采用Galerkin离散方法的T-小波边界元法

王焘; 校金友; 曹衍闯; 张铎

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采用Galerkin离散方法的T-小波边界元法

更新时间：2025-07-09

- 采用Galerkin离散方法的T-小波边界元法
- Fast T-Wavelet Boundary Element Method Using Galerkin Discretization Scheme
- 西安交通大学学报 2010年44卷第12期页码：99-104
- 作者机构：
  
  西北工业大学航天学院,西安,710072
- 作者简介：
- 基金信息：
  
  : 2010-07-05. 作者简介: 王焘(1960-),男,博士,高级工程师. 基金项目: 国家自然科学基金资助项目(10674109);西北工业大学博士学位论文创新基金资助项目(CX200601)
- DOI：
  中图分类号： TB115
- 网络首发：2010-12-10，
  
  纸质出版：2010
- 稿件说明：
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王焘, 校金友, 曹衍闯, 等. 采用Galerkin离散方法的T-小波边界元法[J]. 西安交通大学学报, 2010,44(12):99-104.

Fast T-Wavelet Boundary Element Method Using Galerkin Discretization Scheme[J]. 2010, 44(12): 99-104.
王焘, 校金友, 曹衍闯, 等. 采用Galerkin离散方法的T-小波边界元法[J]. 西安交通大学学报, 2010,44(12):99-104. DOI：

Fast T-Wavelet Boundary Element Method Using Galerkin Discretization Scheme[J]. 2010, 44(12): 99-104. DOI：

摘要

提出一种采用Galerkin离散方法的T-小波边界元新方法.通过边界元形函数的正交变换构造T-小波

以T-小波为试函数和测试函数

采用Galerkin方法离散积分方程

对所形成的系数矩阵进行压缩

有效地降低了边界元分析的计算和存储量.此外

还提出一种系数矩阵快速计算方法

通过泰勒多项式的矩量矩阵变换得到关于泰勒多项式法向导数的矩量矩阵.此新方法的特点是只需构造1组T-小波作为基函数

克服了现有T-小波边界元法采用Petrov-Galerkin方法离散边界积分方程需分别构造试函数和测试函数、用于小波构造的计算和存储量大的问题.通过对2个中、大规模电容提取问题的算例进行求解

结果表明:此新方法在保持精度不变的情况下

可将用于T-小波构造的计算时间和内存占用量分别降低约一半.

Abstract

A new T-wavelet boundary element method(BEM)in which the boundary integralequations are discretized by Galerkin scheme is proposed. The T-wavelets are transformed from the nodal basis functions and then are used to compress the BEM matrices. Moreover

a fast matrix computation method is presented

where the moment matrices with respect to the normal derivatives of the Taylor polynomials are obtained by a multilevel transformation from the moment matrices with respect to the Taylor polynomials. The proposed method adopts only one T-wavelet basis to reduce the computational complexity. The existing matrix compression methods can be employed in the proposed method. Two representative capacitance extraction examples show that the computational time and memory requirements for wavelet construction can be reduced by half of the original method without obvious reduction of the accuracy.

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references

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DAHMEN W, HARBRECHT H, SCHNEIDER R. Compression techniques for boundary integral equations optimal complexity estimates [J]. SIAM J Numer Anal, 2006, 43(6): 2251-2271.

BEYLKIN G, COIFMAN R, ROKHLIN V. Fast wavelet transforms and numerical algorithms [J]. Comm Pure Appl Math, 1991, 44(2): 141-183.

TAUSCH J, WHITE J. Second-kind integral formulations of the capacitance problem [J]. Advances in Computational Mathematics, 1998, 9(1/2):217-232.

TAUSCH J. A variable order wavelet method for the sparse representation of layer potentials in the non-standard form [J]. J Numer Math, 2004, 12(3): 233-254.

TAUSCH J, WHITE J. Multiscale bases for the sparse representation of boundary integral operators on complex geometry [J]. SIAM J Sci Comput, 2003, 24(5): 1610-1629.

TAUSCH J. Sparse BEM for potential theory and Stokes flow using variable order wavelets [J]. Computational Mechanics, 2003, 32(4/6): 312-319.

XIAO Jinyou, TAUSCH J, WEN Lihua. Approximate moment matrix decomposition in wavelet Galerkin BEM [J]. Comput Methods Appl Mech Engng, 2008, 197(45/48): 4000-4006.

XIAO Jinyou, TAUSCH J, HU Yucai. A-posteriori compression of wavelet-BEM matrices [J]. Computational Mechanics, 2009, 44(5): 705-715.

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