Identification of Pipeline Inner Wall Geometry Based on the POD⁃RBF Method北大核心CSCD

Based on the proper orthogonal decomposition⁃radial basis function (POD⁃RBF), a geometric identification method for pipeline inner wall was proposed to solve the internal corrosion detection problem of natural gas and oil pipelines. In view of the static magnetic field, the simplified finite element model for the pipelines was established, and the variable⁃geometry sample library was constructed, to realize the response prediction of arbitrary geometry by the POD⁃RBF. The proposed method achieves reduced⁃order analysis and avoids repeated solution of the stiffness matrix due to the geometrical change during the identification process. Hence, it can significantly improve the computation efficiency. Finally, the grey wolf optimization (GWO) algorithm was used to optimize the objective function and avoid the calculation of the sensitivity in the process of geometry change. The numerical examples show that, the proposed method has high efficiency and accuracy in the geometric identification of the pipeline inner wall, with good stability even under introduced noises. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Wavelet Collocation Methods for Viscosity Solutions to Swing Options in Natural Gas Storage

This paper presents the wavelet collocation methods for the numerical ap- proximation of swing options for natural gas storage in a mean reverting market. The model is characterized by the Hamilton-Jacobi-Bellman （HJB） equations which only have the viscosity solution due to the irregularity of the swing option. The differential operator is formulated exactly and efficiently in the second generation interpolating wavelet setting. The convergence and stability of the numerical scheme are studied in the framework of viscosity solution theory. Numerical experiments demonstrate the accuracy and computational efficiency of the methods.     

Elastic Analysis of Anisotropic Rotating Sandwich Circular Ring With a Functionally Graded Transition Region北大核心CSCD

The elastic analysis of anisotropic rotating sandwich ring with a functionally graded transition region was carried out. Like the shell sandwich structure in nature, the ring is composed of 3 well⁃bonded regions, of which the inner and outer regions are made of homogeneous anisotropic materials, and the intermediate transi⁃ tion region is made of a material with arbitrary⁃gradient properties along the radial direction. Based on the boundary conditions and the continuity conditions at the interface, the 2nd Fredholm integral equation for the radial stress was obtained with the integral equation method, then the stress and displacement fields of the sandwich ring structure were obtained through numerical solution. The distributions of the stress and displace⁃ ment fields in the sandwich ring structure were given. Different gradient changes encountered in engineering practice can be solved only through substitution of the corresponding function model. The effectiveness and ac⁃ curacy of the integral equation method were verified through comparison of the numerical solutions with the ex⁃ act ones for a special power function gradient variation form. The more general Voigt function model was adopt⁃ ed for the intermediate transition region, and the influences of the anisotropy degree, the gradient parameter, and the thickness on the stress and displacement fields were analyzed. The proposed Fredholm integral equation method provides a powerful tool for the optimal design of anisotropic functionally graded materials and sand⁃ wich ring structures. The numerical results make a theoretical guidance for the safety design of anisotropic functionally graded sandwich ring structures. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

The Mindlin-Medick Plate Theory and Its Application Under Flexoelectricity and Temperature Effects北大核心CSCD

Based on the Hamiltonian variational principle, the 2D field equations and boundary conditions for flexoelectricity were derived, and the corresponding governing equations were obtained through substitution of the constitutive relation and geometric equations into the field equation. The in⁃plane tensile deformation, thick⁃ ness⁃stretch deformation, symmetric thickness⁃shear deformation, and their coupled flexoelectric polarization of flexoelectric nanoplates caused by inhomogeneous temperature changes, were studied. The displacement fields and electric potential fields were solved with the double Fourier series method. The results demonstrate that, all fields are sensitive to the temperature load, which raises the prospect of controlling the mechanical and electrical behaviors of flexoelectric nanoplates by means of the temperature field. The effects of the thermal field and mechanical field on the displacement field were compared and examined. The work extends the Mind⁃ lin⁃Medick plate structure analysis theory in view of the flexoelectric and temperature effects, and provides a reference for the structural design of micro⁃ and nano⁃scale devices. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Recent progresses in studies on wave-current loads on foundation structure with piles and slab?

