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A minimal residual interpolation method for linear equations with multiple right-hand sides
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (Waves and Fluids)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. (Waves and Fluids)
2004 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 25, 2126-2144 p.Article in journal (Refereed) Published
Place, publisher, year, edition, pages
2004. Vol. 25, 2126-2144 p.
National Category
Computational Mathematics Computer Science
Identifiers
URN: urn:nbn:se:uu:diva-71122DOI: 10.1137/S106482750241877XOAI: oai:DiVA.org:uu-71122DiVA: diva2:99033
Projects
GEMS
Available from: 2007-03-13 Created: 2007-03-13 Last updated: 2017-11-21Bibliographically approved
In thesis
1. Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain
Open this publication in new window or tab >>Fast Numerical Techniques for Electromagnetic Problems in Frequency Domain
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The Method of Moments is a numerical technique for solving electromagnetic problems with integral equations. The method discretizes a surface in three dimensions, which reduces the dimension of the problem with one. A drawback of the method is that it yields a dense system of linear equations. This effectively prohibits the solution of large scale problems.

Papers I-III describe the Fast Multipole Method. It reduces the cost of computing a dense matrix vector multiplication. This implies that large scale problems can be solved on personal computers. In Paper I the error introduced by the Fast Multipole Method is analyzed. Paper II and Paper III describe the implementation of the Fast Multipole Method.

The problem of computing monostatic Radar Cross Section involves many right hand sides. Since the Fast Multipole Method computes a matrix times a vector, iterative techniques are used to solve the linear systems. It is important that the solution time for each system is as low as possible. Otherwise the total solution time becomes too large. Different techniques for reducing the work in the iterative solver are described in Paper IV-VI. Paper IV describes a block Quasi Minimal Residual method for several right hand sides and Sparse Approximate Inverse preconditioner that reduce the number of iterations significantly. In Paper V and Paper VI a method based on linear algebra called the Minimal Residual Interpolation method is described. It reduces the work in an iterative solver by accurately computing an initial guess for the iterative method.

In Paper VII a hybrid method between Physical Optics and the Fast Multipole Method is described. It can handle large problems that are out of reach for the Fast Multipole Method.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2003. 38 p.
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 916
Keyword
Fast Multipole Method, Minimal Residual Interpolation, Sparse Approximate Inverse preconditioning, Method of Moments, fast solvers, iterative methods, multiple right-hand sides, error analysis
National Category
Computational Mathematics
Research subject
Numerical Analysis
Identifiers
urn:nbn:se:uu:diva-3884 (URN)91-554-5827-0 (ISBN)
Public defence
2004-01-30, Room 1211, Polacksbacken, Uppsala University, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2003-12-09 Created: 2003-12-09 Last updated: 2011-10-26Bibliographically approved

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