A new global and direct integral formulation for 2D potential problems

Abstract A new global and direct integral formulation (GDIF) is presented for 2D potential problems. The 'global' and 'direct' mean that Gaussian quadrature can be applied directly to the entire body surface if its geometry description is mathematically available. This concept is simple and time-honored. The method has been long pursued by several researchers thanks to its accuracy and efficiency. However, the GDIF is based on the boundary integral equations (BIEs). The most crucial but difficult part in this method is to eliminate the singularities in BIEs, especially the source singularity. In this study, new non-singular boundary integral equations (NSBIEs) with indirect unknowns are developed in association with the average source technique without using the equi-potential method for source singularity. The integrands of all integrals in the NSBIEs are finite at any point on the body surface, which allows them to be considered as a normal function for computation. Based on this, with collocation points chosen in the NSBIEs being exactly the same as Gaussian points, an arbitrary order Gaussian quadrature can be directly applied to evaluate the integrals over the global elements. Three benchmark examples are tested to verify the efficiency and convergence of the proposed scheme.

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