Full wave solution of dielectric loaded waveguides and shielded microstrips utilizing finite difference and the conjugate gradient method

1991 ◽  
Vol 1 (4) ◽  
pp. 346-357
Author(s):  
V. Narayanan ◽  
M. Manela ◽  
R. K. Lade ◽  
T. K. Sarkar
Keyword(s):  
Finite Difference ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Wave Solution ◽  
Full Wave

scholarly journals COMBINING MULTIGRID AND WAVELET IDEAS TO CONSTRUCT MORE EFFICIENT MULTISCALE ALGORITHMS

2003 ◽  
Vol 02 (04) ◽  
pp. 483-495 ◽  
Author(s):  
STEFAN GOEDECKER ◽  
CLAIRE CHAUVIN
Keyword(s):  
Finite Difference ◽  
Plane Wave ◽  
Charge Density ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Preconditioned Conjugate Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Multiscale Algorithms ◽  
Wavelet Transformations

It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods, can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns out to be particularly fruitful. We propose a modified multigrid V cycle scheme that is not only much simpler, but also more efficient than the standard V cycle. Whereas in the traditional V cycle the residue is passed to the coarser grid levels, this new scheme does not require the calculation of a residue. Instead it works with copies of the charge density on the different grid levels that were obtained from the underlying charge density on the finest grid by wavelet transformations. This scheme is not limited to the pure wavelet setting, where it is faster than the preconditioned conjugate gradient method, but equally well applicable for finite difference discretizations.

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