1997
DOI: 10.1121/1.418038
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Rational square-root approximations for parabolic equation algorithms

Abstract: In this article, stable Padé approximations to the function 1+z are derived by choosing a branch cut in the negative half-plane. The Padé coefficients are complex and may be derived analytically to arbitrary order from the corresponding real coefficients associated with the principal branch defined by z<−1, I(z)=0 [I(z) denotes the imaginary part of z]. The characteristics of the corresponding square-root approximation are illustrated for various segments of the complex plane. In particular, for wavegui… Show more

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Cited by 187 publications
(133 citation statements)
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“…The complex Padé approximants to the propagator are obtained using the first method based on the modified Padé approximant with b = 2 [9] while those of the second method based on the rotated Padé approximant propagator are obtained using a rotation angle of h ¼ p 4 [3]. Fig.…”
Section: Numerical Resultsmentioning
confidence: 99%
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“…The complex Padé approximants to the propagator are obtained using the first method based on the modified Padé approximant with b = 2 [9] while those of the second method based on the rotated Padé approximant propagator are obtained using a rotation angle of h ¼ p 4 [3]. Fig.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…Several years ago, Milinazzo [3] proposed the rotation of the square-root operator in the complex plane to address the evanescent waves as follows:…”
Section: Rotated Padé Approximant Operatorsmentioning
confidence: 99%
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“…To realize an efficient estimation of SQR, we use the technique based on a Padé expansion of the square root and a rotating branch-cut technique [23] (θ corresponds to the angle of the rotation):…”
Section: An Approximation Of the Admittance For A Smooth Surfacementioning
confidence: 99%
“…We develop several aspects linked to the implementation of the new integral equations in a Krylov iterative solver in Section 8. An essential aspect is that the approximations of the DN and ND operators are computed by a paraxialization technique [46]. In Section 9, we perform some numerical experiments to show that the generalized integral formulations have some interesting convergence rates.…”
mentioning
confidence: 99%