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.

scholarly journals Improved Generalized Single-Source Tangential Equivalence Principle Algorithm with Contact-Region Modeling Method for Array Structures

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yao Han ◽  
Hanru Shao ◽  
Jianfeng Dong
Keyword(s):  
Equivalence Principle ◽  
Contact Region ◽  
Near Field ◽  
Single Source ◽  
Matrix Vector Multiplication ◽  
The Matrix ◽  
Array Structures ◽  
Fast Multipole Algorithm ◽  
Matrix Vector ◽  
Equivalence Principle Algorithm

An improved generalized single-source tangential equivalence principle algorithm (GSST-EPA) is proposed for analyzing array structures with connected elements. In order to use the advantages of GSST-EPA, the connected array elements are decomposed and computed by a contact-region modeling (CRM) method, which makes that each element has the same meshes. The unknowns of elements can be transferred onto the equivalence surfaces by GSST-EPA. The scattering matrix in GSST-EPA needs to be solved and stored only once due to the same meshes for each element. The shift invariant of translation matrices is also used to reduce the computation of near-field interaction. Furthermore, the multilevel fast multipole algorithm (MLFMA) is used to accelerate the matrix-vector multiplication in the GSST-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.

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 BICGSTAB-FFT Method of Moments with NURBS for Analysis of Planar Generic Layouts Embedded in Large Multilayer Structures

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1476 ◽  
Author(s):  
Rafael Florencio ◽  
Álvaro Somolinos ◽  
Iván González ◽  
Felipe Cátedra
Keyword(s):  
Method Of Moments ◽  
Multilayer Structure ◽  
Fourier Transforms ◽  
Periodic Problem ◽  
Basis Functions ◽  
Multilayer Structures ◽  
Method Of Moment ◽  
Efficient Computation ◽  
Normalized Error ◽  
Nurbs Surfaces

BICGSTAB-FFT method of moment (MM) scheme is proposed to analyze several levels of planar generic layouts embedded in large multilayer structures when the layout geometries are modeled by NURBS surfaces. In this scheme, efficient computation of normalized error defined in iterative bi-conjugate gradient stabilized (BICGSTAB) method for large multilayer structure analysis problems is implemented. The efficient computation is based on pulse expansion with dense equi-spaced mesh of generalized rooftop basis functions (BFs) defined on NURBS surfaces and equivalent periodic problem (EPP) in order to apply fast Fourier transforms (FFT). Moreover, efficient computation of Green’s functions for multilayer structure is implemented for near and far field regions. Experimental and numerical validations of whole printed reflect array antennas of electrical size between 8 and 16 times the vacuum wavelengths are shown. In these validations, CPU time consumptions of the proposed method are obtained with results between few minutes and half an hour using a conventional laptop.

scholarly journals Sparse Matrix-Vector Multiplication on GPGPUs

2017 ◽  
Vol 43 (4) ◽  
pp. 1-49 ◽  
Author(s):  
Salvatore Filippone ◽  
Valeria Cardellini ◽  
Davide Barbieri ◽  
Alessandro Fanfarillo
Keyword(s):  
Sparse Matrix ◽  
Matrix Vector Multiplication ◽  
Matrix Vector

scholarly journals Private and rateless adaptive coded matrix-vector multiplication

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rawad Bitar ◽  
Yuxuan Xing ◽  
Yasaman Keshtkarjahromi ◽  
Venkat Dasari ◽  
Salim El Rouayheb ◽  
...  
Keyword(s):  
Computing Methods ◽  
Erasure Codes ◽  
Time Varying ◽  
New Paradigm ◽  
Matrix Vector Multiplication ◽  
Processing Data ◽  
Computationally Intensive ◽  
Matrix Vector ◽  
Monitoring Devices ◽  
Theoretical Results

AbstractEdge computing is emerging as a new paradigm to allow processing data near the edge of the network, where the data is typically generated and collected. This enables critical computations at the edge in applications such as Internet of Things (IoT), in which an increasing number of devices (sensors, cameras, health monitoring devices, etc.) collect data that needs to be processed through computationally intensive algorithms with stringent reliability, security and latency constraints. Our key tool is the theory of coded computation, which advocates mixing data in computationally intensive tasks by employing erasure codes and offloading these tasks to other devices for computation. Coded computation is recently gaining interest, thanks to its higher reliability, smaller delay, and lower communication costs. In this paper, we develop a private and rateless adaptive coded computation (PRAC) algorithm for distributed matrix-vector multiplication by taking into account (1) the privacy requirements of IoT applications and devices, and (2) the heterogeneous and time-varying resources of edge devices. We show that PRAC outperforms known secure coded computing methods when resources are heterogeneous. We provide theoretical guarantees on the performance of PRAC and its comparison to baselines. Moreover, we confirm our theoretical results through simulations and implementations on Android-based smartphones.

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