Accurate Evaluation of Ellipsoidal Harmonics Using Tanh-Sinh Quadrature

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dc.contributor.advisorKnepley, Matthew Gen_US
dc.creatorKlotz, Thomas Sen_US
dc.date.accessioned2017-08-01T16:13:27Zen_US
dc.date.available2017-08-01T16:13:27Zen_US
dc.date.created2017-05en_US
dc.date.issued2017-07-20en_US
dc.date.submittedMay 2017en_US
dc.date.updated2017-08-01T16:13:27Zen_US
dc.description.abstractEllipsoidal 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.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationKlotz, Thomas S. "Accurate Evaluation of Ellipsoidal Harmonics Using Tanh-Sinh Quadrature." (2017) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/96000">https://hdl.handle.net/1911/96000</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/96000en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectellipsoidal harmonicsen_US
dc.subjectpotential theoryen_US
dc.subjectpartial differential equationsen_US
dc.subjectquadratureen_US
dc.subjectsolvationen_US
dc.subjectelectrostaticsen_US
dc.subjectimplicit solvationen_US
dc.subjectmultipole expansionen_US
dc.subjecttanh-sinhen_US
dc.titleAccurate Evaluation of Ellipsoidal Harmonics Using Tanh-Sinh Quadratureen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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