In this paper, frequencies of electromagnetic wave in a conductive wire are investigated theoretically. The conductive wire has specific variable material properties along the length of itself. Furthermore, material p...In this paper, frequencies of electromagnetic wave in a conductive wire are investigated theoretically. The conductive wire has specific variable material properties along the length of itself. Furthermore, material properties varying along the length of the wire are determined according to a specific mathematical function. In addition, the central finite difference method is applied to the Maxwell equations. The accuracy of the mode 1 frequency parameter is obtained to be 0.06%. This result can be obtained by assuming the number of conductive wire nodes 20. The obtained results show a very good agreement with the exact solution results.展开更多
Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ways.Here,we compare one important scheme to ordinary finite differences by a mixture of numerical experim...Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ways.Here,we compare one important scheme to ordinary finite differences by a mixture of numerical experiments and theoretical Fourier analysis,that is,by deriving and discussing analytical formulas for the error in differentiating exp(ikx)for arbitrary k.‘Truncated RBF differences”are derived from the same strategy as Fourier and Chebyshev pseudospectral methods:Differentiation of the Fourier,Chebyshev or RBF interpolant generates a differentiation matrix that maps the grid point values or samples of a function u(x)into the values of its derivative on the grid.For Fourier and Chebyshev interpolants,the action of the differentiation matrix can be computed indirectly but efficiently by the Fast Fourier Transform(FFT).For RBF functions,alas,the FFT is inapplicable and direct use of the dense differentiation matrix on a grid of N points is prohibitively expensive(O(N2))unless N is tiny.However,for Gaussian RBFs,which are exponentially localized,there is another option,which is to truncate the dense matrix to a banded matrix,yielding“truncated RBF differences”.The resulting formulas are identical in form to finite differences except for the difference weights.On a grid of spacing h with the RBF asφ(x)=exp(−α^(2)(x/h)^(2)),d f dx(0)≈∑^(∞)_(m)=1 wm{f(mh)−f(−mh)},where without approximation wm=(−1)m+12α^(2)/sinh(mα^(2)).We derive explicit formula for the differentiation of the linear function,f(X)≡X,and the errors therein.We show that Gaussian radial basis functions(GARBF),when truncated to give differentiation formulas of stencil width(2M+1),are significantly less accurate than(2M)-th order finite differences of the same stencil width.The error of the infinite series(M=∞)decreases exponentially asα→0.However,truncated GARBF series have a second error(truncation error)that grows exponentially asα→0.Even forα∼O(1)where the sum of these two errors is minimized,it is shown that the finite difference formulas are always superior.We explain,less rigorously,why these arguments extend to more general species of RBFs and to an irregular grid.There are,however,a variety of alternative differentiation strategies which will be analyzed in future work,so it is far too soon to dismiss RBFs as a tool for solving differential equations.展开更多
To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal h...This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal heat generation resulting from optical absorption,grounded in the physical equations governing light-matter interactions within the module’smultilayer structure.The model accounts for reflection and transmission at each interface between adjacent layers,as well as absorption within individual layers,using the wavelength-dependent dielectric properties of constituent materials.These properties are used to calculate the spectral reflectance,transmittance,and absorption coefficients,enabling precise quantification of internal heat sources from irradiance incidents on both the front and rear surfaces of the module.The study further examines the influence of irradiance reflection on thermal behavior,evaluates the thermal impact of various supporting materials placed beneath the module,and analyzes the role of albedo in modifying heat distribution.By incorporating spectrally resolved heat generation across each layer often simplified or omitted in conventional models,the proposed approach enhances physical accuracy.The transient heat equation is solved using a one-dimensional finite difference(FD)method to produce detailed temperature profiles under multiple operating scenarios,including Standard Test Conditions(STC),Bifacial Standard Test Conditions(BSTC),Normal Operating Cell Temperature(NOCT),and Bifacial NOCT(BNOCT).The results offer valuable insights into the interplay between optical and thermal phenomena in bifacial systems,informing the design and optimization of more efficient photovoltaic technologies.展开更多
Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and ...Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.展开更多
In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving th...In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.展开更多
A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficien...A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficients(k)are constructed based on FDM.The rock bridge area was divided through k-means algorithm and the optimal number of clusters was determined by sum of squared errors(SSE)and elbow method.The influence of maximum principal stress and stress change rate as clustering indexes on the clustering results of rock bridges was compared by using Euclidean distance.The results show that using stress change rate as clustering index is more effective.When the joint coalescence coefficient is less than 0.6,there is no significant stress concentration in the middle area of adjacent joints,that is,no generation of rock bridge.In addition,the range of rock bridge is affected by the coalescence coefficient(k),the relative position of joints and the parameters of weak interlayer.展开更多
