Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

Wind-sand flow simulation and radius optimization of highway embankment under different vertical curve radius

It is of great practical value to explore the correlation between the vertical curve radius of desert highway and the increase of sand accumulation in local lines,and to select the appropriate vertical curve radius for reducing the risk of sand accumulation.In this study,three-dimensional models of desert highway embankments with different vertical curve radii were constructed,and Fluent software was used to simulate the wind-sand flow field and sand accumulation distribution of vertical curve embankments.The results show that:(1)Along the direction of the road,the concave and the convex vertical curve embankments have the effect of collecting and diverging the wind-sand flow,respectively.When the radius of the concave vertical curve is 3000 m,5000 m,8000 m,10000 m and 20000 m,the wind velocity in the middle of the vertical curve is 31.76%,22.58%,10.78%,10.53%and 10.44%,higher than that at both ends.When the radius of the convex vertical curve is 6500 m,8000 m,10000 m,20000 m and 30000 m,the wind velocity at both ends of the vertical curve is 14.06%,9.99%,6.14%,3.22%and 2.41%,higher than that in the middle.The diversion effect also decreases with the increase of the radius.(2)The conductivity of the concave and convex vertical curve embankments with different radii is greater than 1,which is the sediment transport roadbed.The conductivity increases with the increase of radius and gradually tends to be stable.When the radius of the concave and convex vertical curves reaches 8000 m and 20000 m respectively,the phenomenon of sand accumulation is no longer serious.Under the same radius condition,the concave vertical curve embankment is more prone to sand accumulation than the convex one.(3)Considering the strength of the collection and diversion of the vertical curve embankment with different radii,and the sand accumulation of the vertical curve embankment in the desert section of Wuma Expressway,the radius of the concave vertical curve is not less than 8000 m,and the radius of the convex vertical curve is not less than 20000 m,which can effectively reduce the sand accumulation of the vertical curve embankment.In the desert highway area,the research results of this paper can provide reference for the design of vertical curve to ensure the safe operation of desert highway.

Determining the Planning Period of a Distribution Substation Based on Acceptable Errors

The distribution substation planning is faced with numerous uncertainties so that the planning result can only be a“rough outline,”and the problem of determining the planning period arises.On the basis of the assessment of uncertainties in distribution planning,a specific approach to determine the planning period of a distribution substation based on acceptable errors is proposed,indicating that the load forecast error is the key factor to affect the planning period.In order to provide a clearer understanding of this paper’s primary objective,the proposed approach is applied to determining the planning period of a power supply radius optimization(PSRO)model in distribution substation planning.Finally,an example is illustrated which validates the suggested approach of this paper.