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Fast numerical methods for mixed, si...
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Akhmetgaliyev, Eldar.
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Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems---with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems---with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry./
作者:
Akhmetgaliyev, Eldar.
面頁冊數:
152 p.
附註:
Source: Dissertation Abstracts International, Volume: 77-02(E), Section: B.
Contained By:
Dissertation Abstracts International77-02B(E).
標題:
Applied mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3723583
ISBN:
9781339063935
Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems---with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry.
Akhmetgaliyev, Eldar.
Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems---with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry.
- 152 p.
Source: Dissertation Abstracts International, Volume: 77-02(E), Section: B.
Thesis (Ph.D.)--California Institute of Technology, 2016.
This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.
ISBN: 9781339063935Subjects--Topical Terms:
2122814
Applied mathematics.
Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems---with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry.
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