Effective preconditioners for iterative solutions of large-scale surface-integral-equation problems
Author
Malas, Tahir
Advisor
Gürel, Levent
Date
2010Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Show full item recordAbstract
A popular method to study electromagnetic scattering and radiation of threedimensional
electromagnetics problems is to solve discretized surface integral
equations, which give rise to dense linear systems. Iterative solution of such
linear systems using Krylov subspace iterative methods and the multilevel fast
multipole algorithm (MLFMA) has been a very attractive approach for large
problems because of the reduced complexity of the solution. This scheme works
well, however, only if the number of iterations required for convergence of the
iterative solver is not too high. Unfortunately, this is not the case for many
practical problems. In particular, discretizations of open-surface problems and
complex real-life targets yield ill-conditioned linear systems. The iterative solutions
of such problems are not tractable without preconditioners, which can be
roughly defined as easily invertible approximations of the system matrices.
In this dissertation, we present our efforts to design effective preconditioners for
large-scale surface-integral-equation problems. We first address incomplete LU
(ILU) preconditioning, which is the most commonly used and well-established
preconditioning method. We show how to use these preconditioners in a blackbox
form and safe manner. Despite their important advantages, ILU preconditioners
are inherently sequential. Hence, for parallel solutions, a sparseapproximate-inverse
(SAI) preconditioner has been developed. We propose a
novel load-balancing scheme for SAI, which is crucial for parallel scalability.
Then, we improve the performance of the SAI preconditioner by using it for the
iterative solution of the near-field matrix system, which is used to precondition
the dense linear system in an inner-outer solution scheme. The last preconditioner
we develop for perfectly-electric-conductor (PEC) problems uses the same
inner-outer solution scheme, but employs an approximate version of MLFMA for
inner solutions. In this way, we succeed to solve many complex real-life problems
including helicopters and metamaterial structures with moderate iteration counts
and short solution times. Finally, we consider preconditioning of linear systems
obtained from the discretization of dielectric problems. Unlike the PEC case,
those linear systems are in a partitioned structure. We exploit the partitioned
structure for preconditioning by employing Schur complement reduction. In this
way, we develop effective preconditioners, which render the solution of difficult
real-life problems solvable, such as dielectric photonic crystals.
Keywords
Preconditioningincomplete-LU preconditioners
sparse-approximateinverse preconditioners
flexible solvers
variable preconditioning
computational electromagnetics
surface integral equations
multilevel fast multipole algorithm
electromagnetic scattering
parallel computing