Internal field error reduction in boundary element analysis for Helmholtz equation
A systematic analysis has been made to clarify the cause of very large errors in the boundary element solutions at internal points near the boundary. Following the results of the analysis, two new ideas have been developed to reduce the errors when solving the Helmholtz equation. The first idea, which is an extended application of the equipotential condition to Helmholtz type problem, is easily applied to any existing program. The second idea which gives us more accurate solutions is based on the analytic integration of boundary integrals by expanding the fundamental solutions into a sum of elementary functions. Test calculations demonstrate that the two present techniques are efficient to reduce the errors near the boundary.
error reduction helmholtz equation internal points equipotential condition analytical integration boundary element method