A New Algorithm of B-Spline FEM for Solving 2-D Electromagnetic Field Boundary Problem in Rectangular Regions─Transferable Gauss Integral Matrix Algorithm

JI Wu-sheng; LI Ying; YOU Bin; ZHAO Ting-gang; LI Bin-ying

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A New Algorithm of B-Spline FEM for Solving 2-D Electromagnetic Field Boundary Problem in Rectangular Regions─Transferable Gauss Integral Matrix Algorithm

更新时间：2025-07-16

- A New Algorithm of B-Spline FEM for Solving 2-D Electromagnetic Field Boundary Problem in Rectangular Regions─Transferable Gauss Integral Matrix Algorithm
- Acta Electronica Sinica Vol. 31, Issue 12, Pages: 1771-1775(2003)
- 作者机构：
  
  1. 上海大学通信工程系,上海,200072
  2. 兰州师范高等专科学校数学系,甘肃,兰州,730070
  3. 兰州大学信息科学与工程学院,甘肃,兰州,730000
  4. 上海大学通信工程系上海,200072
  5. 兰州师范高等专科学校数学系甘肃兰州,730070
  6. 兰州大学信息科学与工程学院甘肃兰州,730000
- 作者简介：
- 基金信息：
- DOI：
  CLC： O441.4
- Published：2003
- 稿件说明：
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JI Wu-sheng, LI Ying, YOU Bin, et al. A New Algorithm of B-Spline FEM for Solving 2-D Electromagnetic Field Boundary Problem in Rectangular Regions─Transferable Gauss Integral Matrix Algorithm[J]. Acta Electronica Sinica, 2003, 31(12): 1771-1775.
DOI：

JI Wu-sheng, LI Ying, YOU Bin, et al. A New Algorithm of B-Spline FEM for Solving 2-D Electromagnetic Field Boundary Problem in Rectangular Regions─Transferable Gauss Integral Matrix Algorithm[J]. Acta Electronica Sinica, 2003, 31(12): 1771-1775. DOI：

摘要

B样条有限元法是解决二维矩形场域中电磁场问题的一种理想的数值计算方法.该方法计算精度高

并且能保证场量应有的连续性.本文构造了一种能快速实施B样条有限元方法的高斯积分矩阵传递算法(TGIMA).该算法通过矩阵形式积运算将每一个高斯积分点的B样条函数值传递到B样条有限元方程的总体系数矩阵中

避免了B样条子段函数互乘的积分运算

从而极大地降低了计算的复杂度.这种算法易于程序实现

有效地减少了计算量.

Abstract

The B-Spline FEM is an effective numerical computation method for solving 2-D electromagnetic field problem of rectangular regions.This method has high computational accuracy without destroying the continuity of adjacent field value.In this paper

a transferable Gauss integral matrix algorithm(TGIMA)which can perform fleetly the B-spline FEM was proposed.By the algorithm

the B-spline function value of every Gauss point was transferred to general coefficient matrix of B-spline FEM equation without integral operations of product of B-spline subinterval function.Consequently the computational complexity can be largely reduced.The algorithm can be programmed conveniently and make the computation easier.

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