A posteriori upper and lower bounds are derived for the linear finite element method (FEM) Helmholtz equation with large wavenumber. It is proved rigorously that standard residual type error estimator seriously underestimates true of FE solution mesh size h in preasymptotic regime, which first observed by Babuška et al. (Int J Numer Methods Eng 40:3443–3462, 1997) a one dimensional problem. By ...

in this article, we propose and analyze a computational method for numerical solution of general two point boundary value problems. method is tested on problems to ensure the computational eciency. we have compared numerical results with results obtained by other method in literature. we conclude that propose method is computationally ecient and eective.

We consider the high-frequency Helmholtz equation with a given source term, and a small absorption parameter α > 0. The high-frequency (or:

We present an iterative domain decomposition method to solve the Helmholtz equation and related optimal control problems. The proof of convergence of this method relies on energy techniques. This method leads to eecient algorithms for the numerical resolution of harmonic wave propagation problems in heterogeneous media and their control. Une m ethode de d ecomposition de domaine pour l' equatio...

This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the Schrödinger equation as examples. This approach transforms the dense system of the pseudospectral discretization approximately into a sparse system via an equivalent i...

Abstract. We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media, with online parallel complexity that scales empirically as O(NP ), where N is the number of volume unknowns, and P is the number of processors, as long as P = O(N1/5). This sublinear scaling is achieved by domain decomposition, not distributed linear algebra, and improv...

Abstract. The Ultra Weak Variational Formulation (UWVF) of the Helmholtz equation provides a variational framework suitable for discretization using plane wave solutions of the adjoint of the underlying equation. Currently convergence of the method is only proved on the boundary of the domain. However substantial computational evidence exists that shows that the method also converges throughout...