The Watson transformation is essentially the idea that a series can be converted into an integral in the complex plane via an “inverse residue” calculation. This idea has a long history of being used to convert expressions for the solutions of boundary value problems (BVPs) into alternative expressions from which it is easier to extract information about… (More)

We give an overview of variational formulations of second-order linear elliptic PDEs that are based on integration by parts (or, equivalently, on Green’s identities).

In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation −∆u − (k2 + iε)u = f , with absorption parameter ε ∈ R. Multigrid approximations of this equation with ε 6= 0 are commonly used as preconditioners for the pure Helmholtz case (ε = 0).… (More)