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The interpolating boundary element-free method (IBEFM) is a direct solution method of the meshless boundary integral equation method, which has high efficiency and accuracy. The IBEFM is developed based on the interpolating moving least-squares (IMLS) method and the boundary integral equation method. Since the shape function of the IMLS method satisfies the interpolation characteristics, the IBEFM can directly and accurately impose the essential boundary conditions, which overcomes the shortcomings of the original boundary element-free method in enforcing the essential boundary approximately. This paper will study the error estimations of the IBEFM for two-dimensional potential problems and the relationship between the errors and the influence radius and the condition number of the coefficient matrix. Two numerical examples are presented to verify the correctness of the theoretical results in this paper.

This paper considers some multiscale radial basis function collocation methods for solving the two-dimensional Monge–Ampère equation with Dirichlet boundary. We discuss and study the performance of the three kinds of multiscale methods. The first method is the cascadic meshfree method, which was proposed by Liu and He (2013). The second method is the stationary multilevel method, which was proposed by Floater and Iske (1996), and is used to solve the fully nonlinear partial differential equation in the paper for the first time. The third is the hierarchical radial basis function method, which is constructed by employing successive refinement scattered data sets and scaled compactly supported radial basis functions with varying support radii. Compared with the first two methods, the hierarchical radial basis function method can not only solve the present problem on a single level with higher accuracy and lower computational cost but also produce highly sparse nonlinear discrete system. These observations are obtained by taking the direct approach of numerical experimentation.

During the construction of the tunnel, there may be water-bearing anomalous structures such as fault fracture zone. In order to ensure the safety of the tunnel, it is necessary to carry out advanced tunnel detection. The traditional linear inversion method is highly dependent on the initial model in the tunnel resistivity inversion, which makes the inversion results falling into the local optimal optimum rather than the global one. Therefore, an inversion method for tunnel resistivity advanced detection based on ant colony algorithm is proposed in this paper. In order to improve the accuracy of tunnel advanced detection of deep anomalous bodies, an ant colony optimization (ACO) inversion is used by integrating depth weighting into the inversion function. At the same time, in view of the high efficiency and low cost of one-dimension inversion and the advantages of L1 norm in boundary characterization, a one-dimensional ant colony algorithm is adopted in this paper. In order to evaluate the performance of the algorithm, two sets of numerical simulations were carried out. Finally, the application of the actual tunnel water-bearing anomalous structure was carried out in a real example to evaluate the application effect, and it was verified by excavation exposure.

Aiming at car design, a parametric design method is proposed in this paper. There are two contents in this method, a novel parametric surface, a shape-adjustable automobile styling template, and a design method of integrating the two contents. The surface termed extended SQ-Coons surface constructed in this paper has the advantage of being fine adjusted while always interpolating at the given boundary curves, which is suitable for its application in automobile modeling design. Matching with the surface, a car model template built by multiple quadrilateral surfaces is proposed. The car models built by the template could achieve the parametric adjustability of all modeling features on the premise of maintaining G 1 continuity between subsurfaces. Finally, after the integration of the surface and the template, a whole set of parametric automobile surface modeling design method is proposed. In this method, the overall shape of the car body is determined through multi angle hand drawing, and curve control points, segmentation parameters, and shape parameters are used to adjust the detail modeling. The final results show that the novel surface and template proposed could be used to parametrically establish the vehicle models of various shapes and improve the design efficiency in the conceptual design stage.

In mechanics, the solution of soil stresses and displacements field caused by shallow rectangular jacking pipe construction can be simplified as half-plane problem. Both the boundary conditions of the surface and the cavity boundary must be taken into account. It is the essential prerequisite for mechanical analysis of the pipe jacking with the complex variable theory that the mechanical boundary must be transformed from the half-plane with a rectangle cavity to the concentric ring. According to Riemann’s existence theorem and basic complex variable theory, a conformal mapping function is established. Both sides of boundary conditions equation are developed into Laurent series, and then the coefficients of complex stress function are solved by power series method. The derived solution is applied to an example and a comparison is made using FEM method to show the accuracy of the methods. The result shows the following: (1) the method presented in this paper is applicable to a shallow-buried rectangular tunnel; (2) the complex function method proposed in this paper is characterized by clear steps, fast convergence, and simple operation.

