ZHOU Fenglin, XIE Guizhong, ZHANG Jianming, LI Luoxing. Near-Singularity Cancellation With the Angle-Distance Transformation Method for Boundary Integral Equations[J]. Applied Mathematics and Mechanics, 2020, 41(5): 530-540. doi: 10.21656/1000-0887.400229
Citation: ZHOU Fenglin, XIE Guizhong, ZHANG Jianming, LI Luoxing. Near-Singularity Cancellation With the Angle-Distance Transformation Method for Boundary Integral Equations[J]. Applied Mathematics and Mechanics, 2020, 41(5): 530-540. doi: 10.21656/1000-0887.400229

Near-Singularity Cancellation With the Angle-Distance Transformation Method for Boundary Integral Equations

doi: 10.21656/1000-0887.400229
Funds:  China Postdoctoral Science Foundation(2016M602403;2019M652753);The National Natural Science Foundation of China(11602082;11602229)
  • Received Date: 2019-07-27
  • Rev Recd Date: 2019-09-03
  • Publish Date: 2020-05-01
  • To address the nearsingularity computation problem involved in the boundary element analysis of thinwalled structures, an angledistance combined transformation method was developed. With this combined method, the computational accuracy and efficiency can be significantly improved. The near singularity was found not only in the radial direction of the basic transformed space, but also in the circumferential direction. In the case that the nearest point in the integral element to the collocation point is close to the edge of the integral element, the integral kernel exhibits significant near singularity with regard to the circumferential direction. Through angle transformation for circumferential variables and distance transformation for radial variables, the near singularity with regard to both directions can be cancelled. Numerical examples illustrate the efficiency and accuracy of the presented method.
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