Local strategies for improving the conditioning of the plane-wave Ultra-Weak Variational Formulation

Element-wise techniques based on SVD or QR Decomposition completely get rid of the usual ill-conditioning inherent to plane-wave discretizations Ultra-Weak Variational Formulation (UWVF) for Helmholtz equation. Associated preconditioning strategies lead very low condition numbers corresponding linear system matrices, without any limitation number plane waves per element. In addition, some these procedures have advantage considerably reducing size final be solved altering accuracy numerical solution.