scholarly journals Application of a Sparsity Pattern and Region Clustering for Near Field Sparse Approximate Inverse Preconditioners in Method of Moments Simulations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Carlos Delgado ◽  
Javier Moreno ◽  
Felipe Cátedra
Keyword(s):  
Method Of Moments ◽  
Near Field ◽  
Least Square ◽  
Approximate Inverse ◽  
Sparsity Pattern ◽  
Field Coupling ◽  
Sparse Approximate Inverse ◽  
Coupling Terms ◽  
Linear Least Square ◽  
Least Square Problems

This document presents a technique for the generation of Sparse Inverse Preconditioners based on the near field coupling matrices of Method of Moments simulations where the geometry has been partitioned in terms of regions. A distance parameter is used to determine the sparsity pattern of the preconditioner. The rows of the preconditioner are computed in groups at a time, according to the number of unknowns contained in each region of the geometry. Two filtering thresholds allow considering only the coupling terms with a significant weight for a faster generation of the preconditioner and storing only the most significant preconditioner coefficients in order to decrease the memory required. The generation of the preconditioner involves the computation of as many independent linear least square problems as the number of regions in which the geometry is partitioned, resulting in very good scalability properties regarding its parallelization.

scholarly journals Comparison Results on Preconditioned GAOR Methods for Weighted Linear Least Squares Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Guangbin Wang ◽  
Yanli Du ◽  
Fuping Tan
Keyword(s):  
Least Squares ◽  
Least Square ◽  
Linear Least Squares ◽  
Least Squares Problems ◽  
Numerical Example ◽  
Comparison Results ◽  
Linear Least Squares Problems ◽  
Linear Least Square ◽  
Least Square Problems ◽  
Theoretical Results

We present preconditioned generalized accelerated overrelaxation methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give a numerical example to confirm our theoretical results.

scholarly journals Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1938
Author(s):  
Rafael Florencio ◽  
Álvaro Somolinos ◽  
Iván González ◽  
Felipe Cátedra
Keyword(s):  
Near Field ◽  
Periodic Problem ◽  
Coefficient Matrix ◽  
Multilayer Structures ◽  
Method Of Moment ◽  
Approximate Inverse ◽  
Matrix Vector Multiplication ◽  
Sparse Approximate Inverse ◽  
Matrix Vector ◽  
Discrete Functions

Fast computation of the coefficients of the reduced impedance matrix of the method of moment (MM) is proposed by expanding the basis functions (BFs) in pulses and solving an equivalent periodic problem (EPP) for analyzing large multilayer structures with non-uniform rational basis spline (NURBS) modeling of the embedded layout. These coefficients are required by the computation of sparse approximate inverse (SAI) preconditioner, which leads an efficient iterative version of the MM. This reduced coefficient matrix only considers the near field part of the MM matrix. Discrete functions of small sizes are required to implement the pulse expansion and EPP. These discrete functions of small size lead to discrete cyclic convolutions that are computed in a very fast way by fast Fourier transform (FFT)-accelerated matrix–vector multiplication. Results obtained using a conventional laptop show an analysis of very large multilayer structures with resonant layouts, as whole reflectarrays of electrical size 40 times the vacuum wavelengths, where the iterative MM with a SAI preconditioner can be 22.7 times faster than the pure iterative MM without any preconditioner.

GPS-DERIVED SECULAR VELOCITY FIELD AROUND SANGIHE ISLAND AND ITS IMPLICATION TO THE MOLUCCA SEA SEISMICITY

GEOMATIKA ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 107
Author(s):  
Leni Sophia Heliani ◽  
Cecep Pratama ◽  
Parseno Parseno ◽  
Nurrohmat Widjajanti ◽  
Dwi Lestari
Keyword(s):  
Surface Displacement ◽  
Active Regions ◽  
Least Square ◽  
The Other ◽  
Gps Data ◽  
West Side ◽  
Active Deformation ◽  
Secular Motion ◽  
Small Change ◽  
Linear Least Square

<p><em>Sangihe-Moluccas region is the most active seismicity in Indonesia. Between 2015 to 2018 there is four M6 class earthquake occurred close to the Sangihe-Moluccas region. These seismic active regions representing active deformation which is recorded on installed GPS for both campaign and continuous station. However, the origin of those frequent earthquakes has not been well understood especially related to GPS-derived secular motion. Therefore, we intend to estimate the secular motion inside and around Sangihe island. On the other hand, we also evaluate the effect of seismicity on GPS sites. Since our GPS data were conducted on yearly basis, we used an empirical global model of surface displacement due to coseismic activity. We calculate the offset that may be contained in the GPS site during its period</em><em>. </em><em>We remove the offset and estimate again the secular motion using linear least square. Hence, in comparison with the secular motion without considering the seismicity, we observe small change but systematically shifting the motion. We concluded the seismicity in the Molucca sea from 2015 to 2018 systematically change the secular motion around Sangihe Island at the sub-mm level. Finally, we obtained the secular motion toward each other between the east and west side within 1 to 5.5 cm/year displacement. </em></p>

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