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Radial basis functions methods for boundary value problems: Performance comparison

机译：边值问题的径向基函数方法：性能比较

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摘要

We present in this paper comparisons on the performances among five typical radial basis functions methods, namely radial basis collocation method (RBCM), radial basis Galerkin method (RBGM), compactly supported radial basis collocation method (CSRBCM), compactly supported radial basis Galerkin method (CSRBGM), and finite subdomain radial basis collocation method (FSRBCM), for solving problems arising from engineering industries and applied sciences. Numerical comparison results demonstrate that the RBCM and FSRBCM possess high accuracy and superior convergence rates in which the FSRBCM particularly attains higher accuracy for problems with large gradients. The FSRBCM, CSRBCM and RBCM are computationally efficient while the CSRBCM, CSRBGM and FSRBCM can greatly improve the ill-conditioning of the resultant matrix. In conclusion, its advantages on high accuracy; exponential convergence; well-conditioning; and effective computation make the FSRBCM a first-choice among the five radial basis functions methods.
机译：我们在本文中比较了五个典型的径向基函数方法的性能，即径向基搭配方法（RBCM），径向基Galerkin方法（RBGM），紧支撑径向基搭配方法（CSRBCM），紧支撑径向基Galerkin方法（CSRBGM）和有限子域径向基配置法（FSRBCM），用于解决工程行业和应用科学领域出现的问题。数值比较结果表明，RBCM和FSRBCM具有较高的精度和较高的收敛速度，其中FSRBCM特别适用于大梯度问题。 FSRBCM，CSRBCM和RBCM的计算效率很高，而CSRBCM，CSRBGM和FSRBCM可以极大地改善所得矩阵的不适状况。综上所述，其优势在于精度高；指数收敛状况良好；有效的计算使FSRBCM成为五种径向基函数方法中的首选。

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