International Journal of Modeling, Simulation, and Scientific Computing

Aiming at the problem that the mesh simplification algorithm loses the geometric features of the model in large-scale simplification, an improved half-edge collapse mesh simplification algorithm is proposed. The concept of approximate measurement of edge curvature is introduced, and the edge curvature is added to the error measure, so that the order of half-edge collapse of the mesh is changed, and the simplified details of the mesh model can be preserved accurately. At the same time, by analyzing the quality of simplified triangular mesh, optimizing triangular mesh locally, reducing the amount of narrow triangles, the quality of the simplified model is improved. The proposed algorithm was tested on Cow model, Car model and Bunny model, and compared with another three algorithms, one of them is a classical mesh simplification algorithm based on edge collapse, the other is an improved algorithm of the classical one. The experimental results show that the improved algorithm can better retain the detail features of the original model at the same reduction ratio, and has reasonable mesh allocation, fast execution speed and small error.

According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial, a variable-order and variable-step-size numerical method for solving differential equations is designed. The stability properties of the formulas are discussed and the stability regions are analyzed. The deduced methods are applied to a simulation problem. The results show that the numerical method can satisfy calculation accuracy, reduce the number of calculation steps and accelerate calculation speed.

The approach to optimization of finite-difference (FD) schemes for the linear advection equation (LAE) is proposed. The FD schemes dependent on the scalar dimensionless parameter are considered. The parameter is included in the expression, which approximates the term with spatial derivatives. The approach is based on the considering of the dispersive and dissipative characteristics of the schemes as the functions of the parameter. For the proper choice of the parameter, these functions are minimized. The approach is applied to the optimization of two-step schemes with an asymmetric approximation of time derivative and with various approximations of the spatial term. The cases of schemes from first to fourth approximation orders are considered. The optimal values of the parameter are obtained. Schemes with the optimal values are applied to the solution of test problems with smooth and discontinuous initial conditions. Also, schemes are used in the FD-based lattice Boltzmann method (LBM) for modeling of the compressible gas flow. The obtained numerical results demonstrate the convergence of the schemes and decaying of the numerical dispersion.

Singular integral equations arisen in axisymmetric problems of elastostatics are under consideration in this paper. These equations are received after applying the integral transformation and Gauss–Ostrogradsky’s theorem to the Green tensor for equilibrium equations of the infinite isotropic medium. Initially, three-dimensional problems expressed in Cartesian coordinates are transformed to cylindrical ones and integrated with respect to the circumference coordinate. So, the three-dimensional axisymmetric problems are reduced to systems of one-dimensional singular integral equations requiring the evaluation of linear integrals only. The thorough analysis of both displacement and traction kernels is accomplished, and similarity in behavior of both kernels is established. The kernels are expressed in terms of complete elliptic integrals of first and second kinds. The second kind elliptic integrals are nonsingular, and standard Gaussian quadratures are applied for their numerical evaluation. Analysis of external integrals proved the existence of logarithmic and Cauchy’s singularities. The numerical treatment of these integrals takes into account the presence of this integrable singularity. The numerical examples are provided to testify accuracy and efficiency of the proposed method including integrals with logarithmic singularity, Catalan’s constant, the Gaussian surface integral. The comparison between analytical and numerical data has proved high precision and availability of the proposed method.

Numerical simulation for concrete aggregate models (CAMs) with different shape aggregates usually requires high accuracy and convergence near the material interfaces. But high memory usage will be needed for those traditional finite element methods such as the method by using mesh refinement throughout the domain. Thus, an adaptive $p$-version finite element method ($p$-FEM) is proposed in this paper for the solution of 3D CAM problems, and meanwhile the resulting adaptive computational algorithm and post-processing program are presented. We firstly focused two typical 3D weak discontinuity problems on the influence of different convergence criterions for the computational results of each point on the interface in order to verify the efficiency and convergence of the resulting $p$-FEM, and then this method is successfully applied to the numerical simulation of CAMs with different shape aggregates. In addition, an efficient hybrid realization method which combines ANSYS and Hypermesh software is also presented in order to quickly establish the geometric models of 3D CAMs. The numerical results have been shown that the proposed $p$-FEM can efficiently solve the concrete-like particle-reinforced composite problems and more accurate numerical results can be obtained under the case of fewer elements used in simulation of CAMs, even there being some elements with poor quality.

In this paper, we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method (FNDM). The proposed method is a graceful blend of decomposition scheme with natural transform, and three examples are considered to validate and illustrate its efficiency. The nature of FNDM solution has been captured for distinct arbitrary order. In order to illustrate the proficiency and reliability of the considered scheme, the numerical simulation has been presented. The obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology.

Atherosclerosis, a continual inflammatory disease occurring due to plaque cumulation in the arterial intima, is one of the main reasons behind deaths from diverse cardiovascular diseases. The basic interactions between oxidized low density lipoprotein (LDL) and macrophages in the formation of atherosclerotic plaque are modeled here in terms of a reaction–diffusion system in one-dimensional (1D) space under Neumann boundary conditions. Two simple mathematical models are considered which differ by the influx term only in the case of the interaction of oxidized LDL. Both the spatial and nonspatial systems are simply analyzed theoretically and numerically. Numerical bifurcation analysis confirms the existence of Hopf bifurcation concerning four significant model parameters. Examining the gravity of the model offered in this investigation, an obvious insight into this inflammatory response can be achieved both qualitatively and quantitatively.

In this paper, two problems that exist in parking spot layout of bike-sharing which need to be solved are addressed. One is the size of parking spot, while another is the location of parking spot. First, the generation and attraction model of traffic travel is used to predict the usage requirements of bike-sharing, to acquire the parking requirements of bike-sharing. Then, we establish the best station spacing model to calculate the optimal quantity of parking spots. Moreover, the method of shortest distance clustering is applied to cluster the parking demand spots. Finally, the location optimization of bike-sharing parking spot is carried out by using gravity location model. In summary, the layout of bike-sharing parking spot is finished based on the abovementioned four steps.

This paper investigates the velocity and altitude tracking control problem for air-breathing hypersonic vehicle (AHV) in the presence of external disturbances and parameter uncertainties. A composite controller containing improved lines cluster approaching mode control (LCAMC) and nonlinear disturbance observer (NDO) is developed to guarantee the tracking errors converge to zero and enhance the robustness of control system. Meanwhile, considering the multiple uncertain parameters, a genetic algorithm (GA) based Pareto uncertainty estimation is employed to predict the parameter uncertainties of the AHV dynamics. Besides, the mathematical proofs of proposed method are analyzed by utilizing Lyapunov theory. Simulation results demonstrate the effective tracking performance, excellent disturbance estimation and uncertainty estimation ability of the composite method.