Search results

The purpose of this paper is to develop highly efficient decomposition finite difference methods for computing solutions of highly oscillatory beam propagation partial differential equations.

Highly oscillatory optical wave equations, such as the multidimensional paraxial Helmholtz equation, have been used extensively in modelling propagation of the light from lens to the focal region in various engineering applications. Numerical approximations of solutions of such equations contain crucial light information in focal regions even when the f-number is small. However, it has been difficult to acquire highly oscillatory numerical solutions efficiently. This paper proposes two correlated eikonal decomposition strategies for fast computations of the oscillatory solutions. Structures of the numerical methods are designed via an eikonal, or exponential, transformation. The approach converts successfully the oscillatory problems to non-oscillatory subproblems. Therefore, the underlying beam simulation equations can be solved readily with great accuracy and stability.

It is found that the two correlated eikonal transformation based decomposition methods effectively remove the highly oscillatory features of the wave equations. The coupled non-oscillatory subproblems resulted are easier to solve. Discretization steps in computations can be chosen to be relatively large and this ensures the efficiency of computations. The decomposed finite difference schemes are simple to use in different optical applications.

The computational approach provides a valuable tool to practical applications, such as those in the defence industry.

Although the eikonal transformation has been used in the theory of nonlinear optics, this is the first time it has been utilized for effective engineering computations.

This meshless collocation method is applicable not only to the Helmholtz equation with Dirichlet boundary condition but also mixed boundary conditions. It can calculate not only the high wavenumber problems, but also the variable wave number problems.

In this paper, the authors developed a meshless collocation method by using barycentric Lagrange interpolation basis function based on the Chebyshev nodes to deduce the scheme for solving the three-dimensional Helmholtz equation. First, the spatial variables and their partial derivatives are treated by interpolation basis functions, and the collocation method is established for solving second order differential equations. Then the differential matrix is employed to simplify the differential equations which is on a given test node. Finally, numerical experiments show the accuracy and effectiveness of the proposed method.

The numerical experiments show the advantages of the present method, such as less number of collocation nodes needed, shorter calculation time, higher precision, smaller error and higher efficiency. What is more, the numerical solutions agree well with the exact solutions.

Compared with finite element method, finite difference method and other traditional numerical methods based on grid solution, meshless method can reduce or eliminate the dependence on grid and make the numerical implementation more flexible.

The Helmholtz equation has a wide application background in many fields, such as physics, mechanics, engineering and so on.

This meshless method is first time applied for solving the 3D Helmholtz equation. What is more the present work not only gives the relationship of interpolation nodes but also the test nodes.

As wheeled mobile robots find increasing use in outdoor applications, it becomes more important to reduce energy consumption to perform more missions efficiently with limit energy supply. The purpose of this paper is to survey the current state-of-the-art on energy-efficient motion planning (EEMP) for wheeled mobile robots.

The use of wheeled mobile robots has been increased to replace humans in performing risky missions in outdoor applications, and the requirement of motion planning with efficient energy consumption is necessary. This study analyses a lot of motion planning technologies in terms of energy efficiency for wheeled mobile robots from 2000 to present. The dynamic constraints play a key role in EEMP problem, which derive the power model related to energy consumption. The surveyed approaches differ in the used steering mechanisms for wheeled mobile robots, in assumptions on the structure of the environment and in computational requirements. The comparison among different EEMP methods is proposed in optimal, computation time and completeness.

According to lots of literature in EEMP problem, the research results can be roughly divided into online real-time optimization and offline optimization. The energy consumption is considered during online real-time optimization, which is computationally expensive and time-consuming. The energy consumption model is used to evaluate the candidate motions offline and to obtain the optimal energy consumption motion. Sometimes, this optimization method may cause local minimal problem and even fail to track. Therefore, integrating the energy consumption model into the online motion planning will be the research trend of EEMP problem, and more comprehensive approach to EEMP problem is presented.

EEMP is closely related to robot’s dynamic constraints. This paper mainly surveyed in EEMP problem for differential steered, Ackermann-steered, skid-steered and omni-directional steered robots. Other steering mechanisms of wheeled mobile robots are not discussed in this study.

The survey of performance of various EEMP serves as a reference for robots with different steering mechanisms using in special scenarios.

This paper analyses a lot of motion planning technologies in terms of energy efficiency for wheeled mobile robots from 2000 to present.

During thermal laser processes, heat transfer and fluid flow in the melt pool are primary driven by complex physical phenomena that take place at liquid/vapor interface. Hence, the choice and setting of front description methods must be done carefully. Therefore, the purpose of this paper is to investigate to what extent front description methods may bias physical representativeness of numerical models of laser powder bed fusion (LPBF) process at melt pool scale.

