[图书][B] An introduction to domain decomposition methods: algorithms, theory, and parallel implementation
The purpose of this text is to offer an overview of the most popular domain decomposition
methods for partial differential equations (PDEs). The presentation is kept as much as …
methods for partial differential equations (PDEs). The presentation is kept as much as …
A class of iterative solvers for the Helmholtz equation: Factorizations, sweeping preconditioners, source transfer, single layer potentials, polarized traces, and …
Solving time-harmonic wave propagation problems by iterative methods is a difficult task,
and over the last two decades an important research effort has gone into developing …
and over the last two decades an important research effort has gone into developing …
Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption
This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations
with absorption, where the PDE is discretised using curl-conforming finite-element methods …
with absorption, where the PDE is discretised using curl-conforming finite-element methods …
The method of polarized traces for the 2D Helmholtz equation
L Zepeda-Núnez, L Demanet - Journal of Computational Physics, 2016 - Elsevier
We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous
acoustic media, with online parallel complexity that scales optimally as O (NL), where N is …
acoustic media, with online parallel complexity that scales optimally as O (NL), where N is …
A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems
A non-overlapping domain decomposition method (DDM) is proposed for the parallel finite-
element solution of large-scale time-harmonic wave problems. It is well-known that the …
element solution of large-scale time-harmonic wave problems. It is well-known that the …
A comparison of coarse spaces for Helmholtz problems in the high frequency regime
Solving time-harmonic wave propagation problems in the frequency domain and within
heterogeneous media brings many mathematical and computational challenges, especially …
heterogeneous media brings many mathematical and computational challenges, especially …
A non-overlapping domain decomposition method with perfectly matched layer transmission conditions for the Helmholtz equation
It is well-known that the convergence rate of non-overlapping domain decomposition
methods (DDMs) applied to the parallel finite-element solution of large-scale time-harmonic …
methods (DDMs) applied to the parallel finite-element solution of large-scale time-harmonic …
Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonself-adjoint problems
Generalized eigenvalue problems on the overlap (GenEO) is a method for computing an
operator-dependent spectral coarse space to be combined with local solves on subdomains …
operator-dependent spectral coarse space to be combined with local solves on subdomains …
3D finite-difference and finite-element frequency-domain wave simulation with multilevel optimized additive Schwarz domain-decomposition preconditioner: A tool for …
Efficient frequency-domain full-waveform inversion (FWI) of long-offset node data can be
designed with a few discrete frequencies, which lead to modest data volumes to be …
designed with a few discrete frequencies, which lead to modest data volumes to be …