In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)deriva...In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.展开更多
This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the acc...This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.展开更多
This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed...This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interlace method（IIM） divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two that the domain decomposition technique can placed around the discontinuity. The present reached, in spite of the enlarged computational discontinuous problems are tested to verify the present method. The results show reduce the error of the spectral IIM, especially when more collocation points are method is t：avorable for the reason that the same level of the accuracy can be domain.展开更多
Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic ...Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.展开更多
As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initiall...As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.展开更多
Results on the composite generalized Laguerre-Legendre interpolation in unbounded domains are established. As an application,a composite Laguerre-Legendre pseudospectral scheme is presented for nonlinear Fokker-Planck...Results on the composite generalized Laguerre-Legendre interpolation in unbounded domains are established. As an application,a composite Laguerre-Legendre pseudospectral scheme is presented for nonlinear Fokker-Planck equations on the whole line. The convergence and the stability of the proposed scheme are proved. Numerical results show the efficiency of the scheme and conform well to theoretical analysis.展开更多
Accurate determination of rockhead is crucial for underground construction.Traditionally,borehole data are mainly used for this purpose.However,borehole drilling is costly,time-consuming,and sparsely distributed.Non-i...Accurate determination of rockhead is crucial for underground construction.Traditionally,borehole data are mainly used for this purpose.However,borehole drilling is costly,time-consuming,and sparsely distributed.Non-invasive geophysical methods,particularly those using passive seismic surface waves,have emerged as viable alternatives for geological profiling and rockhead detection.This study proposes three interpretation methods for rockhead determination using passive seismic surface wave data from Microtremor Array Measurement(MAM)and Horizontal-to-Vertical Spectral Ratio(HVSR)tests.These are:(1)the Wavelength-Normalized phase velocity(WN)method in which a nonlinear relationship between rockhead depth and wavelength is established;(2)the Statistically Determined-shear wave velocity(SD-V_(s))method in which the representative V_(s) value for rockhead is automatically determined using a statistical method;and(3)the empirical HVSR method in which the rockhead is determined by interpreting resonant frequencies using a reliably calibrated empirical equation.These methods were implemented to determine rockhead depths at 28 locations across two distinct geological formations in Singapore,and the results were evaluated using borehole data.The WN method can determine rockhead depths accurately and reliably with minimal absolute errors(average RMSE=3.11 m),demonstrating robust performance across both geological formations.Its advantage lies in interpreting dispersion curves alone,without the need for the inversion process.The SD-V_(s) method is practical in engineering practice owing to its simplicity.The empirical HVSR method reasonably determines rockhead depths with moderate accuracy,benefiting from a reliably calibrated empirical equation.展开更多
This study presents a new boundary element method(BEM)framework for the numerical solution of general time-dependent or transient problems.By reformulating the time derivative as a domain integral,the framework effect...This study presents a new boundary element method(BEM)framework for the numerical solution of general time-dependent or transient problems.By reformulating the time derivative as a domain integral,the framework effectively decouples the treatment of spatial and temporal variables,allowing for the independent application of specialized discretization methods.For the temporal domain,we introduce an innovative time-spectral integration technique,which is based on Gaussian-quadrature-based orthogonal polynomial expansions.This method not only achieves arbitrary orders of accuracy but also significantly enhances computational efficiency and stability,particularly for simulations involving rapid transients or long-time dynamic simulations.The domain integrals in the spatial domain are calculated using the scaled coordinate transformation BEM(SCT-BEM),a mathematically rigorous technique that converts domain integrals into equivalent boundary integrals,preserving the boundary-only discretization advantage inherent in BEM.Numerical experiments on transient heat conduction and dynamic wave propagation further demonstrate the framework’s performance and capabilities.These experiments show that the proposed framework outperforms traditional time-stepping BEM methods,particularly in terms of stability,convergence rates,and computational cost,making it a highly promising tool for practical engineering applications.展开更多
We analyzed the infrared 0R）-near infrared （NIR） 2D correlation spectra of drugs perturbed by temperature. By identification of functional groups by IR spectrum and by the correlation analysis of IR-NIR spectrum, w...We analyzed the infrared 0R）-near infrared （NIR） 2D correlation spectra of drugs perturbed by temperature. By identification of functional groups by IR spectrum and by the correlation analysis of IR-NIR spectrum, we identified the characteristic spectral bands that were closely related to the structure of a drug substance of interest. These characteristic spectral bands were relatively less interfered by other ingredients for analysis by the NIR correlation coefficient method. With these characteristic spectral bands, the accuracy of screening illegally added Sildenafil citrate, Tadalafil and Metforrnin hydrochloride in Chinese patent drugs and healthcare products reached about 90%, which met the requirements of rapid screening.展开更多
