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    Accurate Evaluation of Ellipsoidal Harmonics Using Tanh-Sinh Quadrature

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    Author
    Klotz, Thomas S
    Date
    2017-07-20
    Advisor
    Knepley, Matthew G
    Degree
    Master of Arts
    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.
    Keyword
    ellipsoidal harmonics; potential theory; partial differential equations; quadrature; solvation; More... electrostatics; implicit solvation; multipole expansion; tanh-sinh Less...
    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.
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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map