Evaluating RBF methods for solving PDEs using Padua points distribution

Koushki, Masoumeh; Jabbari, Ehsan; Ahmadinia, M.

doi:10.1016/j.aej.2020.04.047

Cited by 14 publications

(9 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, we consider the collocation points in the Chebyshev-type scheme, which is generated in the interval (−1, 1), instead of the traditional uniformly distributed source points. e novelty of the idea lies in that the computational cost remains the same as traditional way with more accurate solutions and there is no need to consider the fictitious points used in the other methods [13][14][15][16]. e definite generation of collocation points on each direction of the physical domain by Chebyshev-type is shown as follows:…”

Section: The Crbf Methodsmentioning

confidence: 99%

See 1 more Smart Citation

The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note

Zhang

Sun

Hou

et al. 2021

Journal of Mathematics

View full text Add to dashboard Cite

The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurate and stable numerical solution, while the shape parameter values are almost independent. In this paper, we give a quasi-optimal conical spline which can improve the numerical results. Besides, we consider the collocation points in the Chebyshev-type which improves solution accuracy of the method with no additional computational cost.

show abstract

Section: The Crbf Methodsmentioning

confidence: 99%

“…e novelty of the Chebyshev-type scheme lies in that the computational cost remains the same as traditional way with more accurate solutions, and there is no need to consider the fictitious points used in the other methods [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note

Zhang

Sun

Hou

et al. 2021

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

“…where w i is the i-th weight coefficient, and ϕ(r) = ϕ x i − x is the basic function determined by the Euclidean distance between the prescribed observed point x i and the untried point x [19,37,38]. To determine the weight coefficient w i , a set of interpolation points of x j that have known results from CFD simulations are introduced to substitute the untried points of x, where all the interpolation points should satisfy:…”

Section: Optimization Of Aerodynamic Performance In Ducted Multi-propeller Configurationmentioning

confidence: 99%

“…Besides, the optimal observed points are determined in the vicinity of the interpolation points correspondingly, in a manner of random selection. The Inverse Multiquadric (IMQ) function is adopted through trial-and-error from multiple basic function options in the RBFs model [19,37,38] and utilized in Equation ( 3), which is capable of providing reasonable results in approximating the lift force at all points, and is defined as:…”

Section: Optimization Of Aerodynamic Performance In Ducted Multi-propeller Configurationmentioning

confidence: 99%

“…The consistency between CFD-and surrogate model-based results is verified through a comparison of three variables of 35 test points between CFD and surrogate model based results. The comparison is conducted by utilizing the average relative error (e), the R-squared (R 2 ), and the root mean squared error (σ e ) with the convergence criteria of e < 0.0025, R 2 > 0.945, and σ e < 0.0025 [19,37,38], where e is defined as:…”

Section: Optimization Of Aerodynamic Performance In Ducted Multi-propeller Configurationmentioning

confidence: 99%

See 1 more Smart Citation

Effect of Ducted Multi-Propeller Configuration on Aerodynamic Performance in Quadrotor Drone

Yonezawa

2021

Drones

View full text Add to dashboard Cite

Motivated by a bioinspired optimal aerodynamic design of a multi-propeller configuration, here we propose a ducted multi-propeller design to explore the improvement of lift force production and FM efficiency in quadrotor drones through optimizing the ducted multi-propeller configuration. We first conducted a CFD-based study to explore a high-performance duct morphology in a ducted single-propeller model in terms of aerodynamic performance and duct volume. The effect of a ducted multi-propeller configuration on aerodynamic performance is then investigated in terms of the tip distance and the height difference of propellers under a hovering state. Our results indicate that the tip distance-induced interactions have a noticeable effect in impairing the lift force production and FM efficiency but are limited to small tip distances, whereas the height difference-induced interactions have an impact on enhancing the aerodynamic performance over a certain range. An optimal ducted multi-propeller configuration with a minimal tip distance and an appropriate height difference was further examined through a combination of CFD simulations and a surrogate model in a broad-parameter space, which enables a significant improvement in both lift force production and FM efficiency for the multirotor, and thus provides a potential optimal design for ducted multirotor UAVs.

show abstract

Determining approximate solution of partial differential equations using radial basis function model trained with parallel symbiotic organisms search algorithm

Panda

2022

Concurrency and Computation

View full text Add to dashboard Cite

show abstract

Evaluating RBF methods for solving PDEs using Padua points distribution

Cited by 14 publications

References 38 publications

The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note

The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note

Effect of Ducted Multi-Propeller Configuration on Aerodynamic Performance in Quadrotor Drone

Determining approximate solution of partial differential equations using radial basis function model trained with parallel symbiotic organisms search algorithm

Contact Info

Product

Resources

About