Related papers: An improved sweeping domain decomposition precondi…
We present an efficient matrix-free geometric multigrid method for the elastic Helmholtz equation, and a suitable discretization. Many discretization methods had been considered in the literature for the Helmholtz equations, as well as many…
We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). To ensure the consistency of…
We investigate the Helmholtz equation with suitable boundary conditions and uncertainties in the wavenumber. Thus the wavenumber is modeled as a random variable or a random field. We discretize the Helmholtz equation using finite…
We explain how to use smooth bivariate splines of arbitrary degree to solve the exterior Helmholtz equation based on a Perfectly Matched Layer (PML) technique. In a previous study (cf. [26]), it was shown that bivariate spline functions of…
Domain decomposition has been shown to be a computationally efficient distributed method for solving large scale entropic optimal transport problems. However, a naive implementation of the algorithm can freeze in the limit of very fine…
For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better…
Due to its significance in terms of wave phenomena a considerable effort has been put into the design of preconditioners for the Helmholtz equation. One option to derive a preconditioner is to apply a multigrid method on a shifted operator.…
In this paper we design, analyse and test domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations, namely for $\mathbf{H}(\mathbf{curl})$…
In this paper, we propose a two-level overlapping additive Schwarz domain decomposition preconditioner for the symmetric interior penalty discontinuous Galerkin method for the second order elliptic boundary value problem with highly…
The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are…
Shuffling has been shown to amplify differential privacy guarantees, enabling a more favorable privacy-utility trade-off. To characterize and compute this amplification, two fundamental analytical frameworks have been proposed: the…
We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…
We study for the first time Schwarz domain decomposition methods for the solution of the Navier equations modeling the propagation of elastic waves. These equations in the time harmonic regime are difficult to solve by iterative methods,…
Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…
The development of scalable and wavenumber-robust iterative solvers for Helmholtz problems is challenging but also relevant for various application fields. In this work, two-level Schwarz domain decomposition preconditioners are enhanced by…
Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…