Laplace–Fourier(L-F)domain finite-difference(FD)forward modeling is an important foundation for L-F domain full-waveform inversion(FWI).An optimal modeling method can improve the efficiency and accuracy of FWI.A fl e...Laplace–Fourier(L-F)domain finite-difference(FD)forward modeling is an important foundation for L-F domain full-waveform inversion(FWI).An optimal modeling method can improve the efficiency and accuracy of FWI.A fl exible FD stencil,which requires pairing and centrosymmetricity of the involved gridpoints,is used on the basis of the 2D L-F domain acoustic wave equation.The L-F domain numerical dispersion analysis is then performed by minimizing the phase error of the normalized numerical phase and attenuation propagation velocities to obtain the optimization coefficients.An optimal FD forward modeling method is finally developed for the L-F domain acoustic wave equation and applied to the traditional standard 9-point scheme and 7-and 9-point schemes,where the latter two schemes are used in discontinuous-grid FD modeling.Numerical experiments show that the optimal L-F domain FD modeling method not only has high accuracy but can also be applied to equal and unequal directional sampling intervals and discontinuous-grid FD modeling to reduce computational cost.展开更多
Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurat...Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurate and not affected by strong subsurface structure complexity and horizontal velocity variations. The difference method based on triangular grids maintains the simplicity of the difference method and the precision of the finite element method. It can be used directly for forward modeling on models with complex top surfaces and migration without statics preprocessing. We apply a finite difference method based on triangular grids for post-stack reverse-time migration for the first time. Tests on model data verify that the combination of the two methods can achieve near-perfect results in application.展开更多
The transmission and dispersive characteristics of slotline are calculated in this paper. The tail of Gaussion pulse is improved because a modified dispersive boundary condition (DBC) is adopted. It leads to a reduct...The transmission and dispersive characteristics of slotline are calculated in this paper. The tail of Gaussion pulse is improved because a modified dispersive boundary condition (DBC) is adopted. It leads to a reduction in computer memory requirements and computational time. The computational domain is greatly reduced to enable performance in personal computer. At the same time because edges of a boundary and summits are treated well, the computational results is more accurate and more collector.展开更多
In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theo...In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theorems, ΔV is not required to be always negative, where ΔV(n,x n)≡V(n+1,x(n+1)) -V(n,x(n))=V(n+1,f(n,x n))-V(n,x(n)), especially, in Theorem 1, ΔV may be even positive, which greatly improve the known results and are more convenient to use.展开更多
The paper is concerned with strongly nonlinear singularly perturbed bound- ary value problems in one dimension.The problems are solved numerically by finite- difference schemes on special meshes which are dense in the...The paper is concerned with strongly nonlinear singularly perturbed bound- ary value problems in one dimension.The problems are solved numerically by finite- difference schemes on special meshes which are dense in the boundary layers.The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed.For the central scheme,error estimates are derived in a discrete L^1 norm.They are of second order and decrease together with the perturbation parameterε.The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically.Numerical results showε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.展开更多
Contact bounce of relay, which is the main cause of electric abrasion and material erosion, is inevitable. By using the mode expansion form, the dynamic behavior of two different reed systems for aerospace relays is a...Contact bounce of relay, which is the main cause of electric abrasion and material erosion, is inevitable. By using the mode expansion form, the dynamic behavior of two different reed systems for aerospace relays is analyzed. The dynamic model uses Euler-Bernoulli beam theory for cantilever beam, in which the driving force (or driving moment) of the electromagnetic system is taken into account, and the contact force between moving contact and stationary contact is simulated by the Kelvin-Voigt vis-coelastic...展开更多
In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered gri...In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.展开更多
An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aero...An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.展开更多
D seismic modeling can be used to study the propagation of seismic wave exactly and it is also a tool of 3-D seismic data processing and interpretation. In this paper the arbitrary difference and precise integration a...D seismic modeling can be used to study the propagation of seismic wave exactly and it is also a tool of 3-D seismic data processing and interpretation. In this paper the arbitrary difference and precise integration are used to solve seismic wave equation, which means difference scheme for space domain and analytic integration for time domain. Both the principle and algorithm of this method are introduced in the paper. Based on the theory, the numerical examples prove that this hybrid method can lead to higher accuracy than the traditional finite difference method and the solution is very close to the exact one. Also the seismic modeling examples show the good performance of this method even in the case of complex surface conditions and complicated structures.展开更多
