A BOUNDARY ELEMENT METHOD FOR THE NEUMANN PROBLEM OF HELMHOLTZ EQUATION BY USE OF A DOUBLE LAYER POTENTIAL IN R~3
Jin Chaosong
DOI:10.11835/j.issn.1674-4764.1990.03.004
Received ,Revised , Accepted , Available online July 01, 2015
Volume ,1990,Pages -
- Abstract
This paper presents a new numerical solution for Neumann problem of Helmholtz equation in R~3. The expression of the solution for this problem is obtained by use of a double layer potential and it leads to a Fredholm boundary integral equation of the first kind. Then, the existence and unicity of the integral equation which is equivalent to the boundary value problem are obtained in a suitable Sobolev space. Finally, a variational form which is equivalent to the integral equation is applied to the construction of a finite element method and the error estimate is given.