A shear flow motivated by relatively moving half-planes is theoretically studied in this paper. Either the mass influx or the mass efflux is allowed on the boundary. This flow is called the extended Stokes' problems. Traditionally, exact solutions to the Stokes' problems can be readily obtained by directly applying the integral transforms to the momentum equation and the associated boundary and initial conditions. However, it fails to solve the extended Stokes' problems by using the integral-transform method only. The reason for this difficulty is that the inverse transform cannot be reduced to a simpler form. To this end, several crucial mathematical techniques have to be involved together with the integral transforms to acquire the exact solutions. Moreover, new dimensionless parameters are defined to describe the flow phenomena more clearly. On the basis of the exact solutions derived in this paper, it is found that the mass influx on the boundary hastens the development of the flow, and the mass efflux retards the energy transferred from the plate to the far-field fluid.

An inverse problem for reconstructing arbitrary-shaped thin penetrable electromagnetic inclusions concealed in a homogeneous material is considered in this paper. For this purpose, the level-set evolution method is adopted. The topological derivative concept is incorporated in order to evaluate the evolution speed of the level-set functions. The results of the corresponding numerical simulations with and without noise are presented in this paper.

Thermally induced stress is an important scientific problem in engineering applications. In this paper, an accurate and efficient method for the two-dimensional quasi-static thermal elastic problem is established to explore the thermal stress problem. First, the compact quasi-static two-dimensional general solution is derived in terms of simple potential functions. The general solution is simple in form and can be derived for arbitrary boundary problems subjected to a line heat load. This is completely new to the literature. Second, Green’s function solutions of an infinite plane under the line pulse heat source based on the general solutions are presented to analyze the thermal stress field. Lastly, numerical results are taken into account to study the temperature and stress field induced by the dynamic heat source load. The corresponding analysis can constitute to reveal the mechanism of thermal elastic problems and provide some guidance for experiments or engineering structural design in the future work.

Of interest is a wave equation with memory-type boundary oscillations, in which the forced oscillations of the rod is given by a memory term at the boundary. We establish a new general decay rate to the system. And it possesses the character of damped oscillations and tends to a finite value for a large time. By assuming the resolvent kernel that is more general than those in previous papers, we establish a more general energy decay result. Hence the result improves earlier results in the literature.

In this paper, the finite-time bounded control problem for coupled parabolic PDE-ODE systems subject to time-varying boundary disturbances and to time-invariant boundary disturbances is considered. First, the concept of finite-time boundedness is extended to coupled parabolic PDE-ODE systems. A Neumann boundary feedback controller is then designed in terms of the state variables. By applying the Lyapunov-like functional method, sufficient conditions which ensure the finite-time boundedness of closed-loop systems in the presence of time-varying boundary disturbances and time-invariant boundary disturbances are provided, respectively. Finally, the issues regarding the finite-time boundedness of coupled parabolic PDE-ODE systems are converted into the feasibility of linear matrix inequalities (LMIs), and the effectiveness of the proposed results is validated with two numerical simulations.

In this paper, boundary element and augmented Lagrangian methods for Coulomb friction contact problems are presented. Based on the projection technique, both unilateral contact and Coulomb friction conditions are reformulated as fixed point problems. The original problem is deduced to a variational formulation with boundary integral operators. Then, we propose a new augmented Lagrangian method which can be dealt with the semismooth Newton method. Short theoretical results and the algorithm description are given. Numerical simulations show the performance of the method proposed.

Modeling plays an important role in engineering exploration. However, the traditional rectangular mesh cannot meet the requirement because the actual shape of the model may be very complex. Therefore, this paper chooses the Delaunay grid for modeling and applies this method to magnetic numerical simulation. At the same time, we make use of the advantages of the Delaunay grid and choose to use grid encryption technology in the boundary and complex area of the model. Then, the formula for calculating the magnetic anomaly of tetrahedron is deduced in detail, and the magnetic anomaly with surface fluctuation is calculated. For a synthetic data model, Delaunay grids with different densities are used to model and calculate surface anomalies. The two results are compared with the analytical solution of the model. The results show that the method has high accuracy. Then, the method is applied to the actual geological body modeling in the Jinchuan mining area. According to local needs, a three-dimensional model with inhomogeneous grid density is established and the surface magnetic field of the model is calculated. Finally, the simulation data are compared with the measured data. The results show that the Delaunay grid modeling method has strong applicability.