The nonlinear finite element（FE） analysis has been widely used in the design and analysis of structural or geotechnical systems.The response sensitivities（or gradients） to the model parameters are of significant i...The nonlinear finite element（FE） analysis has been widely used in the design and analysis of structural or geotechnical systems.The response sensitivities（or gradients） to the model parameters are of significant importance in these realistic engineering problems.However the sensitivity calculation has lagged behind,leaving a gap between advanced FE response analysis and other research hotspots using the response gradient.The response sensitivity analysis is crucial for any gradient-based algorithms,such as reliability analysis,system identification and structural optimization.Among various sensitivity analysis methods,the direct differential method（DDM） has advantages of computing efficiency and accuracy,providing an ideal tool for the response gradient calculation.This paper extended the DDM framework to realistic complicated soil-foundation-structure interaction（SFSI） models by developing the response gradients for various constraints,element and materials involved.The enhanced framework is applied to three-dimensional SFSI system prototypes for a pilesupported bridge pier and a pile-supported reinforced concrete building frame structure,subjected to earthquake loading conditions.The DDM results are verified by forward finite difference method（FFD）.The relative importance（RI） of the various material parameters on the responses of SFSI system are investigated based on the DDM response sensitivity results.The FFD converges asymptotically toward the DDM results,demonstrating the advantages of DDM（e.g.,accurate,efficient,insensitive to numerical noise）.Furthermore,the RI and effects of the model parameters of structure,foundation and soil materials on the responses of SFSI systems are investigated by taking advantage of the sensitivity analysis results.The extension of DDM to SFSI systems greatly broaden the application areas of the d gradient-based algorithms,e.g.FE model updating and nonlinear system identification of complicated SFSI systems.展开更多
Based on some assumptions, the dynamic analysis model of anchorage system is established. The dynamic governing equation is expressed as finite difference format and programmed by using MATLAB language. Compared with ...Based on some assumptions, the dynamic analysis model of anchorage system is established. The dynamic governing equation is expressed as finite difference format and programmed by using MATLAB language. Compared with theoretical method, the finite difference method has been verified to be feasible by a case study. It is found that under seismic loading, the dynamic response of anchorage system is synchronously fluctuated with the seismic vibration. The change of displacement amplitude of material points is slight, and comparatively speaking, the displacement amplitude of the outside point is a little larger than that of the inside point, which shows amplification effect of surface. While the axial force amplitude transforms considerably from the inside to the outside. It increases first and reaches the peak value in the intersection between the anchoring section and free section, then decreases slowly in the free section. When considering damping effect of anchorage system, the finite difference method can reflect the time attenuation characteristic better, and the calculating result would be safer and more reasonable than the dynamic steady-state theoretical method. What is more, the finite difference method can be applied to the dynamic response analysis of harmonic and seismic random vibration for all kinds of anchor, and hence has a broad application prospect.展开更多
An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for ...An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.展开更多
An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite...An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite elementdiscrete model is formed by using the artificial boundary and finite element method, and the dynamic equationsof local nodes in the discrete model are obtained according to the theory of the special finite element method similar to the finite difference method, and then the explicit step-by-step integration formulas are presented by usingthe explicit difference method for solving the visco-elastic dynamic equation and Generalized Multi-transmittingBoundary. The method has the advantages of saving computing time and computer memory space, and it is suitable for any case of topography and has high computing accuracy and good computing stability.展开更多
文摘In this paper, frequencies of electromagnetic wave in a conductive wire are investigated theoretically. The conductive wire has specific variable material properties along the length of itself. Furthermore, material properties varying along the length of the wire are determined according to a specific mathematical function. In addition, the central finite difference method is applied to the Maxwell equations. The accuracy of the mode 1 frequency parameter is obtained to be 0.06%. This result can be obtained by assuming the number of conductive wire nodes 20. The obtained results show a very good agreement with the exact solution results.