The foundation structure with piles and slab is widely used in o?shore wind farm construction in shallow water. Experimental studies on the hydrodynamic loads acting on the piles and slab under irregular waves and currents are summarized with discussion on the e?ects of pile grouping on the wave forces and wave impact loads on the slab locating near the free surface. By applying the theoretical solution of the wave di?racted by the slab and using the Morison equation to evaluate the wave force on the piles, the e?ects of the slab on the wave forces acting on the piles are analyzed. Based on the Reynolds-averaged Navier-Stokes (RANS) equations and the volume of ?uid (VOF) method, a numerical wave basin is developed to simulate the wave-structure interaction. The computed maximum wave force on the foundation structure with piles and slab agrees well with the measured data. The violent deformation, breaking, and run-up of the wave around the structure are presented and discussed. Further work on the turbulent ?ow structures and large deformation of the free surface due to interaction of the waves and foundation structures of o?shore wind farms needs more e?cient approaches for evaluating hydrodynamic loads under the e?ects of nonlinear waves and currents.     

Integral formulas and the Ohsawa-Takegoshi extension theorem

We construct a semiexplicit integral representation of the canonical solution to the (?)-equation with respect to a plurisubharmonic weight function in a pseudoconvex domain. The construction is based on a construction related to the Ohsawa-Takegoshi extension theorem combined with a method to construct weighted integral representations due to M. Andersson.     

A numerical algorithm for determination of a control parameter in two-dimensional parabolic inverse problems

Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown control parameter and unknown solution of two-dimensional parabolic inverse problem with overspecialization at a point in the spatial domain. In this approach, a compact fourth-order scheme is used to discretize spatial derivatives of equation and reduces the problem to a system of ordinary differential equations(ODEs).Then we apply a fourth order boundary value method to the solution of resulting system of ODEs. So the proposed method has fourth order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes in the literature.Also we will investigate the effect of noise in data on the approximate solutions.     

关于非定常不可压Navier-Stokes方程的时间高精度隐式差分方法

The incompressible Navier-Stokes equations,upon spatial discretization,become a system of differential algebraic equations,formally of index2.But due to the special forms of the discrete gradient and disrete divergence,its index can be regarded as 1.Thus,in this paper,a systematic approach following the ODE theory and methods is presented for the construction of high-order time-accurate implicit schemes for the incompressible Navier-Stokes equations,with projection methods for efficiency of numerical solution.The 3rd order 3-step BDF with componentconsistent pressure-correction projection method is a first attempt in this direction;the related iterative solution of the auxiliary velocyty,the boundary conditions and the stability of the algorithm are discussed.Results of numerical tests on the incompressible Navier-Stokes equations with an exact solution are presented,confirming the accureacy,stability and component-consistency of the proposed method.     

Analytic and Experimental Studies of the Errors in Numerical Methods for the Valuation of Options

The value of a European option satisfies the Black-Scholes equation with appropriately specified final and boundary conditions.We transform the problem to an initial boundary value problem in dimensionless form.There are two parameters in the coefficients of the resulting linear parabolic partial differential equation.For a range of values of these parameters,the solution of the problem has a boundary or an initial layer.The initial function has a discontinuity in the first-order derivative,which leads to the appearance of an interior layer.We construct analytically the asymptotic solution of the equation in a finite domain.Based on the asymptotic solution we can determine the size of the artificial boundary such that the required solution in a finite domain in x and at the final time is not affected by the boundary.Also,we study computationally the behaviour in the maximum norm of the errors in numerical solutions in cases such that one of the parameters varies from finite (or pretty large) to small values,while the other parameter is fixed and takes either finite (or pretty large) or small values. Crank-Nicolson explicit and implicit schemes using centered or upwind approximations to the derivative are studied.We present numerical computations,which determine experimentally the parameter-uniform rates of convergence.We note that this rate is rather weak,due probably to mixed sources of error such as initial and boundary layers and the discontinuity in the derivative of the solution.     

A FAST AND HIGH ACCURACY NUMERICAL SIMULATION FOR A FRACTIONAL BLACK-SCHOLES MODEL ON TWO ASSETS

In this paper, a two dimensional(2D) fractional Black-Scholes(FBS) model on two assets following independent geometric Lévy processes is solved numerically. A high order convergent implicit difference scheme is constructed and detailed numerical analysis is established. The fractional derivative is a quasidifferential operator, whose nonlocal nature yields a dense lower Hessenberg block coefficient matrix. In order to speed up calculation and save storage space, a fast bi-conjugate gradient stabilized(FBi-CGSTAB) method is proposed to solve the resultant linear system. Finally, one example with a known exact solution is provided to assess the effectiveness and efficiency of the presented fast numerical technique. The pricing of a European Call-on-Min option is showed in the other example, in which the influence of fractional derivative order and volatility on the 2D FBS model is revealed by comparing with the classical 2D B-S model.     

Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays北大核心CSCD

The stability of traveling wave solutions of the reaction diffusion model is a very important research topic. The globally nonlinear stability of traveling wavefronts for a discrete cooperative Lotka-Volterra system with delays was studied. More precisely, for the initial perturbation decaying exponentially to the traveling wavefronts with a relatively large speed at infinity, but arbitrarily large speeds in other positions, by means of the L2⁃ weighted energy method, the comparison principle and the squeezing technique, such traveling wavefronts were obtained and proved to be of exponentially asymptotic stability. Moreover, the problem of establishing the energy estimates was solved under the actions of the discrete dispersal operator and the time delays. In short, the extension of the weighted energy method to discrete systems with delays, enriches the relative research. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition

We consider the numerical solution for the Helmholtz equation in R~2 with mixed boundary conditions.The solvability of this mixed boundary value problem is estab- lished by the boundary integral equation method.Based on the Green formula,we express the solution in terms of the boundary data.The key to the numerical real- ization of this method is the computation of weakly singular integrals.Numerical performances show the validity and feasibility of our method.The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

Weighted Profile Least Squares Estimation for a Panel Data Varying-Coefficient Partially Linear Model

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model （due to Baltagi 1995） to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator （WPLSE） and a weighted local polynomial estimator （WLPE） for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator （PLSE）, and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator （LPE）. The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll （2000） and Lin and Carroll （2000）, ignoring the correlation structure entirely and ＂pretending＂ that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups illustrate the finite sample performances of the Some simulation studies are conducted to proposed procedures.     

SUPERCONVERGENCE OF DG METHOD FOR ONE-DIMENSIONAL SINGULARLY PERTURBED PROBLEMS

The convergence and superconvergence properties of the discontinuous Galerkin （DG） method for a singularly perturbed model problem in one-dimensional setting are studied. By applying the DG method with appropriately chosen numerical traces, the existence and uniqueness of the DG solution, the optimal order L2 error bounds, and 2p＋ 1-order superconvergence of the numerical traces are established. The numerical results indicate that the DG method does not produce any oscillation even under the uniform mesh. Numerical experiments demonstrate that, under the uniform mesh, it seems impossible to obtain the uniform superconvergence of the numerical traces. Nevertheless, thanks to the implementation of the so-called Shishkin-type mesh, the uniform 2p ＋ 1-order superconvergence is observed numerically.     

The Brio System with Initial Conditions Involving Dirac Masses: A Result Afforded by a Distributional Product

The Brio system is a 2 × 2 fully nonlinear system of conservation laws which arises as a simplified model in the study of plasmas. The present paper offers explicit solutions to this system subjected to initial conditions containing Dirac masses. The concept of a solution emerges within the framework of a distributional product and represents a consistent extension of the concept of a classical solution. Among other features, the result shows that the space of measures is not sufficient to contain all solutions of this problem.     

THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution.It is of great value in rational evaluation of prospecting and exploiting oil-gas resources.The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values.The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set.Some techniques,such as change of variables,calculus of variations, multiplicative commutation rule of difference operators,decomposition of high order difference operators and prior estimates,are adopted.The estimates in l~2 norm are derived to determine the error in the approximate solution.This method was already applied to the numerical simulation of migration-accumulation of oil resources.     

Periodic Solutions of a Model of Mitosis in Prog Eggs

In this paper,we discuss a simplified model of mitosis in frog eggs proposed by M.T. Borisuk and J.J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property.     

A Penalty Approach for Generalized Nash Equilibrium Problem

The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP),in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players.This problem has been used to model various problems in applications.However,the convergent solution algorithms are extremely scare in the literature.In this paper,we present an incremental penalty method for the GNEP,and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs.We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.     

A PARAMETER-UNIFORM TAILORED FINITE POINT METHOD FOR SINGULARLY PERTURBED LINEAR ODE SYSTEMS＊

In scientific applications from plasma to chemical kinetics, a wide range of temporal scales can present in a system of differential equations. A major difficulty is encountered due to the stiffness of the system and it is required to develop fast numerical schemes that are able to access previously unattainable parameter regimes. In this work, we consider an initial-final value problem for a multi-scale singularly perturbed system of linear ordi- nary differential equations with discontinuous coefficients. We construct a tailored finite point method, which yields approximate solutions that converge in the maximum norm, uniformly with respect to the singular perturbation parameters, to the exact solution. A parameter-uniform error estimate in the maximum norm is also proved. The results of numerical experiments, that support the theoretical results, are reported.