Boundary pixel blur and category imbalance are common problems that occur during semantic segmentation of urban remote sensing images. Inspired by DenseU-Net, this paper proposes a new end-to-end network—SiameseDenseU-Net. First, the network simultaneously uses both true orthophoto (TOP) images and their corresponding normalized digital surface model (nDSM) as the input of the network structure. The deep image features are extracted in parallel by downsampling blocks. Information such as shallow textures and high-level abstract semantic features are fused throughout the connected channels. The features extracted by the two parallel processing chains are then fused. Finally, a softmax layer is used to perform prediction to generate dense label maps. Experiments on the Vaihingen dataset show that SiameseDenseU-Net improves the F1-score by 8.2% and 7.63% compared with the Hourglass-ShapeNetwork (HSN) model and with the U-Net model. Regarding the boundary pixels, when using the same focus loss function based on median frequency balance weighting, compared with the original DenseU-Net, the small-target “car” category F1-score of SiameseDenseU-Net improved by 0.92%. The overall accuracy and the average F1-score also improved to varying degrees. The proposed SiameseDenseU-Net is better at identifying small-target categories and boundary pixels, and it is numerically and visually superior to the contrast model.

Adaptive wavelet collocation methods use wavelet transform and filtering to generate adaptive grids. However, if the boundary moves, the grid becomes aberrant. It baffles wavelet transform and makes the adaptive wavelet methods lose advantages on computational efficiency. This paper develops a series of methods or skills to effectively perform wavelet transform and to generate adaptive grids for one-dimensional movable boundary problems. The methods remain the original inner grid points and keep the grid in the original-nested structure, in order to remain scanty during the whole computing process. For boundary extending, the adaptive wavelet program begins to run on the very new grid beyond the original boundary once it reaches a nested structure, which is called the Intermittent Adaptive Method as a consequence. If the boundary extends tremendously, the new nested grids can be combined to a greater nested grid for further efficiency, which is named the Grid Combine Method. While for boundary contracting, a fictitious boundary is addressed to replace the original boundary that will recede, so wavelet transform can be successfully performed on the original nested grid. Finally, two numerical tests, local features moving and gas gun, were resolved and discussed to show the evolution process of the adaptive grids with the boundaries moving. For boundary contracting, the valid points decrease because the computation domain recedes; while for boundary extending, the valid point numbers vary between a range that almost remains unchanged.

In order to control pests and eventually maintain the number of pests below the economic threshold, in this paper, based on the nonsmooth dynamical system, a two-stage-structured pest control Filippov model is proposed. We take the total number of juvenile and adult pest population as the control index to determine whether or not to implement chemical control strategies. The sliding-mode domain and conditions for the existence of regular and virtual equilibria, pseudoequilibrium, boundary equilibria, and tangent points are given. Further, the sufficient condition of the locally asymptotic stability of pseudoequilibrium is obtained. By numerical simulations, the local bifurcations of the equilibria are discussed. Our results show that the total number of pest populations can be successfully controlled below the economic threshold by taking suitable threshold policy.

The concentric two-zone composite reservoir model is a boundary value problems (BVPs) of modified Bessel equations. In this paper, we propose a constructive method to solve the BVPs for the system of modified Bessel equations with Robin mixed outer boundary condition and apply it to solve a two-zone fractal composite reservoir seepage model with stress-sensitivity formation. By using Pedrosa variable substitution, regular perturbation technique, Laplace transform, and Stehfest numerical inversion technique, the unified expression for the solutions of the reservoir model with three outer boundary (infinite, impermeable, and constant pressure) conditions is constructed. Type curves of bottom-hole pressure and pressure derivative are drawn, and sensitivity analysis of reservoir parameters are carried out. In comparison with the traditional approach, the solutions of this model are simple and regular, with continued fraction form, the constructive method is efficient and easy to operate. The application of this method avoids the complicated and trivial derivative operation and the use of Cramer’s rule to solve the system of linear equations. It can help to better understand the relationship between the solutions of the reservoir model and the inner and outer boundary conditions. The constructive method can be applied not only to solve the fractal composite reservoir model but also to solve more general reservoir model, BVPs of fluid diffusion, heat conduction, and so on.