文摘Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ways.Here,we compare one important scheme to ordinary finite differences by a mixture of numerical experiments and theoretical Fourier analysis,that is,by deriving and discussing analytical formulas for the error in differentiating exp(ikx)for arbitrary k.‘Truncated RBF differences”are derived from the same strategy as Fourier and Chebyshev pseudospectral methods:Differentiation of the Fourier,Chebyshev or RBF interpolant generates a differentiation matrix that maps the grid point values or samples of a function u(x)into the values of its derivative on the grid.For Fourier and Chebyshev interpolants,the action of the differentiation matrix can be computed indirectly but efficiently by the Fast Fourier Transform(FFT).For RBF functions,alas,the FFT is inapplicable and direct use of the dense differentiation matrix on a grid of N points is prohibitively expensive(O(N2))unless N is tiny.However,for Gaussian RBFs,which are exponentially localized,there is another option,which is to truncate the dense matrix to a banded matrix,yielding“truncated RBF differences”.The resulting formulas are identical in form to finite differences except for the difference weights.On a grid of spacing h with the RBF asφ(x)=exp(−α^(2)(x/h)^(2)),d f dx(0)≈∑^(∞)_(m)=1 wm{f(mh)−f(−mh)},where without approximation wm=(−1)m+12α^(2)/sinh(mα^(2)).We derive explicit formula for the differentiation of the linear function,f(X)≡X,and the errors therein.We show that Gaussian radial basis functions(GARBF),when truncated to give differentiation formulas of stencil width(2M+1),are significantly less accurate than(2M)-th order finite differences of the same stencil width.The error of the infinite series(M=∞)decreases exponentially asα→0.However,truncated GARBF series have a second error(truncation error)that grows exponentially asα→0.Even forα∼O(1)where the sum of these two errors is minimized,it is shown that the finite difference formulas are always superior.We explain,less rigorously,why these arguments extend to more general species of RBFs and to an irregular grid.There are,however,a variety of alternative differentiation strategies which will be analyzed in future work,so it is far too soon to dismiss RBFs as a tool for solving differential equations.
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
文摘This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal heat generation resulting from optical absorption,grounded in the physical equations governing light-matter interactions within the module’smultilayer structure.The model accounts for reflection and transmission at each interface between adjacent layers,as well as absorption within individual layers,using the wavelength-dependent dielectric properties of constituent materials.These properties are used to calculate the spectral reflectance,transmittance,and absorption coefficients,enabling precise quantification of internal heat sources from irradiance incidents on both the front and rear surfaces of the module.The study further examines the influence of irradiance reflection on thermal behavior,evaluates the thermal impact of various supporting materials placed beneath the module,and analyzes the role of albedo in modifying heat distribution.By incorporating spectrally resolved heat generation across each layer often simplified or omitted in conventional models,the proposed approach enhances physical accuracy.The transient heat equation is solved using a one-dimensional finite difference(FD)method to produce detailed temperature profiles under multiple operating scenarios,including Standard Test Conditions(STC),Bifacial Standard Test Conditions(BSTC),Normal Operating Cell Temperature(NOCT),and Bifacial NOCT(BNOCT).The results offer valuable insights into the interplay between optical and thermal phenomena in bifacial systems,informing the design and optimization of more efficient photovoltaic technologies.
基金supported by the National Natural Science Foundation of China(No.42372287 and No.U24A20178)the Fundamental Research Funds for the Central Universities CHD(No.2024SHEEAR002)+3 种基金the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shaanxi Province(No.2020024)the China Postdoctoral Science Foundation(GZC20232955,2024M753472,and 2024MD763937)the Science-Technology Foundation for Young Scientists of Gansu Province,China(No.24JRRA097)the Study of biodiversity survey and limiting factor analysis of Yinkentala(2023ZL01).
文摘Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.
基金supported by the National Natural Science Foundation of China(12201228,12171047)the Fundamental Research Funds for the Central Universities(3034011102)supported by National Key R&D Program of China(2020YFA0713701).
文摘In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.
基金supported by the National Natural Science Foundation of China(No.42277175)Guangxi Emergency Management Department 2024 Innovation and Technology Research Project,China(No.2024GXYJ006)+2 种基金Hunan Provincial Department of Natural Resources Geological Exploration Project,China(No.2023ZRBSHZ056)The First National Natural Disaster Comprehensive Risk Survey in Hunan Province,China(No.2022-70)Guizhou Provincial Major Scientific and Technological Program,China(No.2023-425).
