Radial Basis Functions

Chen, Wen; Chen, C. S.

doi:10.1007/978-3-642-39572-7_2

Cited by 12 publications

(4 citation statements)

References 42 publications

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“…The different RBF models are denoted with H = G, H = M, H = I, H = T for the Gaussian, the multiquadratic, the inverse multiquadratic and the thin plate RBF, respectively [11]. A more detailed view of RBFs is for instance given in [70].…”

Section: Sobol' Indicesmentioning

confidence: 99%

On the sensitivity of DEM parameters on pile experiments

Jahn,

Meywerk

2024

Comp. Part. Mech.

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The discrete element method (DEM) is suitable to investigate problems where large deformations occur especially in granular material. The fitting of reliable DEM parameters is crucial and a challenge which is caused by the high number of DEM parameters and the computational effort. Despite its drawbacks, a trial and error approach is often used for the DEM parameter calibration. The knowledge of the DEM parameter influence on the model response is necessary to improve the calibration and to check whether the experiment is suitable to calibrate specific parameters or not. It is possible to reduce the dimensionality of the optimisation problem by omitting parameters whose influence on the model response is negligibly small. One approach is to perform a global sensitivity analysis based on Sobol’ indices. A frequently used calibration experiment in literature is the pile experiment. The deviation between the experiment and the simulation is evaluated with the angle of repose. In the present paper, an algorithm to determine the angle of repose considering the three-dimensional shape of the heap is discussed. The global sensitivity analysis is performed for two different experimental heap set-ups. To decrease the computational effort of the sensitivity analysis, the model response is approximated with metamodels whose predictability is evaluated using the root mean squared error (RMSE) based on a separate sampling point set.

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Section: Sobol' Indicesmentioning

confidence: 99%

On the sensitivity of DEM parameters on pile experiments

Jahn,

Meywerk

2024

Comp. Part. Mech.

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“… The duration of infectiousness. Derivation and discussion of the basic reproduction number make evaluating the effectiveness of different containment measures more clear, as the dependence of transmission in terms of the model parameters becomes explicit (for more details, see [ 11 , 16 ])…”

Section: Covid-19 Mathematical Modelmentioning

confidence: 99%

The numerical solution of a mathematical model of the Covid-19 pandemic utilizing a meshless local discrete Galerkin method

Asadi‐Mehregan

Assari

Dehghan

2022

Engineering with Computers

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It was in early December 2019 that the terrible news of the outbreak of new coronavirus disease (Covid-19) was reported by the world media, which appeared in Wuhan, China, and is rapidly spreading to other parts of China and several overseas countries. In the field of infectious diseases, modeling, evaluating, and predicting the rate of disease transmission are very important for epidemic prevention and control. Several preliminary mathematical models for Covid-19 are formulated by various international study groups. In this article, the SEIHR(D) compartmental model is proposed to study this epidemic and the factors affecting it, including vaccination. The proposed model can be used to compute the trajectory of the spread of the disease in different countries. Most importantly, it can be used to predict the impact of different inhibition strategies on the development of Covid-19. A computational approach is applied to solve the offered model utilizing the Galerkin method based on the moving least squares approximation constructed on a set of scattered points as a locally weighted least square polynomial fitting. As the method does not need any background meshes, its algorithm can be easily implemented on computers. Finally, illustrative examples clearly show the reliability and efficiency of the new technique and the obtained results are in good agreement with the known facts about the Covid-19 pandemic.

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“…In recent years the method of fundamental solutions (MFS), a boundary meshless method, has attracted great attention for solving homogeneous differential equations [1][2][3][4][5][6][7][8][9]. The MFS is quite simple, efficient and easy for implementation, and has avoided the singular integrals which is necessary in certain boundary meshless methods, such as BNM [10], LBIE [11], HBNM [12], BCM [13], BFM [14].…”

Section: Introductionmentioning

confidence: 99%

Generalized method of fundamental solutions (GMFS) for boundary value problems

Yang

Zheng

Wen

2018

Engineering Analysis with Boundary Elements

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In order to cope with the instability of the method of fundamental solutions (MFS), which caused by source offset, or source location, or fictitious boundary, a generalized method of fundamental solutions (GMFS) is proposed. The crucial part of the GMFS is used a generalized fundamental solution approximation (GFSA), which adopts a bilinear combination of fundamental solutions to approximate, rather than the linear combination of the MFS. Then the numerical solution of the GMFS is decided by a group of offsets corresponding to an intervention-point diffuse (IPD), instead of the MFS' only offset of a single source. To demonstrate the effectiveness of the proposed approach, four numerical tests are given. The results have shown that the GMFS is more accurate, stable, and better convergence than the traditional MFS.

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Radial Basis Functions

Cited by 12 publications

References 42 publications

On the sensitivity of DEM parameters on pile experiments

On the sensitivity of DEM parameters on pile experiments

The numerical solution of a mathematical model of the Covid-19 pandemic utilizing a meshless local discrete Galerkin method

Generalized method of fundamental solutions (GMFS) for boundary value problems

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