Author: Roman Wienands
Publisher:
ISBN: 9783884574034
Category :
Languages : en
Pages : 176
Book Description
Extended Local Fourier Analysis for Multigrid
Author: Roman Wienands
Publisher:
ISBN: 9783884574034
Category :
Languages : en
Pages : 176
Book Description
Publisher:
ISBN: 9783884574034
Category :
Languages : en
Pages : 176
Book Description
Practical Fourier Analysis for Multigrid Methods
Author: Roman Wienands
Publisher: CRC Press
ISBN: 1420034995
Category : Mathematics
Languages : en
Pages : 235
Book Description
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detaile
Publisher: CRC Press
ISBN: 1420034995
Category : Mathematics
Languages : en
Pages : 235
Book Description
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detaile
Extending and Automating Fourier Analysis for Multigrid Methods
Author: Hannah Rittich
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Local Fourier Analysis for Saddle-point Problems
Author: Yunhui He
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The numerical solution of saddle-point problems has attracted considerable interest in recent years, due to their indefiniteness and often poor spectral properties that make efficient solution difficult. While much research already exists, developing efficient algorithms remains challenging. Researchers have applied finite-difference, finite element, and finite-volume approaches successfully to discretize saddle-point problems, and block preconditioners and monolithic multigrid methods have been proposed for the resulting systems. However, there is still much to understand. Magnetohydrodynamics (MHD) models the flow of a charged fluid, or plasma, in the presence of electromagnetic fields. Often, the discretization and linearization of MHD leads to a saddle-point system. We present vector-potential formulations of MHD and a theoretical analysis of the existence and uniqueness of solutions of both the continuum two-dimensional resistive MHD model and its discretization. Local Fourier analysis (LFA) is a commonly used tool for the analysis of multigrid and other multilevel algorithms. We first adapt LFA to analyse the properties of multigrid methods for both finite-difference and finite-element discretizations of the Stokes equations, leading to saddle-point systems. Monolithic multigrid methods, based on distributive, Braess-Sarazin, and Uzawa relaxation are discussed. From this LFA, optimal parameters are proposed for these multigrid solvers. Numerical experiments are presented to validate our theoretical results. A modified two-level LFA is proposed for high-order finite-element methods for the Lapalce problem, curing the failure of classical LFA smoothing analysis in this setting and providing a reliable way to estimate actual multigrid performance. Finally, we extend LFA to analyze the balancing domain decomposition by constraints (BDDC) algorithm, using a new choice of basis for the space of Fourier harmonics that greatly simplifies the application of LFA. Improved performance is obtained for some two- and three-level variants.
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The numerical solution of saddle-point problems has attracted considerable interest in recent years, due to their indefiniteness and often poor spectral properties that make efficient solution difficult. While much research already exists, developing efficient algorithms remains challenging. Researchers have applied finite-difference, finite element, and finite-volume approaches successfully to discretize saddle-point problems, and block preconditioners and monolithic multigrid methods have been proposed for the resulting systems. However, there is still much to understand. Magnetohydrodynamics (MHD) models the flow of a charged fluid, or plasma, in the presence of electromagnetic fields. Often, the discretization and linearization of MHD leads to a saddle-point system. We present vector-potential formulations of MHD and a theoretical analysis of the existence and uniqueness of solutions of both the continuum two-dimensional resistive MHD model and its discretization. Local Fourier analysis (LFA) is a commonly used tool for the analysis of multigrid and other multilevel algorithms. We first adapt LFA to analyse the properties of multigrid methods for both finite-difference and finite-element discretizations of the Stokes equations, leading to saddle-point systems. Monolithic multigrid methods, based on distributive, Braess-Sarazin, and Uzawa relaxation are discussed. From this LFA, optimal parameters are proposed for these multigrid solvers. Numerical experiments are presented to validate our theoretical results. A modified two-level LFA is proposed for high-order finite-element methods for the Lapalce problem, curing the failure of classical LFA smoothing analysis in this setting and providing a reliable way to estimate actual multigrid performance. Finally, we extend LFA to analyze the balancing domain decomposition by constraints (BDDC) algorithm, using a new choice of basis for the space of Fourier harmonics that greatly simplifies the application of LFA. Improved performance is obtained for some two- and three-level variants.
Automated Local Fourier Analysis (aLFA) and Geometric Multigrid for Graphene
Author: Nils Kintscher
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The Fourier Analysis of Multigrid-type Iterative Methods
Author: Naomi H. Decker
Publisher:
ISBN:
Category :
Languages : en
Pages : 264
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 264
Book Description
Computational Local Fourier Mode Analysis in the Multigrid Solution of Coupled Systems
Author: David Michael Alber
Publisher:
ISBN:
Category :
Languages : en
Pages : 82
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 82
Book Description
Fourier Analysis of Multigrid Methods for General Systems of PDE
Author: Per Lötstedt
Publisher:
ISBN:
Category :
Languages : en
Pages : 35
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 35
Book Description
Multigrid Techniques
Author: Achi Brandt
Publisher: SIAM
ISBN: 1611970741
Category : Mathematics
Languages : en
Pages : 217
Book Description
This revised edition of a classic text presents the best practices of developing multigrid solvers for large-scale computational problems. This book will be useful to practitioners and researchers, as well as students and instructors, in many areas of computational science and engineering, applied mathematics and numerical analysis.
Publisher: SIAM
ISBN: 1611970741
Category : Mathematics
Languages : en
Pages : 217
Book Description
This revised edition of a classic text presents the best practices of developing multigrid solvers for large-scale computational problems. This book will be useful to practitioners and researchers, as well as students and instructors, in many areas of computational science and engineering, applied mathematics and numerical analysis.
A Multigrid Tutorial
Author: William L. Briggs
Publisher: SIAM
ISBN: 9780898714623
Category : Mathematics
Languages : en
Pages : 318
Book Description
Mathematics of Computing -- Numerical Analysis.
Publisher: SIAM
ISBN: 9780898714623
Category : Mathematics
Languages : en
Pages : 318
Book Description
Mathematics of Computing -- Numerical Analysis.