for Linear Elliptic Problems on Nonconvex Polygonal Domains

The subject of this work is to propose adaptive finite element methods based on an optimal maximum norm error control estimate.Using estimators of the local regularity of the unknown exact solution derived from computed approximate solutions,the proposed procedures are analyzed in detail for a non-trivial class of corner problems and shown to be efficient in the sense that they generate the correct type of refinement and lead to the desired control under consideration.

Adaptive split-step Fourier method for simulating ultrashort laser pulse propagation in photonic crystal fibres

In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.

An adaptive method for high-resolution topology design

For the purpose of achieving high-resolution optimal solutions this paper proposes a nodal design variablebased adaptive method for topology optimization of continuum structures. The analysis mesh-independent density field, interpolated by the nodal design variables at a given set of density points, is adaptively refined/coarsened accord- ing to a criterion regarding the gray-scale measure of local regions. New density points are added into the gray regions and redundant ones are removed from the regions occupied by purely solid/void phases for decreasing the number of de- sign variables. A penalization factor adaptivity technique is employed-to prevent premature convergence of the optimiza- tion iterations. Such an adaptive scheme not only improves the structural boundary description quality, but also allows for sufficient further topological evolution of the structural layout in higher adaptivity levels and thus essentially enables high-resolution solutions. Moreover, compared with the case with uniformly and finely distributed density points, the proposed adaptive method can achieve a higher numerical efficiency of the optimization process.

Prediction of Rural Residents’ Consumption Expenditure Based on Lasso and Adaptive Lasso Methods

When the variable of model is large, the Lasso method and the Adaptive Lasso method can effectively select variables. This paper prediction the rural residents’ consumption expenditure in China, based on respectively using the Lasso method and the Adaptive Lasso method. The results showed that both can effectively and accurately choose the appropriate variable, but the Adaptive Lasso method is better than the Lasso method in prediction accuracy and prediction error. It shows that in variable selection and parameter estimation, Adaptive Lasso method is better than the Lasso method.

Characteristics of permanent magnet linear synchronous motor fed by spwm inverter based on field-circuit coupled method

Presented field-circuit coupled adaptive time-stepping finite element method to study on permanent magnet linear synchronous motor (PMLSM) characteristics fed by SPWM voltage source inverter.In air-gap field where the direction or magnitude of the field is changing rapidly,the smallest elements are demanded due to high accuracy to use adaptive meshing technique.The co-simulation was used with the status space functions and time-step finite element functions,in which time-step of the status space functions was the smallest than finite element functions'.The magnitude relation of the normal elec- tromagnetic force and tangential electromagnetic force and the period were attained,and current curve was very abrupt at current zero area due to the bigger resistance and leak- age reactance,including main characteristics of motor voltage and velocity.The simulation results compare triumphantly with the experiments results.

METHOD FOR ADAPTIVE MESH GENERATION BASED ON GEOMETRICAL FEATURES OF 3D SOLID

In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical features and the elements of 3D solid. Various modes based on different datum geometrical elements, such as vertex, curve, surface, and so on, are then designed for generating local refined mesh. With the guidance of the defmed criteria, different modes are automatically selected to apply on the appropriate datum objects to program the element size in the local special areas. As a result, the control information of element size is successfully programmed covering the entire domain based on the geometrical features of 3D solid. A new algorithm based on Delatmay triangulation is then developed for generating 3D adaptive finite element mesh, in which the element size is dynamically specified to catch the geometrical features and suitable tetrahedron facets are selected to locate interior nodes continuously. As a result, adaptive mesh with good-quality elements is generated. Examples show that the proposed method can be successfully applied to adaptive finite element mesh automatic generation based on the geometrical features of 3D solid.

The Adaptive Wavelet Collocation Method and Its Application in Front Simulation

The adaptive wavelet collocation method （AWCM） is a variable grid technology for solving partial differential equations （PDEs） with high singularities. Based on interpolating wavelets, the AWCM adapts the grid so that a higher resolution is automatically attributed to domain regions with high singularities. Accuracy problems with the AWCM have been reported in the literature, and in this paper problems of efficiency with the AWCM are discussed in detail through a simple one-dimensional （1D） nonlinear advection equation whose analytic solution is easily obtained. A simple and efficient implementation of the AWCM is investigated. Through studying the maximum errors at the moment of frontogenesis of the 1D nonlinear advection equation with different initial values and a comparison with the finite difference method （FDM） on a uniform grid, the AWCM shows good potential for modeling the front efficiently. The AWCM is also applied to a two-dimensional （2D） unbalanced frontogenesis model in its first attempt at numerical simulation of a meteorological front. Some important characteristics about the model are revealed by the new scheme.