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SCEE-2000
Scientific Computing in Electrical Engineering
August 20 - 23, 2000
Warnemünde, Germany

 
 
Thomas Vaupel, (University of Wuppertal)
Convergence properties of linear equation solvers applied to iterative spectral domain integral equation methods

   Integral equation techniques for the simulation of (M)MIC-structures have become very popular in the last years since they offer a high versatility combined with a minimum of discretization effort. On the other hand the computational and storage complexity increases with O(N^2) or even O(N^3) using conventional implementations of the Method of Moments (MoM).In order to reduce this increasing computational effort we currently develop several strategies for a combination within an overall simulation framework. Up to a certain number of unknowns, the efficient generation of the explicit system matrix with the subsequent solution of the linear system of equations remains the best choice for the analysis of circuits of moderate size.  A promising method for larger structures is the iterative MoM based on a fast implicit spectral domain matrix-vector product evaluation as part of any iterative linear equation solver. In contrast to Conjugate Gradient type FFT-iterative methods, our method is not restricted on uniform discretization strategies, but it still suffers from the poor convergence properties of the iterative solvers in context with strongly nonuniform discretized structures.In this context we present the convergence behavior of different solvers applied to structures with a strictly uniform discretization up to antenna subarrays with a strongly nonuniform discretization.  Furthermore we have applied matrix scaling techniques and a complex matrix mapping to equivalent real valued equation systems and diagonal preconditioning. Unfortunately all measures applied so far lead to a nonsatisfactory convergence in context with structures modeled with a strongly nonuniform discretization and we cannot observe a significant advantage of any solver. The most stable solution process we get so far with the Transpose Free Quasi Minimal Residual (TFQMR)-method, but the number of necessary matrix-vector products remains nearly the same as with other Krylov subspace methods like the Standard Conjugate Gradient or Conjugate Residual methods. 

* University of Wuppertal, Chair of Electromagnetic Theory, Fuhlrottstr. 10, 42097 Wuppertal, Germany .
 

 

SCEE-2000
last updated 14.06.2000