Localization is one of the essential problems in the Internet of Things (IoT) and other wireless sensor applications. Most traditional range-free localization algorithms ignore the anisotropy factors, which are frequently observed in wireless sensor networks (WSNs) and result in low positioning precision. To mitigate the impact of anisotropy on localization, this paper proposes an extended area multihop node localization method. The proposed method classifies and discusses the boundaries of the concave area within the communication range of the node and then uses the maximum split communication distance of the node to identify and mark the boundary of the concave area. When the shortest communication path between the nodes is affected by the concave area, the boundary of the concave area is expanded to obtain the new shortest communication path, and the node distance is obtained by comparing the changes in the communication path. After a large number of simulation tests, it is shown that the calculation accuracy of this scheme is better than that of similar modern mainstream localization algorithms.

In this paper, a fault identification method combining adaptive local iterative filtering and permutation entropy is proposed. The adaptive local iterative filtering can decompose the nonstationary signal into a finite number of stationary intrinsic mode functions. And the experiment gear fault data are decomposed into several intrinsic mode functions by this method. Then, using the permutation entropy to calculate each intrinsic mode function, it is found that the permutation entropy of the first several intrinsic mode functions can represent the characteristics of different fault types, and the permutation entropy of the intrinsic mode function corresponding to the rotating frequency signal of the gear system could be the boundary. Finally, the fault type of gear is identified by calculating the gray correlation degree of permutation entropy of essential mode function of vibration signal decomposition under different working conditions. The example analysis results show that the proposed method can be effectively applied to the fault diagnosis of the gear system.

This paper investigates the three-way clustering involving fuzzy covering, thresholds acquisition, and boundary region processing. First of all, a valid fuzzy covering of the universe is constructed on the basis of an appropriate fuzzy similarity relation, which helps capture the structural information and the internal connections of the dataset from the global perspective. Due to the advantages of valid fuzzy covering, we explore the valid fuzzy covering instead of the raw dataset for RFCM algorithm-based three-way clustering. Subsequently, from the perspective of semantic interpretation of balancing the uncertainty changes in fuzzy sets, a method of partition thresholds acquisition combining linear and nonlinear fuzzy entropy theory is proposed. Furthermore, boundary regions in three-way clustering correspond to the abstaining decisions and generate uncertain rules. In order to improve the classification accuracy, the k-nearest neighbor (kNN) algorithm is utilized to reduce the objects in the boundary regions. The experimental results show that the performance of the proposed three-way clustering based on fuzzy covering and kNN-FRFCM algorithm is better than the compared algorithms in most cases.

In this paper, a semianalytical solution for the in-plane vibration analysis of annular panel with arbitrary distribution of internal point constraints is established for the first time. In-plane dynamic behavior of such panel structure is described via energy principle. A modified version of Fourier series is constructed for the in-plane vibration displacement expansion supplemented with the boundary smoothed terms, and the arbitrarily concentrated constraint in each field point is described in conjunction with Dirac delta function. A standard matrix eigenvalue problem containing various in-plane modal information of such annular panel is derived and solved through Rayleigh–Ritz procedure. Several numerical examples are presented to demonstrate the correctness and effectiveness of the proposed model by comparing the results with those from other approaches. Three representative types of point constraints, including point, line, and area configurations, are considered by collection of point constraints, and it is shown that the current model can make an accurate and efficient modal parameter prediction for annular panel with such most general case of point constraints.

For affine switched systems, the existence of multiple equilibria is related to subsystems owing to the affine terms, which makes asymptotic and finite-time stability analysis nontrivial. In this paper, the problems of finite-time boundedness (FTB) analysis and stabilization are addressed for affine switched systems, and several definitions and sufficient conditions are proposed to study FTB and H∞ performance. At first, the definition of FTB for affine switched systems is improved concerning the affine terms and multiple equilibria. Based on the FTB definition, sufficient conditions ensuring finite-time boundedness for affine switched systems under a prespecified state boundary are given. Then the results are extended to solve H∞ finite-time boundedness problem, in which the H∞ controllers are designed to guarantee the finite-time boundedness of affine switched system with H∞ performance. In our investigation, average dwell-time approach is employed to study the time-dependent constrained switching case. Finally, several numerical examples are given to illustrate the effectiveness of the proposed results.

