Null field preconditioner for fast 3D full-wave MoM package-board extraction

Negi, Yoginder Kumar; Balakrishnan, N.; Rao, Sadasiva M.; Gope, Dipanjan

doi:10.1109/edaps.2014.7030822

Cited by 6 publications

(5 citation statements)

References 7 publications

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“…where, I 11 , I 22, I 33, and I 44 are the identity block matrices. In the null-field method [9,10], either left-or right-hand scaling is performed for the near-field scaling to diagonal blocks ignoring the fill-in blocks. In contrast, in the proposed Schur's complement method, both left-and right-hand scaling are performed simultaneously, considering fill-in blocks for complete farfield scaling to diagonal blocks.…”

Section: A Preparing For Power Series Computationmentioning

confidence: 99%

“…It is well known that an ill-conditioned matrix will lead to a high number of iterations, thus increasing the overall solution time. To improve the condition number of the matrix, researchers have suggested various types of matrix preconditioning methods like incomplete LU factorized ILUT [8], diagonal blockbased Null-Field [9,10] and Schur complement [11,12]. But the effectiveness of these preconditioners is limited by precondition computation time and condition number improvement of the entire matrix.…”

Section: Introductionmentioning

confidence: 99%

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Fast Power Series Solution of Large 3-D Electrodynamic Integral Equation for PEC Scatterers

2021

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This paper presents a new fast power series solution method to solve the Hierarchal Method of Moment (MoM) matrix for a large complex, perfectly electric conducting (PEC) 3D structures. The proposed power series solution converges in just two (2) iterations which is faster than the conventional fast solver–based iterative solution. The method is purely algebraic in nature and, as such applicable to existing conventional methods. The method uses regular fast solver Hierarchal Matrix (H-Matrix) and can also be applied to Multilevel Fast Multipole Method Algorithm (MLFMA). In the proposed method, we use the scaling of the symmetric near-field matrix to develop a diagonally dominant overall matrix to enable a power series solution. Left and right block scaling coefficients are required for scaling near-field blocks to diagonal blocks using Schur’s complement method. However, only the right-hand scaling coefficients are computed for symmetric near-field matrix leading to saving of computation time and memory. Due to symmetric property, the left side-block scaling coefficients are just the transpose of the right-scaling blocks. Next, the near-field blocks are replaced by scaled near-field diagonal blocks. Now the scaled near-field blocks in combination with far-field and scaling coefficients are subjected to power series solution terminating after only two terms. As all the operations are performed on the near-field blocks, the complexity of scaling coefficient computation is retained as O(N)O⁢(N). The power series solution only involves the matrix-vector product of the far-field, scaling coefficients blocks, and inverse of scaled near-field blocks. Hence, the solution cost remains O(NlogN)O⁢(N⁢l⁢o⁢g⁢N). Several numerical results are presented to validate the efficiency and robustness of the proposed numerical method.

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Section: A Preparing For Power Series Computationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast Power Series Solution of Large 3-D Electrodynamic Integral Equation for PEC Scatterers

2021

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“…Right scaling coefficient

false[{bold-italicα}_{1} false]

for scaling the first row blocks

Z_{11}

and

Z_{13}

can be represented as:

false[{bold-italicα}_{1} false] = (][, \begin{matrix} 1em4pt \\ I_{11} & α_{12} & \begin{matrix} 1em4pt \\ α_{13} & 0 \end{matrix} \\ 0 & I_{22} & \begin{matrix} 1em4pt \\ 0 & 0 \end{matrix} \\ \begin{matrix} 1em4pt \\ 0 \\ 0 \end{matrix} & \begin{matrix} 1em4pt \\ 0 \\ 0 \end{matrix} & \begin{matrix} 1em4pt \\ \begin{matrix} 1em4pt \\ I_{33} \\ 0 \end{matrix} & \begin{matrix} 1em4pt \\ 0 \\ I_{44} \end{matrix} \end{matrix} \end{matrix})

where

\begin{matrix} 1em4pt \\ \begin{matrix} 1em4pt \\ I_{11} & I_{22} \end{matrix} & I_{33} \end{matrix}

and

I_{44}

are the identity block matrices. In the null‐field method [25, 26] either left or right scaling is performed for the near‐field scaling to diagonal blocks ignoring the fill‐in blocks. In contrast, in the proposed Schur's complement method both left and right scaling are performed simultaneously considering fill‐in blocks for complete near‐field scaling to diagonal block.…”

Section: Schur's Complement Preconditionermentioning

confidence: 99%

“…Typically, an inverse of the near‐field MoM blocks can act as a good preconditioner. Block diagonal forms of preconditioner is proposed in [25, 26] where the null‐field method is used to scale the symmetric near‐field matrix to diagonal blocks. In the case of the null‐field method, the fill‐in blocks for scaling is not considered which limits the effective scaling of the near‐field to diagonal block thus giving high storage and matrix–vector product time.…”

Section: Introductionmentioning

confidence: 99%

Symmetric near‐field Schur's complement preconditioner for hierarchal electric field integral equation solver

Negi

Rao

2020

IET Microwaves, Antennas & Propagation

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“…The near-field matrix [21] of a fast solver can also be used as a preconditioner, but the high factorization cost limits the application as a preconditioner. A scaled near-field block-diagonal preconditioner is presented in [22]- [25], but the diagonalization process is complex. The preconditioner should be simple and low-cost in computation, and effective in improving the condition number of the matrix.…”

Section: Introductionmentioning

confidence: 99%

Tridiagonal and Block Tridiagonal Computed Sparse Preconditioners for Large Electrodynamic Electric Field Integral Equation (EFIE) Solution

Negi

Balakrishnan

2022

IEEE Trans. Antennas Propagat.

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In this work, we propose simple and efficient tridiagonal computed sparse preconditioners for improving the condition number for large compressed electric field integral equation (EFIE) method of moment (MoM) matrix. The preconditioner computation is based on the triangle and block triangle interaction and filled tridiagonally. The computed preconditioner is highly sparse and retains the O(N ) complexity of computation and preconditioner matrix solution time. Numerical results show the efficiency and accuracy of the proposed preconditioner.

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Null field preconditioner for fast 3D full-wave MoM package-board extraction

Cited by 6 publications

References 7 publications

Fast Power Series Solution of Large 3-D Electrodynamic Integral Equation for PEC Scatterers

Fast Power Series Solution of Large 3-D Electrodynamic Integral Equation for PEC Scatterers

Symmetric near‐field Schur's complement preconditioner for hierarchal electric field integral equation solver

Tridiagonal and Block Tridiagonal Computed Sparse Preconditioners for Large Electrodynamic Electric Field Integral Equation (EFIE) Solution

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