uu.seUppsala University Publications

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Fast Numerical Techniques for Electromagnetic Problems in Frequency DomainPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2003 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis , 2003. , p. 38
##### Series

Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 916
##### Keywords [en]

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: urn:nbn:se:uu:diva-3884ISBN: 91-554-5827-0 (print)OAI: oai:DiVA.org:uu-3884DiVA, id: diva2:163813
##### Public defence

2004-01-30, Room 1211, Polacksbacken, Uppsala University, Uppsala, 10:15 (English)
##### Opponent

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt831",{id:"formSmash:j_idt831",widgetVar:"widget_formSmash_j_idt831",multiple:true}); Available from: 2003-12-09 Created: 2003-12-09 Last updated: 2011-10-26Bibliographically approved
##### List of papers

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.

1. Stability of the High Frequency Fast Multipole Method for Helmholtz’ Equation in Three Dimensions$(function(){PrimeFaces.cw("OverlayPanel","overlay99036",{id:"formSmash:j_idt925:0:j_idt935",widgetVar:"overlay99036",target:"formSmash:j_idt925:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. A fast multipole method solver for large scale scattering problems$(function(){PrimeFaces.cw("OverlayPanel","overlay99045",{id:"formSmash:j_idt925:1:j_idt935",widgetVar:"overlay99045",target:"formSmash:j_idt925:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. A Parallel Shared Memory Implementation of the Fast Multipole Method for Electromagnetics$(function(){PrimeFaces.cw("OverlayPanel","overlay76937",{id:"formSmash:j_idt925:2:j_idt935",widgetVar:"overlay76937",target:"formSmash:j_idt925:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. A fast multipole accelerated block quasi minimum residual method for solving scattering from perfectly conducting bodies$(function(){PrimeFaces.cw("OverlayPanel","overlay99047",{id:"formSmash:j_idt925:3:j_idt935",widgetVar:"overlay99047",target:"formSmash:j_idt925:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. A minimal residual interpolation method for linear equations with multiple right-hand sides$(function(){PrimeFaces.cw("OverlayPanel","overlay99033",{id:"formSmash:j_idt925:4:j_idt935",widgetVar:"overlay99033",target:"formSmash:j_idt925:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Rapid solution of parameter-dependent linear systems for electromagnetic problems in the frequency domain$(function(){PrimeFaces.cw("OverlayPanel","overlay99038",{id:"formSmash:j_idt925:5:j_idt935",widgetVar:"overlay99038",target:"formSmash:j_idt925:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

7. The minimum residual interpolation method applied to multiple scattering in MM-PO$(function(){PrimeFaces.cw("OverlayPanel","overlay99043",{id:"formSmash:j_idt925:6:j_idt935",widgetVar:"overlay99043",target:"formSmash:j_idt925:6:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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