A least-squares method for the Helmholtz equation Original Research Article

A least-squares method for the Helmholtz equation Original Research Article Pages 121-136 P. Monk, Da-Qing Wang Close preview | Related articles | Related reference work articles Abstract | References Abstract We investigate the use of least-squares methods to approximate the Helmholtz equation. The basis used in the discrete method consists of solutions of the Helmholtz equation (either consisting of plane waves or Bessel functions) on each element of a finite element grid. Unlike previous methods of this type, we do not use polynomial based finite elements. The use of small elements (and relatively few basis functions per element) allows us to prove convergence theorems for the method and, to some extent, control the conditioning of the resulting linear sy stem. Numerical results show the efficiency of the new method and suggest that it may be possible to obtain accurate results with a coarser grid than is usual for standard finite element methods.