Fast-Factorization Acceleration of MoM Compressive Domain-Decomposition

Freni, A.; Vita, P. De; Pirinoli, Paola; Matekovits, Ladislau; Vecchi, G.

doi:10.1109/tap.2011.2165474

Cited by 45 publications

(20 citation statements)

References 19 publications

(70 reference statements)

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“…We obtain which, in turn, gives us the expression of as (30) where This expression for is then substituted alongside the expression of into the last row of (20), which helps to solve for , (31) where (32) Now for the solution to the system given by (20), once (31) is solved for , it is substituted into (30) to solve for , and finally the solution is obtained from (29). It can be seen from (29)-(31) that none involves an inversion of a matrix comprising contributions from both magnetic vector potential and electric scalar potential.…”

Section: B Derivation Of a Well-conditioned Reduced System Matrix Sumentioning

confidence: 99%

A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials

Omar

Jiao

2015

IEEE Trans. Microwave Theory Techn.

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An -matrix based linear complexity direct matrix solution is developed for the volume integral equation (VIE) based broadband full-wave extraction of general 3-D circuits. Such circuits are in general electrically small or moderate, but contain arbitrarily shaped lossy conductors immersed in inhomogeneous dielectrics with ports located anywhere in the physical layout of the circuit. In the proposed direct solver, we first develop a well-conditioned VIE formulation without sacrificing the rigor and the advantages of the prevailing formulations. This formulation facilitates a robust direct solution of good accuracy even with a rank-1 representation. We then overcome the numerical challenge of solving the resultant highly unstructured system matrix mixed with both square and rectangular dense and sparse matrices by developing a fast linear complexity direct solution. This direct solution is capable of inverting dense matrices involving over 2 million unknowns in less than 1 h on a single CPU core running at 3 GHz. Numerical simulations of large-scale 3-D circuits and comparisons with state-of-the-art linear complexity iterative VIE solvers have demonstrated the accuracy, efficiency, and linear complexity of the proposed direct VIE solver.

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Section: B Derivation Of a Well-conditioned Reduced System Matrix Sumentioning

confidence: 99%

A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials

Omar

Jiao

2015

IEEE Trans. Microwave Theory Techn.

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“…During the execution of the algorithm, the matrices B1 and B2 do not need to be explicitly generated. For the multisubdomain case, the global model equation (12) does not have to be fully constructed when such a fast algorithm as the MLFMA is applied. Note that all the matrix elements in (12) are from proper integrals and/or convergent improper integrals, where all the singularities are accurately processed by using the method in [17].…”

Section: B Building the Global Model Equationmentioning

confidence: 99%

Integral Equation-Based Nonoverlapping DDM Using the Explicit Boundary Condition

Zheng

Zhou

Wang

2015

IEEE Trans. Antennas Propagat.

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A new integral equation-based nonoverlapping domain decomposition method (NDDM) is proposed for analyzing electromagnetic (EM) scattering from electrically large PEC objects whose MLFMA models are too large for the user's computer to accommodate. The integral equation is first built on the entire PEC surface, and the entire surface is partitioned into some nonoverlapping subsurfaces. The RWG functions are used to expand the surface current on the entire surface. Then, each full-RWG function across some boundary curve is split into two half-RWG functions whose unknown coefficients are constrained by the boundary current continuity (using the explicit boundary condition). The convergence of the outer-iterative scheme of the proposed NDDM is investigated theoretically and demonstrated to be very good, and hence a very large problem can be effectively solved in an ordinary computer. Some numerical examples are provided to demonstrate the correctness and robustness of the proposed method, and to compare the proposed method with the existing overlapping DDMs having similar attributes.Index Terms-Domain decomposition method (DDM), electromagnetic (EM) scattering, full-RWG function, half-RWG function, method of moments (MoM), nonoverlapping subdomain.

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“…For instance, the works [20], [21] include the precorrected-FFT to speed up matrix-vector multiplications in iterative solutions. The authors of [22] proposed and demonstrated the use of the adaptive integral method (AIM) fast factorization to accelerate the synthetic function expansion (SFX) domain decomposition by exploiting the convolutional nature of the Toeplitz kernel using a 3-D FFT. This method is demonstrated to be efficient for volume and quasi-planar problems.…”

Section: Introductionmentioning

confidence: 99%

Contour-FFT Based Spectral Domain MBF Analysis of Large Printed Antenna Arrays

Jha

Craeye

2014

IEEE Trans. Antennas Propagat.

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A fast spectral-domain method is proposed to evaluate the reaction terms between the macro basis functions in regular and non-regular arrays made of identical printed antennas. The presented technique first exploits the filtering capabilities of the macro basis functions in the spectral domain. The method is then strongly accelerated with the help of a newly formulated fast Fourier transform (FFT)-based technique, which is applicable to a contour integration in the complex plane. We name the method as contour-FFT (C-FFT). Besides an effective homogeneous medium term treated with multipoles, a computational complexity of order is achieved for the tabulation of substrate-related reaction terms for any possible relative positions. The complexity of the proposed method is independent from the complexity of the elements. Numerical results obtained with the proposed method are compared with those from a pre-validated reference solution based on the traditional macro basis functions technique; an excellent agreement is observed. Index Terms-Contour deformation, contour-fast Fourier transform (FFT), Green's function, large irregular arrays, macro basis function (MBF), method of moments (MoM), printed antenna, spectral domain method.

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Fast-Factorization Acceleration of MoM Compressive Domain-Decomposition

Cited by 45 publications

References 19 publications

A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials

A Linear Complexity Direct Volume Integral Equation Solver for Full-Wave 3-D Circuit Extraction in Inhomogeneous Materials

Integral Equation-Based Nonoverlapping DDM Using the Explicit Boundary Condition

Contour-FFT Based Spectral Domain MBF Analysis of Large Printed Antenna Arrays

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