Calculation of spheroidal wave functions

Kirby, Paul B.

doi:10.1016/j.cpc.2006.06.006

Cited by 25 publications

(19 citation statements)

References 12 publications

(19 reference statements)

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“…Mimicking the method of [7,8], this function can then be numerically computed by an ODE solver backward in time. In order to be accurate, this approximation will require a large truncature parameter ξ max and the error of the numerical ODE solver will be difficult to control.…”

Section: Lemma 1 For All (M N) ∈ S We Havementioning

confidence: 99%

Non-reflecting boundary condition on ellipsoidal boundary

Barucq

St-Guirons

Tordeux

2012

Numer. Analys. Appl.

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The modeling of wave propagation problems using finite element methods usually requires the truncation of the computation domain around the scatterer of interest. Absorbing boundary conditions are classically considered in order to avoid spurious reflections. In this paper, we investigate some properties of the Dirichlet to Neumann map posed on a spheroidal boundary in the context of the Helmholtz equation.

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Section: Lemma 1 For All (M N) ∈ S We Havementioning

confidence: 99%

Non-reflecting boundary condition on ellipsoidal boundary

Barucq

St-Guirons

Tordeux

2012

Numer. Analys. Appl.

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“…The spheroidal eigenvalues and the regular angular functions can be calcu lated to high accuracy in a systematic way. Unfortunately, the calculation of the prolate radial functions is diffi cult [20,21].…”

Section: Spheroidal Wave Functionsmentioning

confidence: 99%

“…The prolate radial wave functions, mn R , satisfy the following equation [20,21]: . Due to numerical cancellations and slow convergence of the radial functions, multiple-precision arithmetic is employed to increase the accuracy of computations [20,21].…”

Section: Spheroidal Wave Functionsmentioning

confidence: 99%

Electromagnetic Problems Requiring High-Precision Computations

Stefański

2013

IEEE Antennas Propag. Mag.

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“…The eigenvalues λ mn (c) and the angular expansion coefficients satisfy the following recursion formula for r ≥ 0 [22] (23) in which (24) (25) (26) The eigenvalues are determined by the condition that as r → ∞, and various methods have been proposed to calculate the eigenvalues and the expansion coefficients; see Refs. [22][23][24][25][26][27][28][29][30] and references therein.…”

Section: The Angular Function S Mn (Ic η)mentioning

confidence: 99%

Electrostatic potential of point charges inside dielectric prolate spheroids

Deng¹

2008

Journal of Electrostatics

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The exact solution to an electrostatic problem of finding the electric potential of point charges inside a dielectric prolate spheroid is discussed in this note by using the classical electrostatic theory, where the prolate spheroid is embedded in a dissimilar dielectric medium. Such a problem may find its application in hybrid solvent biomolecular simulations, in which biomolecules and a part of solvent molecules within a dielectric cavity are explicitly modeled while a surrounding dielectric continuum is used to model bulk effects of the solvent beyond the cavity. Numerical experiments have demonstrated the convergence of the proposed series solutions. Keywords A general electrostatic problemA finite number of point charges are set inside a dielectric cavity of electric permittivity ε i , which is embedded in a homogeneous, isotropic dielectric medium of electric permittivity ε o . The point charges will polarize the surrounding dielectric medium, which in turn makes a contribution, called the reaction field, to the electric field throughout the cavity. The electric field inside the cavity is thus expressed asΨ in = Ψ s + Ψ RF , where Ψ s is the Coulomb potential which can be simply calculated by the well-known Coulomb's Law, and Ψ RF is the reaction field which will dominate the computational cost for calculating the electric field inside the cavity. Such a problem could be encountered in many applications such as hybrid explicit/ implicit solvent biomolecular dynamics simulations [1][2][3]. In particular, in this note we are interested in the exact solution of the problem when the dielectric cavity is either a sphere or a prolate spheroid, and the surrounding medium is either the pure water solvent or an ionic solvent of low ionic strength.By the principle of linear superposition, the electrostatic problem with a single source charge q inside a dielectric cavity only needs to be considered. It is then well-known that the total electric potential Ψ in (r) inside the cavity is given by the solution of the Poisson equation *Tel

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Calculation of spheroidal wave functions

Cited by 25 publications

References 12 publications

Non-reflecting boundary condition on ellipsoidal boundary

Non-reflecting boundary condition on ellipsoidal boundary

Electromagnetic Problems Requiring High-Precision Computations

Electrostatic potential of point charges inside dielectric prolate spheroids

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