文摘A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficients(k)are constructed based on FDM.The rock bridge area was divided through k-means algorithm and the optimal number of clusters was determined by sum of squared errors(SSE)and elbow method.The influence of maximum principal stress and stress change rate as clustering indexes on the clustering results of rock bridges was compared by using Euclidean distance.The results show that using stress change rate as clustering index is more effective.When the joint coalescence coefficient is less than 0.6,there is no significant stress concentration in the middle area of adjacent joints,that is,no generation of rock bridge.In addition,the range of rock bridge is affected by the coalescence coefficient(k),the relative position of joints and the parameters of weak interlayer.
基金National Natural Science Foundation of China(no.41604037)Natural Science Foundation of Hubei Province(no.2022CFB125)+2 种基金Open Fund of Key Laboratory of Exploration Technologies for Oil and Gas Resources(Yangtze University)Ministry of Education(no.K2021-09)College Students'Innovation and Entrepreneurship Training Program(no.2019053)。
文摘Laplace–Fourier(L-F)domain finite-difference(FD)forward modeling is an important foundation for L-F domain full-waveform inversion(FWI).An optimal modeling method can improve the efficiency and accuracy of FWI.A fl exible FD stencil,which requires pairing and centrosymmetricity of the involved gridpoints,is used on the basis of the 2D L-F domain acoustic wave equation.The L-F domain numerical dispersion analysis is then performed by minimizing the phase error of the normalized numerical phase and attenuation propagation velocities to obtain the optimization coefficients.An optimal FD forward modeling method is finally developed for the L-F domain acoustic wave equation and applied to the traditional standard 9-point scheme and 7-and 9-point schemes,where the latter two schemes are used in discontinuous-grid FD modeling.Numerical experiments show that the optimal L-F domain FD modeling method not only has high accuracy but can also be applied to equal and unequal directional sampling intervals and discontinuous-grid FD modeling to reduce computational cost.
基金sponsored by National Natural Science Foundation(40474041)National Symposium of 863(2006AA06Z206)+1 种基金National Symposium of 973(2007CB209605)CNPC Geophysical Key Laboratory of the China University of Petroleum (East China) Research Department
文摘Compared with other migration methods, reverse-time migration is based on a precise wave equation, not an approximation, and performs extrapolation in the depth domain rather than the time domain. It is highly accurate and not affected by strong subsurface structure complexity and horizontal velocity variations. The difference method based on triangular grids maintains the simplicity of the difference method and the precision of the finite element method. It can be used directly for forward modeling on models with complex top surfaces and migration without statics preprocessing. We apply a finite difference method based on triangular grids for post-stack reverse-time migration for the first time. Tests on model data verify that the combination of the two methods can achieve near-perfect results in application.
文摘The transmission and dispersive characteristics of slotline are calculated in this paper. The tail of Gaussion pulse is improved because a modified dispersive boundary condition (DBC) is adopted. It leads to a reduction in computer memory requirements and computational time. The computational domain is greatly reduced to enable performance in personal computer. At the same time because edges of a boundary and summits are treated well, the computational results is more accurate and more collector.
文摘In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theorems, ΔV is not required to be always negative, where ΔV(n,x n)≡V(n+1,x(n+1)) -V(n,x(n))=V(n+1,f(n,x n))-V(n,x(n)), especially, in Theorem 1, ΔV may be even positive, which greatly improve the known results and are more convenient to use.
文摘The paper is concerned with strongly nonlinear singularly perturbed bound- ary value problems in one dimension.The problems are solved numerically by finite- difference schemes on special meshes which are dense in the boundary layers.The Bakhvalov mesh and a special piecewise equidistant mesh are analyzed.For the central scheme,error estimates are derived in a discrete L^1 norm.They are of second order and decrease together with the perturbation parameterε.The fourth-order Numerov scheme and the Shishkin mesh are also tested numerically.Numerical results showε-uniform pointwise convergence on the Bakhvalov and Shishkin meshes.
文摘Contact bounce of relay, which is the main cause of electric abrasion and material erosion, is inevitable. By using the mode expansion form, the dynamic behavior of two different reed systems for aerospace relays is analyzed. The dynamic model uses Euler-Bernoulli beam theory for cantilever beam, in which the driving force (or driving moment) of the electromagnetic system is taken into account, and the contact force between moving contact and stationary contact is simulated by the Kelvin-Voigt vis-coelastic...
基金supported by the National Natural Science Foundation of China(NSFC)(Grant No. 41074100)the Program for New Century Excellent Talents in University of Ministry of Education of China(Grant No. NCET-10-0812)
文摘In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.