Based on Timoshenko’s beam theory, this paper adopts segmented strategy in establishing the governing equations of a multibeam system subjected to various boundary conditions, in which free, clamped, hinged, and elastic constraints are considered. Meanwhile, Galerkin method is incorporated as a competitive alternative, in which a new set of unified, efficient, and reliable trial functions are proposed. A further optimization in regard to boundary distributions under forces is implemented and established on the least absorbed energy principle. High agreement is observed between the analytical results and the FEM results, verifying the correctness of the derivations. Complete comparisons between the analytical and the numerical results indicate the Galerkin method is beneficial when slender ratio is larger than 30, in which the continuity of the deformation is proved to be a crucial influencing factor. A modified numerical strategy about optimal boundary is employed and the remarks imply the algorithm can be availably used to reduce the energy absorption of the whole system.

Oxygen diffusion into the cells with simultaneous absorption is an important problem and it is of great importance in medical applications. The problem is mathematically formulated in two different stages. At the first stage, the stable case having no oxygen transition in the isolated cell is investigated, whereas at the second stage the moving boundary problem of oxygen absorbed by the tissues in the cell is investigated. In oxygen diffusion problem, a moving boundary is essential feature of the problem. This paper extends a homotopy perturbation method with time-fractional derivatives to obtain solution for oxygen diffusion problem. The method used in dealing with the solution is considered as a power series expansion that rapidly converges to the nonlinear problem. The new approximate analytical process is based on two-iterative levels. The modified method allows approximate solutions in the form of convergent series with simply computable components.

This paper presented a new method for automatic plant point cloud acquisition and leaves segmentation. Quasi-dense point cloud of the plant is obtained from multiview stereo reconstruction based on surface expansion. In order to overcome the negative effects from complex natural light changes and to obtain a more accurate plant point cloud, the Adaptive Normalized Cross-Correlation algorithm is used in calculating the matching cost between two images, which is robust to radiometric factors and can reduce the fattening effect around boundaries. In the stage of segmentation for each single leaf, an improved region growing method based on fully connected conditional random field (CRF) is proposed to separate the connected leaves with similar color. The method has three steps: boundary erosion, initial segmentation, and segmentation refinement. First, the edge of each leaf point cloud is eroded to remove the connectivity between leaves. Then leaves will be initially segmented by region growing algorithm based on local surface normal and curvature. Finally an efficient CRF inference method based on mean field approximation is applied to remove small isolated regions. Experimental results show that our multiview stereo reconstruction method is robust to illumination changes and can obtain accurate color point clouds. And the improved region growing method based on CRF can effectively separate the connected leaves in obtained point cloud.

The interpolating boundary element-free method (IBEFM) is developed in this paper for boundary-only analysis of unilateral problems which appear in variational inequalities. The IBEFM is a direct boundary only meshless method that combines an improved interpolating moving least-square scheme for constructing interpolation functions with boundary integral equations (BIEs) for representing governing equations. A projection operator is used to formulate the BIEs and then the formulae of the IBEFM are obtained for unilateral problems. The convergence of the developed meshless method is derived mathematically. The capability of the method is also illustrated and assessed through some numerical experiments.

Evolutionary algorithms (EAs) were shown to be effective for complex constrained optimization problems. However, inflexible exploration-exploitation and improper penalty in EAs with penalty function would lead to losing the global optimum nearby or on the constrained boundary. To determine an appropriate penalty coefficient is also difficult in most studies. In this paper, we propose a bidirectional dynamic diversity evolutionary algorithm (Bi-DDEA) with multiagents guiding exploration-exploitation through local extrema to the global optimum in suitable steps. In Bi-DDEA potential advantage is detected by three kinds of agents. The scale and the density of agents will change dynamically according to the emerging of potential optimal area, which play an important role of flexible exploration-exploitation. Meanwhile, a novel double optimum estimation strategy with objective fitness and penalty fitness is suggested to compute, respectively, the dominance trend of agents in feasible region and forbidden region. This bidirectional evolving with multiagents can not only effectively avoid the problem of determining penalty coefficient but also quickly converge to the global optimum nearby or on the constrained boundary. By examining the rapidity and veracity of Bi-DDEA across benchmark functions, the proposed method is shown to be effective.

