[图书][B] Iterative methods and preconditioners for systems of linear equations
G Ciaramella, MJ Gander - 2022 - SIAM
This book gives an introduction to iterative methods and preconditioning for solving
discretized elliptic partial differential equations (PDEs) and optimal control problems …
discretized elliptic partial differential equations (PDEs) and optimal control problems …
On the convergence of overlapping and non-overlapping Schwarz methods for the Cahn–Hilliard equation
In this study, we develop and investigate the Schwarz method with or without overlap for the
Cahn–Hilliard (CH) problem. The CH equation has a wide range of applications, hence it is …
Cahn–Hilliard (CH) problem. The CH equation has a wide range of applications, hence it is …
Convergence of linear and nonlinear Neumann–Neumann method for the Cahn–Hilliard equation
G Garai - Japan Journal of Industrial and Applied Mathematics, 2024 - Springer
In this paper, we propose and analyze a non-overlapping substructuring type algorithm for
the Cahn–Hilliard equation. Being a nonlinear equation, it is of great importance to develop …
the Cahn–Hilliard equation. Being a nonlinear equation, it is of great importance to develop …
Substructured two-grid and multi-grid domain decomposition methods
G Ciaramella, T Vanzan - Numerical Algorithms, 2022 - Springer
Two-level Schwarz domain decomposition methods are very powerful techniques for the
efficient numerical solution of partial differential equations (PDEs). A two-level domain …
efficient numerical solution of partial differential equations (PDEs). A two-level domain …
Convergence of substructuring methods for the Cahn–Hilliard equation
In this paper, we propose and study non-overlapping substructuring type algorithms for the
Cahn–Hilliard (CH) equation, which was originally proposed to describe the phase …
Cahn–Hilliard (CH) equation, which was originally proposed to describe the phase …
On the scalability of the Schwarz method
In this article, we analyse the convergence behaviour and scalability properties of the one-
level Parallel Schwarz method (PSM) for domain decomposition problems in which the …
level Parallel Schwarz method (PSM) for domain decomposition problems in which the …
Closed form optimized transmission conditions for complex diffusion with many subdomains
Optimized transmission conditions in domain decomposition methods have been the focus
of intensive research efforts over the past decade. Traditionally, transmission conditions are …
of intensive research efforts over the past decade. Traditionally, transmission conditions are …
Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues
B Chaudet-Dumas, MJ Gander - Numerical Algorithms, 2023 - Springer
Cross-points in domain decomposition, ie, points where more than two subdomains meet,
have received substantial attention over the past years, since domain decomposition …
have received substantial attention over the past years, since domain decomposition …
A local coarse space correction leading to a well-posed continuous Neumann-Neumann method in the presence of cross points
F Chaouqui, MJ Gander… - … Decomposition Methods in …, 2020 - Springer
Abstract Neumann-Neumann methods (NNMs) are among the best parallel solvers for
discretized partial differential equations, see [12] and references therein. Their common …
discretized partial differential equations, see [12] and references therein. Their common …
Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices
In this work we study the convergence properties of the one-level parallel Schwarz method
with Robin transmission conditions applied to the one-dimensional and two-dimensional …
with Robin transmission conditions applied to the one-dimensional and two-dimensional …