TY - JOUR
T1 - The Numerical Solution of First Kind Integral Equation for the Helmholtz Equation on Smooth Open Arcs
AU - Tang , Wei-Jun
AU - Fu , Hong-Yuan
AU - Shen , Long-Jun
JO - Journal of Computational Mathematics
VL - 5
SP - 489
EP - 500
PY - 2001
DA - 2001/10
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9001.html
KW - Helmholtz equation, Quadrature method.
AB - <p style="text-align: justify;">Consider solving the Dirichlet problem of Helmholtz equation on unbounded region $R^2$\Γ with Γ a smooth open curve in the plane. We use simple-layer potential to construct a solution. This leads to the solution of a logarithmic integral equation of the first kind for the Helmholtz equation. This equation is reformulated using a special change of variable, leading to a new first kind equation with a smooth solution function. This new equation is split into three parts. Then a quadrature method that takes special advantage of the splitting of the integral equation is used to solve the equation numerically. An error analysis in a Sobolev space setting is given. And numerical results show that fast convergence is clearly exhibited. &nbsp;</p>