相关论文: Multipreconditioning with directional sweeping met…
We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz equation, where the subdomain problems satisfy first-order absorbing (impedance) transmission conditions, and exchange of information between subdomains…
Millimeter wave (mmWave) signals experience orders-of-magnitude more pathloss than the microwave signals currently used in most wireless applications. MmWave systems must therefore leverage large antenna arrays, made possible by the…
In this paper, we develop a multigrid preconditioner to solve Darcy flow in highly heterogeneous porous media. The key component of the preconditioner is to construct a sequence of nested subspaces $W_{\mathcal{L}}\subset…
We develop and analyze a new approach for simultaneously computing multiple solutions to the Helmholtz equation for different frequencies and different forcing functions. The new Multi-Frequency WaveHoltz (MFWH) algorithm is an extension of…
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method from the family of spectral coarse spaces that can efficiently rely on local eigensolves in order to build a robust parallel domain decomposition preconditioner for…
GMRES is one of the most popular iterative methods for the solution of large linear systems of equations that arise from the discretization of linear well-posed problems, such as Dirichlet boundary value problems for elliptic partial…
This paper presents a numerical study on multigrid algorithms of $V$-cycle type for problems posed in the Hilbert space $H(\mathbf{curl})$ in three dimensions. The multigrid methods are designed for discrete problems originated from the…
Massive multiple-input multiple-output (MIMO) systems achieve high sum spectral efficiency by offering an order of magnitude increase in multiplexing gains. In time division duplexing systems, however, the reuse of uplink training pilots…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
A fast method is proposed for solving the high frequency Helmholtz equation. The building block of the new fast method is an overlapping source transfer domain decomposition method for layered medium, which is an extension of the source…
We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…
This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…
We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, the discretized equations are solved with a preconditioned…
In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations.The implementation of high order…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
This paper analyzes the Krylov convergence rate of a Helmholtz problem preconditioned with Multigrid. The multigrid method is applied to the Helmholtz problem formulated on a complex contour and uses GMRES as a smoother substitute at each…
In this work we study how the convergence rate of GMRES is influenced by the properties of linear systems arising from Helmholtz problems near resonances or quasi-resonances. We extend an existing convergence bound to demonstrate that the…
We prove sharp bounds on certain impedance-to-impedance maps (and their compositions) for the Helmholtz equation with large wavenumber (i.e., at high-frequency) using semiclassical defect measures. The paper [GGGLS]…