A NUMERICAL SOLUTION OF A HELMHOLTZ EQUATION USING BOUNDARY ELEMENTS - Solekhudin, Imam (2010)
Helmholtz equation is a well known differential equation. Most boundary value problems involving this equation are either difficult or impossible to solve analytically. In this study, we employ a dual reciprocity boundary element method (DRBEM) to solve these problems. On the boundary and in the region bounded by the boundary, a set of collocation points is chosen for the DRBEM. The computational algorithm requires setting up and solving a system of linear algebraic equation of the form, AX = B, based on this set of collocation points. The solution to the boundary value problem is therefore approximated by the solution of the algebraic equations. Examples are presented to test this method, and results obtained are compared with their corresponding analytic solutions.