Using the digamma function for basis functions in mesh-free computational methods
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 Ja...
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| Published in: | Engineering analysis with boundary elements Vol. 131; pp. 218 - 227 |
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| Format: | Journal Article |
| Language: | English |
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01.10.2021
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| ISSN: | 0955-7997, 1873-197X |
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| Abstract | 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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| AbstractList | 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. |
| Author | Hromadka, Theodore V. Wilkins, Bryce D. |
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| Cites_doi | 10.1002/nme.1620200104 10.1137/0714043 10.1002/num.20636 10.1016/j.enganabound.2004.07.004 10.1002/num.20365 10.2495/CMEM-V7-N1-45-56 10.4236/am.2017.86069 10.4236/am.2017.85057 10.1016/j.mex.2015.05.005 10.2495/CMEM-V3-N3-269-278 10.1029/2002RG000111 10.1016/j.enganabound.2009.02.005 10.1016/0165-232X(82)90004-0 10.1061/(ASCE)0733-9429(1984)110:3(329) |
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| Keywords | Complex variable boundary element method (CVBEM) Basis functions Applied complex variables Mesh-free methods Potential flow |
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| References | Trefethen (bib0016) 2020 Strack (bib0019) 2003; 41 Hromadka II, Guymon (bib0002) 1982; 6 Johnson, Hromadka II, Hughes, Horton (bib0014) 2015; 3 Wilkins, Hromadka II, McInvale (bib0008) 2020; 8 Johnson, Hromadka II (bib0017) 2015; 2 Poler, Bohannon, Schowalter, Hromadka II (bib0012) 2009; 25 Hromadka II, Whitley (bib0011) 2005; 29 Hromadka II, Guymon (bib0003) 1984; 20 Wilkins, Greenberg, Redmond, Baily, Flowerday, Kratch (bib0004) 2017; 8 Mathon, Johnston (bib0018) 1977; 14 Stirling (bib0001) 1730 Yen, Hromadka II (bib0010) 1986; 2 Wilkins, Hromadka II, Johnson, Boucher, McInvale, Horton (bib0006) 2019; 7 Dean, Hromadka II, Kastner, Phillips (bib0013) 2010; 28 Demoes, Bann, Wilkins, Grubaugh, Hromadka II (bib0007) 2019 Hromadka II, Guymon (bib0009) 1984; 110 Wilkins, Hromadka II, Boucher (bib0005) 2017; 8 Trefethen L.N.. Rational functions. John von Neumann Lecture; 2020a. Brown, Churchill (bib0020) 2009 Bohannon, Hromadka II (bib0021) 2009; 33 Stirling (10.1016/j.enganabound.2021.06.004_bib0001) 1730 Yen (10.1016/j.enganabound.2021.06.004_bib0010) 1986; 2 Dean (10.1016/j.enganabound.2021.06.004_bib0013) 2010; 28 Hromadka II (10.1016/j.enganabound.2021.06.004_bib0009) 1984; 110 Trefethen (10.1016/j.enganabound.2021.06.004_bib0016) 2020 Poler (10.1016/j.enganabound.2021.06.004_bib0012) 2009; 25 Demoes (10.1016/j.enganabound.2021.06.004_bib0007) 2019 Wilkins (10.1016/j.enganabound.2021.06.004_bib0004) 2017; 8 Brown (10.1016/j.enganabound.2021.06.004_bib0020) 2009 Bohannon (10.1016/j.enganabound.2021.06.004_bib0021) 2009; 33 Wilkins (10.1016/j.enganabound.2021.06.004_bib0008) 2020; 8 10.1016/j.enganabound.2021.06.004_bib0015 Strack (10.1016/j.enganabound.2021.06.004_bib0019) 2003; 41 Wilkins (10.1016/j.enganabound.2021.06.004_bib0005) 2017; 8 Hromadka II (10.1016/j.enganabound.2021.06.004_bib0002) 1982; 6 Johnson (10.1016/j.enganabound.2021.06.004_bib0017) 2015; 2 Hromadka II (10.1016/j.enganabound.2021.06.004_bib0011) 2005; 29 Hromadka II (10.1016/j.enganabound.2021.06.004_bib0003) 1984; 20 Wilkins (10.1016/j.enganabound.2021.06.004_bib0006) 2019; 7 Johnson (10.1016/j.enganabound.2021.06.004_bib0014) 2015; 3 Mathon (10.1016/j.enganabound.2021.06.004_bib0018) 1977; 14 |
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| Title | Using the digamma function for basis functions in mesh-free computational methods |
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