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dc.contributor.advisor Knepley, Matthew G
dc.creatorKlotz, Thomas S
dc.date.accessioned 2017-08-01T16:13:27Z
dc.date.available 2017-08-01T16:13:27Z
dc.date.created 2017-05
dc.date.issued 2017-07-20
dc.date.submitted May 2017
dc.identifier.citation Klotz, Thomas S. "Accurate Evaluation of Ellipsoidal Harmonics Using Tanh-Sinh Quadrature." (2017) Master’s Thesis, Rice University. https://hdl.handle.net/1911/96000.
dc.identifier.urihttps://hdl.handle.net/1911/96000
dc.description.abstract Ellipsoidal coordinates are an orthogonal coordinate system under which the Laplace equation can be solved by separation of variables. While this has many benefits over spherical coordinates for a variety of potential problems, computation in ellipsoidal coordinates is difficult. Most notably, high-order harmonics can lack closed-form solutions and the associated normalization constants require approximating a singular integral. We provide a method for computing normalization constants to machine precision using tanh-sinh quadrature which exhibits exponential convergence for a large class of functions with singular endpoints. Combined with previous efforts to make ellipsoidal harmonics more accessible, the result is a library which makes computation in ellipsoidal coordinates as accessible as computation in spherical coordinates. Finally, we apply our implementation to the mixed-dielectric solvation problem and provide work-precision analysis for the results.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectellipsoidal harmonics
potential theory
partial differential equations
quadrature
solvation
electrostatics
implicit solvation
multipole expansion
tanh-sinh
dc.title Accurate Evaluation of Ellipsoidal Harmonics Using Tanh-Sinh Quadrature
dc.type Thesis
dc.date.updated 2017-08-01T16:13:27Z
dc.type.material Text
thesis.degree.department Computational and Applied Mathematics
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Masters
thesis.degree.name Master of Arts


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