The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical ...The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical profiles within the basin are used to analyze the generation and propagation of surface waves and their relation to the basin structures in both the time and frequency domain.The amplification effects are analyzed by the distribution of peak ground velocity(PGV)and cumulative kinetic energy(Ek) in the basin.The results show that in the 3D basin,the excitation of the fundamental and higher surface wave modes are similar to that of the 2D model.Small bowls in the basin have great influence on the amplification and distribution of strong ground motion,due to their lateral resonances when the wavelengths of the lateral surface waves are comparable to the size of the bowls.Obvious basin edge effects can be seen at the basin edge closer to the source for constructive interference between direct body waves and the basin-induced surface waves.The Ek distribution maps show very large values in small bowls and some corners in the basin due to the interference of waves propagating in different directions.A high impedance contrast model can excite more surface wave modes,resulting in longer shaking durations as well as more complex seismograms and PGV and Ek distributions.展开更多
In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident bou...In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.展开更多
We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorou...We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L^∞ norm and weighted L^2-norm. The numerical examples are given to illustrate the theoretical results.展开更多
The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a m...The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a method to calculate the Q-factor based on the prestack Q-factor inversion and the generalized S-transform. The proposed method specifies a standard primary wavelet and calculates the cumulative Q-factors; then, it finds the interlaminar Q-factors using the relation between Q and offset(QVO) and the Dix formula. The proposed method is alternative to methods that calculate interlaminar Q-factors after horizon picking. Because the frequency spectrum of each horizon can be extracted continuously on a 2D time–frequency spectrum, the method is called the continuous spectral ratio slope(CSRS) method. Compared with the other Q-inversion methods, the method offers nearly effortless computations and stability, and has mathematical and physical significance. We use numerical modeling to verify the feasibility of the method and apply it to real data from an oilfield in Ahdeb, Iraq. The results suggest that the resolution and spatial stability of the Q-profile are optimal and contain abundant interlaminar information that is extremely helpful in making lithology and fluid predictions.展开更多
A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite differen...A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.展开更多
SiO2-CaO-MgO glass and glass-ceramic powder doped with Nd3＋ were synthesized with sol-gel method. Tetraethylorthosilicate （TEOS）, Ca（NO3）2？4H2O, Mg（NO3）2？6H2O, Nd（NO3）3？6H2O, ethanol, distilled water, and ...SiO2-CaO-MgO glass and glass-ceramic powder doped with Nd3＋ were synthesized with sol-gel method. Tetraethylorthosilicate （TEOS）, Ca（NO3）2？4H2O, Mg（NO3）2？6H2O, Nd（NO3）3？6H2O, ethanol, distilled water, and HNO3 were used as starting materials. The synthesized powder’s properties were examined with simultaneous thermal analysis （STA）, X-ray diffraction （XRD）, photoluminescence （PL） and scanning electron microscopy （SEM） analysis. The STA curves showed that the softening point and crystallization temperatures were shifted to higher temperatures with increasing dopant content. Regarding XRD patterns of glass samples, Nd was found to act as an intermediate oxide in glass matrix. The XRD patterns of glass-ceramic samples indicated that bredigite and akermanite crystallized in the glass matrix after heat treating at 900 oC. The fluorescence spectra showed that glass-ceramics emitted much stronger irradiation than glasses with the same dopant content. The SEM images illustrated uniform and homogeneous distribution of applied oxides in glass and glass-ceramic compositions.展开更多
In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means t...In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.展开更多
Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process an...Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation （NLS）. However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral （HOS） method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer＇s formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details.展开更多
In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation ...In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memorysaving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced;therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.展开更多
Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the ...Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to展开更多
基金extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/174/46.
文摘In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.
基金supported by the Advance Research Project of Civil Aerospace Technology(Grant No.D020304)National Nat-ural Science Foundation of China(Grant Nos.52205257 and U22B2083).
文摘This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.
基金National Natural Science Foundation of China(51076006)
文摘This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interlace method（IIM） divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two that the domain decomposition technique can placed around the discontinuity. The present reached, in spite of the enlarged computational discontinuous problems are tested to verify the present method. The results show reduce the error of the spectral IIM, especially when more collocation points are method is t：avorable for the reason that the same level of the accuracy can be domain.
基金National Key Research and Development Program of China under Grant No.2023YFE0102900National Natural Science Foundation of China under Grant Nos.52378506 and 52208164。
文摘Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.
基金supported by the National Natural Science Foundation of China(No.72071202)the Key Laboratory of Mathematics and Engineering Applications,Ministry of Education。
文摘As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.
