Modular Fast Direct Electromagnetic Analysis Using Local-Global Solution Modes

Adams, Robert J.; Xu, Yuan; Xu, Xin; Choi, J.-S.; Gedney, Stephen D.; Canning, F.X.

doi:10.1109/tap.2008.926769

Cited by 45 publications

(56 citation statements)

References 57 publications

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“…Since we need to use the capacitance C generated from a full-matrix based direct computation to assess the accuracy of the capacitance C' extracted by the proposed solver, and C is not available within feasible computational resources for this large example, we tested the solution error of the proposed solver which is defined as The best complexity reported for the IE-based direct solver is O(Nlog α N) [10,[24][25][26], which is higher than O(N). Next, we compare the proposed linear direct solver with an O(Nlog 2 N) complexity -based direct solver [10][11][12]26].…”

Section: |mentioning

confidence: 99%

“…), where N it denotes the total number of iterations required to reach convergence, and N rhs is the number of right hand sides. In state-of-the-art IE-based solvers [1][2][3][4][5][6][7][8][9]22], fast multipole method and hierarchical algorithms were used to perform a matrix-vector multiplication in O(N) complexity, thereby significantly reducing the complexity of iterative solvers; efficient preconditioners [8][9] were developed to reduce the number of iterations; in the limited work reported on the direct IE solutions [6,10,22,24,25], the best complexity is shown to be O(Nlog α N). No linear complexity has been achieved.…”

Section: Introductionmentioning

confidence: 99%

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Dense Matrix Inversion of Linear Complexity for Integral-Equation-Based Large-Scale 3-D Capacitance Extraction

Chai

Jiao

2011

IEEE Trans. Microwave Theory Techn.

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State-of-the-art integral equation based solvers rely on techniques that can perform a dense matrix-vector multiplication in linear complexity. We introduce  2 matrix as a mathematical framework to enable a highly efficient computation of dense matrices. Under this mathematical framework, as yet, no linear complexity has been established for matrix inversion. In this work, we developed a matrix inverse of linear complexity to directly solve the dense system of linear equations for the capacitance extraction involving arbitrary geometry and non-uniform materials.We theoretically proved the existence of the  2 matrix representation of the inverse of the dense system matrix, and revealed the relationship between the block cluster tree of the original matrix and that of its inverse. We analyzed the complexity and the accuracy of the proposed inverse, and proved its linear complexity as well as controlled accuracy. The proposed inverse-based direct solver has demonstrated clear advantages over state-of-the-art capacitance solvers such as FastCap and HiCap: with fast CPU time and modest memory consumption, and without sacrificing accuracy. It successfully inverts a dense matrix that involves more than one million unknowns associated with a large-scale, on-chip, 3-D interconnect embedded in inhomogeneous materials with fast CPU time and less than 5 GB memory.

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Section: |mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dense Matrix Inversion of Linear Complexity for Integral-Equation-Based Large-Scale 3-D Capacitance Extraction

Chai

Jiao

2011

IEEE Trans. Microwave Theory Techn.

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“…Fast and parallel algorithms such as the fast multipole method (FMM) [15][16][17][18], hybrid FMM and fast Fourier transform (FFT) [19], and parallel adaptive integral method [20,21] have been developed to accelerate the dense matrix-vector product (MVP). Other significant developments include the parallel higher-order method of moments [22] and fast direct solver of the SIE linear system [23][24][25]. With these advancements, the solutions with over several hundred millions and a billion unknowns have been possible [17,18,26].…”

Section: Introductionmentioning

confidence: 99%

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

MacKie-Mason¹,

Greenwood²,

Peng³

2015

PIER

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Abstract-This work investigates an adaptive, parallel and scalable integral equation solver for very large-scale electromagnetic modeling and simulation. A complicated surface model is decomposed into a collection of components, all of which are discretized independently and concurrently using a discontinuous Galerkin boundary element method. An additive Schwarz domain decomposition method is proposed next for the efficient and robust solution of linear systems resulting from discontinuous Galerkin discretizations. The work leads to a rapidly-convergent integral equation solver that is scalable for large multi-scale objects. Furthermore, it serves as a basis for parallel and scalable computational algorithms to reduce the time complexity via advanced distributed computing systems. Numerical experiments are performed on large computer clusters to characterize the performance of the proposed method. Finally, the capability and benefits of the resulting algorithms are exploited and illustrated through different types of real-world applications on high performance computing systems.

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“…F AST direct integral-equation methods are important in many engineering applications, for instance, design optimization and simulating high-Q structures [1] [2]. Matrix compression is a key because arithmetic operations of compressed matrix blocks involve less floating point operations (FLOPs).…”

Section: Introductionmentioning

confidence: 99%

“…Matrix compression is a key because arithmetic operations of compressed matrix blocks involve less floating point operations (FLOPs). Studies show much improved computational efficiency when these methods were applied to metallic structures [1] [2]. In this article, we propose a Quasi Block Cholesky (QBC) algorithm for fast direct solution of the Poggio-Miller-Chang-Harrington-Wu-Tsai (PM-CHWT) formulation for dielectric bodies [3].…”

Section: Introductionmentioning

confidence: 99%

A Quasi Block Cholesky algorithm for fast direct solution of integral-equation method based on the PMCHWT formulation

Wang

2010

2010 IEEE Antennas and Propagation Society International Symposium

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Modular Fast Direct Electromagnetic Analysis Using Local-Global Solution Modes

Cited by 45 publications

References 57 publications

Dense Matrix Inversion of Linear Complexity for Integral-Equation-Based Large-Scale 3-D Capacitance Extraction

Dense Matrix Inversion of Linear Complexity for Integral-Equation-Based Large-Scale 3-D Capacitance Extraction

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

A Quasi Block Cholesky algorithm for fast direct solution of integral-equation method based on the PMCHWT formulation

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