This paper proposes a boundary knot method (BKM) formulation in conjunction with the singularity subtraction technique to solve Helmholtz problems with boundary singularities. The solution breaks down into the singular solution and the regular solution. The singular solution is derived analytically and satisfies the governing equation and the corresponding boundary conditions containing singularities. Then the regular solution is approximated by the BKM. Numerical results demonstrate the accuracy and efficiency of the proposed technique.
Shen, De-Jian; Lin, Ji; and Chen, Wen
"BOUNDARY KNOT METHOD SOLUTION OF HELMHOLTZ PROBLEMS WITH BOUNDARY SINGULARITIES,"
Journal of Marine Science and Technology: Vol. 22:
4, Article 5.
Available at: https://jmstt.ntou.edu.tw/journal/vol22/iss4/5