Approximate moment matrix decomposition in wavelet Galerkin BEM

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SUMMARYWe describe a new equivalent charge formulation (ECF), i.e. the combined ECF (CECF), for electrostatic analysis of structures consisting of conductors and dielectrics. The CECF uses a weighted combination of the single-and the adjoint double-layer operators to account for the potential on the conductor-dielectric surface and is found to have better conditioning than the standard ECF. A perturbation approach is presented to insure that the capacitances are computed accurately even when the permittivity ratios of the dielectrics are vary large. Unlike the original perturbation approach, this new approach uses only one system matrix with different right-hand sides.A wavelet Galerkin boundary element method (WGBEM) for solving the ECF and CECF is developed based on the new variable-order WGBEM introduced in (J. Several numerical examples show that the proposed CECF converges faster than the ECF, and that the WGBEM, using both the ECF and CECF, has almost linear complexity in solving large-scale 3-D electrostatic problems. Moreover, since the truncated non-standard form is computed once and then stored, the WGBEM is very suitable for solving problems with multiple right-hand sides, like the perturbation approach in this paper.

Section: Effects Of the Governing Parameterssupporting

confidence: 81%

Section: Wavelet Constructionmentioning

confidence: 92%

“…A proper selection of the value of 0 can largely reduce the memory and time requirements. The optimal value of 0 is case dependent, and we find it is typical in [0.01, 0.1], see [31].…”

Section: Fast Matrix Computationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combined equivalent charge formulations and fast wavelet Galerkin BEM for 3‐D electrostatic analysis

Xiao

Tausch

Cao

et al. 2009

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Wavelet BEM for large‐scale Stokes flows based on the direct integral formulation

Xiao

2011

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SUMMARYThis paper describes a new wavelet boundary element method (WBEM) for large-scale simulations of three-dimensional Stokes problems. It is based on a Galerkin formulation and uses only one set of wavelet basis. A method for the efficient discretization and compression of the double-layer integral operator of Stokes equation is proposed. In addition, a compression strategy for further reducing the setting-up time for the sparse system matrix is also developed. With these new developments, the method has demonstrated a high matrix compression rate for problems with complicated geometries. Applications of the method are illustrated through several examples concerning the modeling of damping forces acting on MEMS resonators including a cantilever resonator oscillating in an unbounded air and a perforated plate resonator oscillating next to a fixed substrate. The numerical results clearly illustrate the efficiency and accuracy of the developed WBEM in these large-scale Stokes flow simulations.

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Wei

Xiang

Zhu

et al. 2023

A novel method of combination of wavelet‐based boundary element method (WBEM) with frequency‐independent fundamental solutions is proposed to determine the band structures of fluid–solid phononic crystals (PCs) with square and triangular lattices. Integral equations established are based on the frequency‐independent fundamental solutions, which can avoid nonlinear eigenvalue problems and reduce computing time. Domain integral terms arising from the use of frequency‐independent fundamental solutions are handled with the radial integration method (RIM) and dual reciprocity method (DRM), respectively. The results show the lower precision in high frequency domain of using RIM to handle domain integral terms than that of using DRM, which can be solved by increasing Gauss point. The B‐spline wavelet on the interval and wavelet coefficients are applied to approximate the physical boundary conditions. It is proved that coupling conditions between matrix and scatterers and Bloch theorem are also applicable to wavelet coefficients. Some small matrix entries generated by wavelet vanishing moment characteristics are truncated by the provided matrix compression technique, and the influence of compressed matrices on the results is studied. Furthermore, the final Eigen equations constructed are modified to avoid numerical instability. Some examples are provided to demonstrate the accuracy and efficiency of the proposed method.