NII Technical Report (NII-2005-010E)：Variable Transformations for Nearly Singular Integrals in the Boundary Element Method

Key Points

• The aim is to review and improve a variable transformation method for evaluating nearly singular integrals in boundary element analysis.
• Introduced polar coordinates at the source projection.
• Employed radial and angular variable transformations to mitigate singularities.
• Presented multiple radial variable transformations relevant to the method.
• Conducted error analysis using complex function theory to find optimal transformations.
• Discussed efficient implementation of the double exponential transformation.
• Successful reduction of near singularity effects in integrals.
• Identified optimal radial variable transformation for better accuracy.
• Demonstrated effectiveness of double exponential transformation in practical applications.

Abstract