A Burton-Miller boundary element-free method for Helmholtz problems

Abstract A Burton-Miller boundary element-free method is developed by using the Burton-Miller formulation for meshless and boundary-only analysis of Helmholtz problems. The method can produce a unique solution at all wavenumbers and is valid for Dirichlet, Neumann and mixed problems simultaneously. An efficient numerical integration procedure is presented to handle both strongly singular and hypersingular boundary integrals directly and uniformly. Numerical results reveal that this direct meshless method only involves boundary nodes and can deal with Helmholtz problems at extremely large wavenumbers.