文摘Results on the composite generalized Laguerre-Legendre interpolation in unbounded domains are established. As an application,a composite Laguerre-Legendre pseudospectral scheme is presented for nonlinear Fokker-Planck equations on the whole line. The convergence and the stability of the proposed scheme are proved. Numerical results show the efficiency of the scheme and conform well to theoretical analysis.
基金partially supported by the Singapore Ministry of National Development and the National Research Foundation,Prime Minister’s Office,Singapore,under the Land and Liveability National Innovation Challenge(L2 NIC)Research Program(Grant No.L2NICCFP2-2015-1)by the National Research Foundation(NRF)of Singapore,under the Virtual Singapore program(Grant No.NRF2019VSG-GMS-001).
文摘Accurate determination of rockhead is crucial for underground construction.Traditionally,borehole data are mainly used for this purpose.However,borehole drilling is costly,time-consuming,and sparsely distributed.Non-invasive geophysical methods,particularly those using passive seismic surface waves,have emerged as viable alternatives for geological profiling and rockhead detection.This study proposes three interpretation methods for rockhead determination using passive seismic surface wave data from Microtremor Array Measurement(MAM)and Horizontal-to-Vertical Spectral Ratio(HVSR)tests.These are:(1)the Wavelength-Normalized phase velocity(WN)method in which a nonlinear relationship between rockhead depth and wavelength is established;(2)the Statistically Determined-shear wave velocity(SD-V_(s))method in which the representative V_(s) value for rockhead is automatically determined using a statistical method;and(3)the empirical HVSR method in which the rockhead is determined by interpreting resonant frequencies using a reliably calibrated empirical equation.These methods were implemented to determine rockhead depths at 28 locations across two distinct geological formations in Singapore,and the results were evaluated using borehole data.The WN method can determine rockhead depths accurately and reliably with minimal absolute errors(average RMSE=3.11 m),demonstrating robust performance across both geological formations.Its advantage lies in interpreting dispersion curves alone,without the need for the inversion process.The SD-V_(s) method is practical in engineering practice owing to its simplicity.The empirical HVSR method reasonably determines rockhead depths with moderate accuracy,benefiting from a reliably calibrated empirical equation.
基金supported by the National Natural Science Foundation of China(Grant Nos.12372199,12422207,and W2431010)the Natural Science Foundation of Shandong Province of China(Grant No.ZR2021JQ02)the Ningbo Municipal Excellence Research Program(Zhejiang Province,China).
文摘This study presents a new boundary element method(BEM)framework for the numerical solution of general time-dependent or transient problems.By reformulating the time derivative as a domain integral,the framework effectively decouples the treatment of spatial and temporal variables,allowing for the independent application of specialized discretization methods.For the temporal domain,we introduce an innovative time-spectral integration technique,which is based on Gaussian-quadrature-based orthogonal polynomial expansions.This method not only achieves arbitrary orders of accuracy but also significantly enhances computational efficiency and stability,particularly for simulations involving rapid transients or long-time dynamic simulations.The domain integrals in the spatial domain are calculated using the scaled coordinate transformation BEM(SCT-BEM),a mathematically rigorous technique that converts domain integrals into equivalent boundary integrals,preserving the boundary-only discretization advantage inherent in BEM.Numerical experiments on transient heat conduction and dynamic wave propagation further demonstrate the framework’s performance and capabilities.These experiments show that the proposed framework outperforms traditional time-stepping BEM methods,particularly in terms of stability,convergence rates,and computational cost,making it a highly promising tool for practical engineering applications.
基金National Key Technology R & D Program-On-site Rapid Identification of Drug Research Project (Grant No. 2008BAI55B06)
文摘We analyzed the infrared 0R）-near infrared （NIR） 2D correlation spectra of drugs perturbed by temperature. By identification of functional groups by IR spectrum and by the correlation analysis of IR-NIR spectrum, we identified the characteristic spectral bands that were closely related to the structure of a drug substance of interest. These characteristic spectral bands were relatively less interfered by other ingredients for analysis by the NIR correlation coefficient method. With these characteristic spectral bands, the accuracy of screening illegally added Sildenafil citrate, Tadalafil and Metforrnin hydrochloride in Chinese patent drugs and healthcare products reached about 90%, which met the requirements of rapid screening.
