重调和外问题的奇异边界法
On Singular Boundary Methods for Exterior Biharmonic Problems
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摘要: 将无网格奇异边界法应用于重调和外问题。利用奇异边界法引入源点强度因子来解决基本解方法中当源点和配点重合而引起的奇异性，从而避免了基本解方法中的虚拟边界选取难题。通过加减法原理和反插值技术求出源点强度因子，将问题的解表示为基本解的线性组合。通过实例验证了方法的准确性和收敛性。Abstract: The meshless singular boundary method (SBM ) is first presented for the numerical solution of exterior biharmonic problems .The SBM uses the source intensity factor to isolate the singularity of funda‐mental solutions ,and thus avoids the fictitious boundary associated withthe method of fundamental solu‐tions .T he solution of the problem is approximated by a linear combination of fundamental solution in this method w hich uses addition and subtraction principle and an inverse interpolation technique (IIT ) to com‐pute the source intensity factor . Some numerical examples illustrate the efficiency and accuracy of the SBM .
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