基金The National Natural Science Foundation of China(No50475073,50775036)the High Technology Research Program of Jiangsu Province(NoBG2006035)
文摘An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.
基金This project is sponsored by the Specialized Prophasic Basic Research of the"973"Programme,contract No:2001cca02300
文摘D seismic modeling can be used to study the propagation of seismic wave exactly and it is also a tool of 3-D seismic data processing and interpretation. In this paper the arbitrary difference and precise integration are used to solve seismic wave equation, which means difference scheme for space domain and analytic integration for time domain. Both the principle and algorithm of this method are introduced in the paper. Based on the theory, the numerical examples prove that this hybrid method can lead to higher accuracy than the traditional finite difference method and the solution is very close to the exact one. Also the seismic modeling examples show the good performance of this method even in the case of complex surface conditions and complicated structures.
基金National Key Research and Development Program of China under Grant No.2016YFC0701106Natural Sciences and Engineering Research Council of Canada via Discovery under Grant No.NSERC RGPIN-2017-05556 Li
文摘The nonlinear finite element（FE） analysis has been widely used in the design and analysis of structural or geotechnical systems.The response sensitivities（or gradients） to the model parameters are of significant importance in these realistic engineering problems.However the sensitivity calculation has lagged behind,leaving a gap between advanced FE response analysis and other research hotspots using the response gradient.The response sensitivity analysis is crucial for any gradient-based algorithms,such as reliability analysis,system identification and structural optimization.Among various sensitivity analysis methods,the direct differential method（DDM） has advantages of computing efficiency and accuracy,providing an ideal tool for the response gradient calculation.This paper extended the DDM framework to realistic complicated soil-foundation-structure interaction（SFSI） models by developing the response gradients for various constraints,element and materials involved.The enhanced framework is applied to three-dimensional SFSI system prototypes for a pilesupported bridge pier and a pile-supported reinforced concrete building frame structure,subjected to earthquake loading conditions.The DDM results are verified by forward finite difference method（FFD）.The relative importance（RI） of the various material parameters on the responses of SFSI system are investigated based on the DDM response sensitivity results.The FFD converges asymptotically toward the DDM results,demonstrating the advantages of DDM（e.g.,accurate,efficient,insensitive to numerical noise）.Furthermore,the RI and effects of the model parameters of structure,foundation and soil materials on the responses of SFSI systems are investigated by taking advantage of the sensitivity analysis results.The extension of DDM to SFSI systems greatly broaden the application areas of the d gradient-based algorithms,e.g.FE model updating and nonlinear system identification of complicated SFSI systems.
基金Projects(51308273,41372307,41272326) supported by the National Natural Science Foundation of ChinaProjects(2010(A)06-b) supported by Science and Technology Fund of Yunan Provincial Communication Department,China
文摘Based on some assumptions, the dynamic analysis model of anchorage system is established. The dynamic governing equation is expressed as finite difference format and programmed by using MATLAB language. Compared with theoretical method, the finite difference method has been verified to be feasible by a case study. It is found that under seismic loading, the dynamic response of anchorage system is synchronously fluctuated with the seismic vibration. The change of displacement amplitude of material points is slight, and comparatively speaking, the displacement amplitude of the outside point is a little larger than that of the inside point, which shows amplification effect of surface. While the axial force amplitude transforms considerably from the inside to the outside. It increases first and reaches the peak value in the intersection between the anchoring section and free section, then decreases slowly in the free section. When considering damping effect of anchorage system, the finite difference method can reflect the time attenuation characteristic better, and the calculating result would be safer and more reasonable than the dynamic steady-state theoretical method. What is more, the finite difference method can be applied to the dynamic response analysis of harmonic and seismic random vibration for all kinds of anchor, and hence has a broad application prospect.
基金supported by the National Natural Science Foundation of China(Nos.11171193 and11371229)the Natural Science Foundation of Shandong Province(No.ZR2014AM033)the Science and Technology Development Project of Shandong Province(No.2012GGB01198)
文摘An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.
文摘An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite elementdiscrete model is formed by using the artificial boundary and finite element method, and the dynamic equationsof local nodes in the discrete model are obtained according to the theory of the special finite element method similar to the finite difference method, and then the explicit step-by-step integration formulas are presented by usingthe explicit difference method for solving the visco-elastic dynamic equation and Generalized Multi-transmittingBoundary. The method has the advantages of saving computing time and computer memory space, and it is suitable for any case of topography and has high computing accuracy and good computing stability.