基金National Natural Science Foundation of China under Grant No.51078337,No.51108431 and No.91315301
文摘The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical profiles within the basin are used to analyze the generation and propagation of surface waves and their relation to the basin structures in both the time and frequency domain.The amplification effects are analyzed by the distribution of peak ground velocity(PGV)and cumulative kinetic energy(Ek) in the basin.The results show that in the 3D basin,the excitation of the fundamental and higher surface wave modes are similar to that of the 2D model.Small bowls in the basin have great influence on the amplification and distribution of strong ground motion,due to their lateral resonances when the wavelengths of the lateral surface waves are comparable to the size of the bowls.Obvious basin edge effects can be seen at the basin edge closer to the source for constructive interference between direct body waves and the basin-induced surface waves.The Ek distribution maps show very large values in small bowls and some corners in the basin due to the interference of waves propagating in different directions.A high impedance contrast model can excite more surface wave modes,resulting in longer shaking durations as well as more complex seismograms and PGV and Ek distributions.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51309050 and 51221961)the National Basic Research Program of China(973 Program,Grant Nos.2013CB036101 and 2011CB013703)
文摘In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.
基金supported by NSFC Project(11301446,11271145)China Postdoctoral Science Foundation Grant(2013M531789)+3 种基金Specialized Research Fund for the Doctoral Program of Higher Education(2011440711009)Program for Changjiang Scholars and Innovative Research Team in University(IRT1179)Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(2013RS4057)the Research Foundation of Hunan Provincial Education Department(13B116)
文摘We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L^∞ norm and weighted L^2-norm. The numerical examples are given to illustrate the theoretical results.
基金supported by The National Key Research and Development Program Plane(No.2017YFC0601505)National Natural Science Foundation(No.41672325)Science&Technology Department of Sichuan Province Technology Project(No.2017GZ0393)
文摘The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a method to calculate the Q-factor based on the prestack Q-factor inversion and the generalized S-transform. The proposed method specifies a standard primary wavelet and calculates the cumulative Q-factors; then, it finds the interlaminar Q-factors using the relation between Q and offset(QVO) and the Dix formula. The proposed method is alternative to methods that calculate interlaminar Q-factors after horizon picking. Because the frequency spectrum of each horizon can be extracted continuously on a 2D time–frequency spectrum, the method is called the continuous spectral ratio slope(CSRS) method. Compared with the other Q-inversion methods, the method offers nearly effortless computations and stability, and has mathematical and physical significance. We use numerical modeling to verify the feasibility of the method and apply it to real data from an oilfield in Ahdeb, Iraq. The results suggest that the resolution and spatial stability of the Q-profile are optimal and contain abundant interlaminar information that is extremely helpful in making lithology and fluid predictions.
基金the National Natural Science Foundation of China
文摘A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.
基金supported by the Iran Nanotechnology Initiative Council(INIC)
文摘SiO2-CaO-MgO glass and glass-ceramic powder doped with Nd3＋ were synthesized with sol-gel method. Tetraethylorthosilicate （TEOS）, Ca（NO3）2？4H2O, Mg（NO3）2？6H2O, Nd（NO3）3？6H2O, ethanol, distilled water, and HNO3 were used as starting materials. The synthesized powder’s properties were examined with simultaneous thermal analysis （STA）, X-ray diffraction （XRD）, photoluminescence （PL） and scanning electron microscopy （SEM） analysis. The STA curves showed that the softening point and crystallization temperatures were shifted to higher temperatures with increasing dopant content. Regarding XRD patterns of glass samples, Nd was found to act as an intermediate oxide in glass matrix. The XRD patterns of glass-ceramic samples indicated that bredigite and akermanite crystallized in the glass matrix after heat treating at 900 oC. The fluorescence spectra showed that glass-ceramics emitted much stronger irradiation than glasses with the same dopant content. The SEM images illustrated uniform and homogeneous distribution of applied oxides in glass and glass-ceramic compositions.
基金supported by the National Key Technology R&D Program (Grant 2011BAJ02B01-02)the National Natural Science Foundation of China (Grant 11602065)
文摘In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.
基金National Key Basic Research Program of China(973 Program)under Grant No.2013CB036300Ministry of Transport Application Foundation Research Project under Grant No.2013319822070+1 种基金the National Natural Science Foundation of China under Grant Nos.91215302,51222809 and 51178353Program for New Century Excellent Talents in University
基金supported by the National Natural Science Foundation of China (Grant No. 41106001)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100094110016)+1 种基金the Special Research Funding of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (Grant No. 2009585812)the Priority Academic Program Development of Jiangsu Higher Education Institutions (Coastal Development and Conservancy)
文摘Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation （NLS）. However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral （HOS） method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer＇s formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details.
基金financial support for this work contributed by the National Key Research and Development Program of China (grant numbers 2016YFC0600101 and 2016YFC 0600201)the National Natural Science Foundation of China (grant numbers 41874065, 41604076, 41674102, 41674095, 41522401, 41574082, and 41774097)
文摘In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memorysaving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced;therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.
文摘Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to
