The Adaptive Cross Approximation Technique for a Volume Integral Equation Method Applied to Nonlinear Magnetostatic Problems

Le-Van, Vinh; Bannwarth, Bertrand; Carpentier, Anthony; Chadebec, Olivier; Guichon, Jean‐Michel; Meunier, G.

doi:10.1109/tmag.2013.2281568

Cited by 12 publications

(9 citation statements)

References 15 publications

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“…In addition, the dimension N is drastically larger than the dimensions M and K. For reasons mentioned above, it takes time to calculate a matrix-vector product Wu as compared with J(S)u, Cu. Hence, we only use the H-matrix method [13,14,15,16] for accelerating the computation of Wu.…”

Section: H-matrix Methodsmentioning

confidence: 99%

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High-speed method for analyzing shielding current density in HTS with cracks: implementation of <i>H</i>-matrix method to GMRES

Takayama

Kamitani

Saitoh

2016

JASSE

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Abstract. A high-speed analysis of a shielding current density in a high-temperature superconducting film containing cracks has been proposed. To this end, a numerical code has been developed for analyzing the shielding current density in an HTS film. In the code, the GMRES(k) with the H-matrix method has been implemented to solve a linear-system obtained by discretizing an initial-boundary-value problem of a nonlinear integro-differential equation with respect to time and space. The results of the computations show that, if the Jacobi scaling is not applied to the linear-system, the Newton method does not converge at a certain time step. Therefore, the Jacobi scaling is an necessary tool for analyzing the shielding current density. Furthermore, by using the GMRES(k) method with the H-matrix method as a linear-system solver, the time evolution of the shielding current can be analyzed with high speed. In conclusion, the speed of the GMRES(k) with H-matrix method is about 221.3 times as fast as that of the LU decomposition.

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Section: H-matrix Methodsmentioning

confidence: 99%

“…For this purpose, we use the GMRES(k) method as a solver of the linear-system and implement the H-matrix method [13,14,15,16] to the GMRES. In addition, we investigate the performance of the GMRES(k) with H-matrix method by simulating the scanning permanent magnet method.…”

Section: Introductionmentioning

confidence: 99%

High-speed method for analyzing shielding current density in HTS with cracks: implementation of <i>H</i>-matrix method to GMRES

Takayama

Kamitani

Saitoh

2016

JASSE

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“…In the present study, the above two transformations are simultaneously performed by means of the H-matrix method [6,7]. In the H-matrix method, a cluster tree is first generated on the basis of the information on node positions.…”

Section: H-matrix Methodsmentioning

confidence: 99%

“…2. Only if a p × q submatrix W (σ,τ) satisfies a specified condition, it is approximated by the ACA decomposition [6,7]: W (σ,τ) UV T . Here, U and V are p × r and q × r matrices, respectively, and r denotes an approximate rank of W (σ,τ) .…”

Section: Acceleration Techniques 41 Speedup Strategymentioning

confidence: 99%

Speedup of Shielding Current Analysis in High-Temperature Superconducting Film: Implementation of H-Matrix Method

Kamitani

Takayama

Saitoh

et al. 2016

Plasma and Fusion Research

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Numerical techniques are proposed for accelerating a linear-system solver appearing in the virtual-voltage method. After the proposed techniques are implemented to a numerical code for analyzing the shielding current density in a high-temperature superconducting film, their performance is numerically evaluated. The results of computations show that, if GMRES is incorporated as a linear-system solver, the speed of the virtual-voltage method will be remarkably enhanced. Moreover, it is also found that the implementation of the H-matrix method to matrix-vector multiplications in GMRES will further improve the speed of the virtual voltage method.

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“…Iterative solvers accelerated by fast methods [13][14][15][16][17][18][19][20][21][22] for matrix vector multiplication can be very effective in many contexts, but their performance is held hostage to the convergence rate of the iteration. In general, VIEs can be well conditioned if the formulation of the second kind integral equation is employed.…”

Section: Introductionmentioning

confidence: 99%

Fast direct solution of 3‐D volume integral equations by skeletonization for dynamic electromagnetic wave problems

Liu

Pan

Sheng

2019

Int J Numerical Modelling

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The skeletonization‐based direct solver is extended to the method of moments (MoM) solution of 3‐D volume integral equations (VIEs) for dynamic electromagnetic wave problems. The direct solver approximates the impedance matrix by the hierarchical data sparse representation through skeletonization and then obtains the inverse matrix implicitly. Improvement is made in the proxy strategy to accelerate the skeletonization. Detailed studies are presented on the behavior of the direct solver with respect to target shape, mesh density, and permittivity. It is revealed that the fast direct solver is promising for nano applications, especially for the cases where large and high‐contrast objects are involved, because iterative solvers always fail in reaching convergence due to the associated ill‐conditioned impedance matrix.

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The Adaptive Cross Approximation Technique for a Volume Integral Equation Method Applied to Nonlinear Magnetostatic Problems

Cited by 12 publications

References 15 publications

High-speed method for analyzing shielding current density in HTS with cracks: implementation of <i>H</i>-matrix method to GMRES

High-speed method for analyzing shielding current density in HTS with cracks: implementation of <i>H</i>-matrix method to GMRES

Speedup of Shielding Current Analysis in High-Temperature Superconducting Film: Implementation of H-Matrix Method

Fast direct solution of 3‐D volume integral equations by skeletonization for dynamic electromagnetic wave problems

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