ORTHOGONAL DECOMPOSITIONS AND BASES FOR 3-DIMENSIONAL VECTOR-FIELDS

被引：9

作者：

AUCHMUTY, G ^{[1
]}

机构：

[1] UNIV HOUSTON,DEPT MATH,HOUSTON,TX 77204

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 1994年 / 15卷 / 5-6期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1080/01630569408816576

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper describes the variational construction of potentials for 3-dimensional vector fields on nice domains in space. Variational principles for the scalar and vector potentials in the Hodge-Weyl decomposition of fields in L2(OMEGA; R3) axe first described. Then a description of orthonormal bases of the associated subspaces is developed. These bases are defined using various eigen-problems involving the scalar and vector Laplacian on the domain. The null eigenspaces of two of these problems define the deRham cohomology groups of the domain. The usual Helmholtz decomposition is also developed, including a description of its spectral expansion, for comparison purposes.

引用

页码：455 / 488

页数：34