Journal
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
Volume 131, Issue -, Pages 218-227Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2021.06.004
Keywords
Complex variable boundary element method (CVBEM); Basis functions; Mesh-free methods; Applied complex variables; Potential flow
Funding
- Hromadka Associates
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This paper discusses the technical aspects of using the digamma function as a basis function for the CVBEM, and demonstrates its utility by applying it to a mixed boundary value problem of the Laplace type.
We examine the utility of a new family of basis functions for use with the Complex Variable Boundary Element Method (CVBEM) and other mesh-free numerical methods for solving partial differential equations. The family of polygamma functions have found use in mathematics since as early as 1730 when James Stirling related the digamma function to the factorial function [1]. Now, we propose using the digamma function, as well as new variants of the digamma function, as basis functions for the CVBEM. This paper discusses technical aspects associated with using the digamma function as a CVBEM basis function. Then, we demonstrate the utility of the proposed basis function by applying it to a mixed boundary value problem of the Laplace type.
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