N-body problems: IES<sup>3</sup>: Efficient electrostatic and electromagnetic simulation

Kapur, Sharad; Long, David E.

doi:10.1109/mcse.1998.7102081

Cited by 95 publications

(81 citation statements)

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“…A hybrid method for kernel independent matrix-vector multiplication algorithm was proposed in [16] and [17]. Based on the fact that large blocks of the particle interaction matrix are low rank, this method uses singular value decomposition to sample and sparsify these blocks.…”

Section: Synopsis Of the New Methodmentioning

confidence: 99%

A kernel-independent adaptive fast multipole algorithm in two and three dimensions

Ying

Biros

Zorin

2004

Journal of Computational Physics

449

505

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We present a new fast multipole method for particle simulations. The main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel, and it is based only on kernel evaluations. Instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical FMM tree, we use a continuous distribution of an equivalent density on a surface enclosing the box. To find this equivalent density we match its potential to the potential of the original sources at a surface, in the far field, by solving local Dirichlet-type boundary value problems. The far field evaluations are sparsified with singular value decomposition in 2D or fast Fourier transforms in 3D. We have tested the new method on the single and double layer operators for the Laplacian, the modified Laplacian, the Stokes, the modified Stokes, the Navier, and the modified Navier operators in two and three dimensions. Our numerical results indicate that our method compares very well with the best known implementations of the analytic FMM method for both the Laplacian and modified Laplacian kernels. Its advantage is the (relative) simplicity of the implementation and its immediate extension to more general kernels.

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Section: Synopsis Of the New Methodmentioning

confidence: 99%

A kernel-independent adaptive fast multipole algorithm in two and three dimensions

Ying

Biros

Zorin

2004

Journal of Computational Physics

449

505

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show abstract

“…There exist a lot of fast integral equation methods that can be used to enhance the efficiency of the solution, for instance, FMM [12,[19][20][21], CGFFT [22,23], Pre-corrected FFT [24], SMCG [25], AIM [26], IceCube [27], IMLMQRF [11,28], and MLGFIM [1,2] and so on. In them, 1) FMM is the fastest method with O(N ) complexity for quasistatic problems; 2) SMCG, CGFFT, Pre-corrected FFT, SMCG, and AIM are FFT based methods with O(N log N ) complexity; 3) Ice Cube and IMLMQRF are the methods based on matrix compression technique, i.e., QR factorization, matrix merging, and matrix column and row sampling techniques; 4) MLGFIM is based on a hierarchical structure that is similar to FMM but using the Green's function matrix interpolation method with QR factorization technique.…”

Section: Introductionmentioning

confidence: 99%

Combing Multilevel Green's Function Interpolation Method With Volume Loop Bases for Inductance Extraction Problems

Wang¹,

Zhao²

2008

PIER

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Abstract-In this paper, a fast integral equation method is developed for extracting the inductances in RF ICs, RF MEMs, IC packages, and deep submicron ICs etc. This method combines a recently developed Multilevel Green's Function Interpolation Method (MLGFIM) [1,2] with the volume integral equation discretized using Volume Loop (VL) basis functions. In it, instead of using the filaments model to simulate the currents flowing in the inductors, we use the conventional SWG basis functions for this kind of basis functions is flexible for problems with complex geometries. The shortest path finding algorithm is also used to find the source loop basis functions. The inductance extractions from the straight line, the spiral inductors, the bump, and the parallel buses in this paper demonstrate the validity and efficiency of this hybrid method.

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“…But this computation can be accelerated using a low-rank QR approximation. Low-rank QR approximation has been demonstrated to be effective at accelerating a variety of electromagnetic integral equations [20] [21] [22] [23]. We do not prove that the low-rank QR approximation is superior to multipole expansions, panel methods, or other acceleration schemes; we employ the low-rank QR approximation because the algorithm is independent of the Green's function and can thus be applied to either form of the Biot-Savart law.…”

Section: Introductionmentioning

confidence: 99%

A QR Accelerated Volume-to-Surface Boundary Condition for the Finite-Element Solution of Eddy-Current Problems

et al. 2007

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We are concerned with the solution of time-dependent electromagnetic eddy current problems using a finite element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. We propose a Biot-Savart law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart law. Index TermsMaxwell's equations, computational electromagnetics, low-rank approximation, Biot-Savart law, eddy currents, electromagnetic diffusion, parallel processing.

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N-body problems: IES³: Efficient electrostatic and electromagnetic simulation

Cited by 95 publications

References 1 publication

A kernel-independent adaptive fast multipole algorithm in two and three dimensions

A kernel-independent adaptive fast multipole algorithm in two and three dimensions

Combing Multilevel Green's Function Interpolation Method With Volume Loop Bases for Inductance Extraction Problems

A QR Accelerated Volume-to-Surface Boundary Condition for the Finite-Element Solution of Eddy-Current Problems

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N-body problems: IES3: Efficient electrostatic and electromagnetic simulation

Cited by 95 publications

References 1 publication

A kernel-independent adaptive fast multipole algorithm in two and three dimensions

A kernel-independent adaptive fast multipole algorithm in two and three dimensions

Combing Multilevel Green's Function Interpolation Method With Volume Loop Bases for Inductance Extraction Problems

A QR Accelerated Volume-to-Surface Boundary Condition for the Finite-Element Solution of Eddy-Current Problems

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N-body problems: IES³: Efficient electrostatic and electromagnetic simulation