An approach for solving of the axisymmetric biharmonic boundary value problems for semi-infinite cylindrical domain was developed in the paper. On the lateral surface of the domain homogeneous Neumann boundary conditions are prescribed. On the remaining part of the domain’s boundary four different biharmonic boundary pieces of data are considered. To solve the formulated biharmonic problems the method of least squares on the boundary combined with the method of homogeneous solutions was used. That enabled reducing the problems to infinite systems of linear algebraic equations which can be solved with the use of reduction method. Convergence of the solution obtained with developed approach was studied numerically on some characteristic examples. The developed approach can be used particularly to solve axisymmetric elasticity problems for cylindrical bodies, the heights of which are equal to or exceed their diameters, when on their lateral surface normal and tangential tractions are prescribed and on the cylinder’s end faces various types of boundary conditions in stresses in displacements or mixed ones are given.

To solve the multiobjective optimization problem on hypersonic glider vehicle trajectory design subjected to complex constraints, this paper proposes a multiobjective trajectory optimization method that combines the boundary intersection method and pseudospectral method. The multiobjective trajectory optimization problem (MTOP) is established based on the analysis of the feature of hypersonic glider vehicle trajectory. The MTOP is translated into a set of general optimization subproblems by using the boundary intersection method and pseudospectral method. The subproblems are solved by nonlinear programming algorithm. In this method, the solution that has been solved is employed as the initial guess for the next subproblem so that the time consumption of the entire multiobjective trajectory optimization problem shortens. The maximal range and minimal peak heat problem is solved by the proposed method. The numerical results demonstrate that the proposed method can obtain the Pareto front of the optimal trajectory, which can provide the reference for the trajectory design of hypersonic glider vehicle.

The fractional Gaussian noise/fractional Brownian motion framework (fGn/fBm) has been widely used for modeling and interpreting physiological and behavioral data. The concept of 1/fnoise, reflecting a kind of optimal complexity in the underlying systems, is of central interest in this approach. It is generally considered that fGn and fBm represent a continuum, punctuated by the boundary of “ideal” 1/fnoise. In the present paper, we focus on the correlation properties of discrete-time versions of these processes (dfGn and dfBm). We especially derive a new analytical expression of the autocorrelation function (ACF) of dfBm. We analyze the limit behavior of dfGn and dfBm when they approach their upper and lower limits, respectively. We show that, asHapproaches 1, the ACF of dfGn tends towards 1 at all lags, suggesting that dfGn series tend towards straight line. Conversely, asHapproaches 0, the ACF of dfBm tends towards 0 at all lags, suggesting that dfBm series tend towards white noise. These results reveal a severe breakdown of correlation properties around the 1/fboundary and challenge the idea of a smooth transition between dfGn and dfBm processes. We discuss the implications of these findings for the application of the dfGn/dfBm model to experimental series, in terms of theoretical interpretation and modeling.

We considered the situation where a container with a permeable boundary is immersed in a larger body of fluid of the same kind. In this paper, we found mathematical expressions at the permeable interfaceΓof a domainΩ, whereΩ⊂R3.Γis defined as a smooth two-dimensional (at least classC2) manifold inΩ. The Sennet-Frenet formulas for curves without torsion were employed to find the expressions on the interfaceΓ. We modelled the flow of Newtonian as well as non-Newtonian fluids through permeable boundaries which results in nonhomogeneous dynamic and kinematic boundary conditions. The flow is assumed to flow through the boundary only in the direction of the outer normaln, where the tangential components are assumed to be zero. These conditions take into account certain assumptions made on the curvature of the boundary regarding the surface density and the shape ofΩ; namely, that the curvature is constrained in a certain way. Stability of the rest state and uniqueness are proved for a special case where a “shear flow” is assumed.

In Ref. [6] the authors constructed analytical solutions including one arbitrary function for the problem of nonlinear, unsteady, supersonic flow analysis concerning slender bodies of revolution due to small amplitude oscillations. An application describing a flow past a right circular cone was presented and the constructed solutions were given in the form of infinite series through a set of convenient boundary and initial conditions in accordance with the physical problem. In the present paper we develop an appropriate convergence analysis concerning the before mentioned series solutions for the specific geometry of a rigid right circular cone. We succeed in estimating the limiting values of the series producing velocity and acceleration resultants of the problem under consideration. Several graphics for the velocity and acceleration flow fields are presented. We must underline here that the proposed convergence technique is unique and can be applied to any other geometry of the considered body of revolution.

