Regularisation of the Helmholtz decomposition and its application to geomagnetic field modelling
Regularisation of the Helmholtz decomposition and its application to geomagnetic field modelling
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DOI：
10.1007/s13137-010-0001-y
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发表时间：
2010-08-01
影响因子：
1.8
通讯作者：
Michel, V.
中科院分区：
文献类型：
--
作者：
Akram, M.;Michel, V.
在本文中，我们提出了 R-3 中的正则化格林函数 for-del(2) 以及 R-3 中有界域上向量场的正则标量和矢量势。我们证明 -del(2) 的正则化格林函数收敛于实际的格林函数。我们还表明，亥姆霍兹分解的正则化部分收敛于实际分解。这种收敛性是在逐点和分布意义上以及相对于 L-1 范数给出的。此外，还讨论了静态电磁场建模的应用。最后，给出了综合示例的数值结果。
In this paper, we present a regularised Green's function for-del(2) in R-3 and a regularised scalar and vector potential of a vector field on a bounded domain in R-3. We prove that the regularised Green's function for -del(2) converges to the actual Green's function. We also show that the regularised parts of the Helmholtz decomposition converge to the actual decomposition. This convergence is given in the pointwise and the distributional sense as well as with respect to the L-1-norm. Moreover, applications to the modelling of static electromagnetic fields are discussed. Finally, numerical results for a synthetic example are presented.