Two multiphysical LPBF models are confronted: a Level-Set (LS) front capturing model based on a C++ code and a front tracking model, developed with COMSOL Multiphysics® and based on Arbitrary Lagrangian–Eulerian (ALE) method. To do so, two minimal test cases of increasing complexity are defined. They are simplified to the largest degree, but they integrate multiphysics phenomena that are still relevant to LPBF process.

LS and ALE methods provide very similar descriptions of thermo-hydrodynamic phenomena that occur during LPBF, providing LS interface thickness is correctly calibrated and laser heat source is implemented with a modified continuum surface force formulation. With these calibrations, thermal predictions are identical. However, the velocity field in the LS model is systematically underestimated compared to the ALE approach, but the consequences on the predicted melt pool dimensions are minor.

This study fulfils the need for comprehensive methodology bases for modeling and calibrating multiphysical models of LPBF at melt pool scale. This paper also provides with reference data that may be used by any researcher willing to verify their own numerical method.

The purpose of this paper is to obtain soliton solution of the Kaup‐Kupershmidt (KK) equation with initial condition. The most important feature of this method is to obtain the solution without direct transformation.

In this paper, the homotopy perturbation method (HPM) is used for obtaining soliton solution of the KK equation. The numerical solutions are compared with the known analytical solutions. The results of numerical examples are presented and only a few terms are required to obtain accurate solutions. Results derived from this method are shown graphically.

The authors obtained the one soliton solution for the KK equation by HPM. The numerical results showed that this method is very accurate. The HPM provides a reliable technique that requires less work if compared with the traditional techniques and the method does not also require unjustified assumptions, linearization, discretization or perturbation. The HPM is very easily applied to both differential equations and linear or nonlinear differential systems.

The paper describes how the authors obtained one soliton solution for the KK equation by HPM. The numerical results presented show that this method is very accurate.

This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM).

The governing Navier–Stokes equations of the flow are reduced to a third-order nonlinear ordinary differential equation by a suitable similarity transformation. Analytic solution of the resulting differential equation is obtained using the HPM. Mathematica software is used to visualize the flow behavior. The effects of the various parameters on velocity field are analyzed through appropriate graphs.

It is found that x component of the velocity increases with the increase of the Hartman number when the transverse direction variable ranges from 0 to 0.2 and the reverse behavior is observed when transverse direction variable takes values between 0.2 and 0.5. It is noted that the y component of the velocity increases rapidly with the increase of the transverse direction variable. The y component of the velocity increases marginally with the increase of the Hartman number M. The effect of the Reynolds number R on the x and y components of the velocity is quite opposite to the effect of the Hartman number on the x and y components of the velocity and the effect of the parameter on the x and y components of the velocity is similar to that of the Reynolds number.

To the best of the author’s knowledge, nobody had tried before two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the HPM.

The purpose of this paper is to develop a scheme to study numerical solution of time fractional nonlinear evolution equations under initial conditions by reduced differential transform method.

The paper considers two models of special interest in physics with fractional‐time derivative of order, namely, the time fractional mKdV equation and time fractional convection diffusion equation with nonlinear source term.

The numerical results demonstrate the significant features, efficiency and reliability of the proposed method and the effects of different values are shown graphically.

The paper shows that the results obtained from the fractional analysis appear to be general.

The purpose of this paper is to analyze the heat transfer effects on the stretched flow of Oldroyd-B fluid in a rotating frame. Cattaneo–Christov heat conduction model is considered, which accounts for the influence of thermal relaxation time.

Based on scale analysis, the usual boundary layer approximations are used to simplify the governing equations. The equations so formed have been reduced to self-similar forms by similarity transformations. A powerful analytic approach, namely, homotopy analysis method (HAM), has been applied to present uniformly convergent solutions for velocity and temperature profiles.

Suitable values of the so-called auxiliary parameter in HAM are obtained by plotting h-curves. The results show that boundary layer thickness has an inverse relation with fluid relaxation time. The rotation parameter gives resistance to the momentum transport and enhances fluid temperature. Thermal boundary layer becomes thinner when larger values of thermal relaxation time are chosen.

To the authors’ knowledge, this is the first attempt to study the three-dimensional rotating flow and heat transfer of Oldroyd-B fluid.

The purpose of this paper is to consider the well‐known Falkner‐Skan equation. This equation appears in the modelling of various phenomena in physics and engineering.

The He's variational iteration method which is a very efficient tool for solving different kinds of problems, is employed for solving this problem.

Some other approaches are introduced to compare the efficiency of the new procedure. Several test examples are given to show the advantages of the present method over other existing techniques.

In this paper, a new and efficient technique is proposed to solve the Falkner‐Skan equation.