The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

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• 作者：Cé ; cile Piret ^{cecile.piret@uclouvain.be}
• 关键词：Radial basis functions ; RBF ; Closest point method ; Implicit surfaces ; Level set method ; Orthogonal gradients method ; OGr method
• 刊名：Journal of Computational Physics
• 出版年：2012
• 期刊代码：136_00219991
• 类别：cp
• 出版时间：20 May, 2012
• 卷：231
• 期：14
• 页码：4662-4675
• 文件大小：1419 K

摘要

Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time.