In this paper we consider Lagrange type control problem for systems involving dynamic boundary conditions that is, with boundary operators containing time derivatives. Assuming the existence of optimal controls,B-evolutions theory is used to present necessary conditions of optimality. The result is illustrated by an example from heat transfer problem and also an algorithm for computing optimal controls is presented.

This paper presents a novel way to calculate the characteristic solutions of the anisotropy V-notch plane problem. The material eigen equation of the anisotropy based on the Stroh theory and the boundary eigen equation of the V-notch plane problem are studied separately. A modified Müller method is utilized to calculate characteristic solutions of anisotropy V-notch plane problem, which are employed to formulate the analytical trial functions (ATF) in the associated finite element method. The numerical examples show that the proposed subregion accelerated Müller method is an efficient method to calculate the solutions of the equation involving the complex variables. The proposed element ATF-VN based on the analytical trial functions, which contain the characteristic solutions of the anisotropy V-notch problem, presents good performance in the benchmarks.

The inverse heat conduction problem on the heat transfer characteristics of cooled/heated laminar flows through finite length thick-walled circular tubes is studied, using temperature measurements taken at several different locations within the fluid in this paper. The method of radial basis functions is coupled with the boundary control technique to estimate the unknown temperature on the external surface of the circular pipe. The main idea of the proposed method is to solve the direct problem instead of solving the inverse problem directly. The temperature data obtained from the direct problem are used to simulate the temperature measurement for the inverse problem, and during the calculation, the Tikhonov regularization and L-curve methods are employed to solve the inverse problem. Therefore, this study also considers the influence of errors in these measurements upon the precision of the estimated results as well as the influence of the locations and number of sensors used upon the accuracy of the estimated results. The results indicate that the accuracy of the estimated results is improved by taking temperature measurements in locations close to the the unknown boundary. Finally, the results confirm that the proposed method is capable of yielding accurate results even when errors in the temperature measurements are present.

This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs) with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.

Previous work on time-optimal satellite slewing maneuvers, with one satellite axis (sensor axis) required to obey multiple path constraints (exclusion from keep-out cones centered on high-intensity astronomical sources) reveals complex motions with no part of the trajectory touching the constraint boundaries (boundary points) or lying along a finite arc of the constraint boundary (boundary arcs). This paper examines four cases in which the sensor axis is either forced to follow a boundary arc, or has initial and final directions that lie on the constraint boundary. Numerical solutions, generated via a Legendre pseudospectral method, show that the forced boundary arcs are suboptimal. Precession created by the control torques, moving the sensor axis away from the constraint boundary, results in faster slewing maneuvers. A two-stage process is proposed for generating optimal solutions in less time, an important consideration for eventual onboard implementation.

Combining the hybrid displacement variational formulation and the radial basis point interpolation, a truly meshless and boundary-only method is developed in this paper for the numerical solution of solid mechanics problems in two and three dimensions. In this method, boundary conditions can be applied directly and easily. Besides, it is truly meshless, that is, it only requires nodes generated on the boundary of the domain, and does not require any element either for variable interpolation or for numerical integration. Some numerical examples are presented to demonstrate the efficiency of the method.

We present a numerical technique based on the coupling of boundary and finite element methods for the steady Oseen equations in an unbounded plane domain. The present paper deals with the implementation of the coupled program in the two-dimensional case. Computational results are given for a particular problem which can be seen as a good test case for the accuracy of the method.

Homotopy perturbation method (HPM) and boundary element method (BEM) for calculating the exact and numerical solutions of Poisson equation with appropriate boundary and initial conditions are presented. Exact solutions of electrostatic potential problems defined by Poisson equation are found using HPM given boundary and initial conditions. The same problems are also solved using the BEM. The cell integration approach is used for solving Poisson equation by BEM. The problem region containing the charge density is subdivided into triangular elements. In addition, this paper presents a numerical comparison with the HPM and BEM.