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Bates, R. H. T.; Hagelin, S. I.; Itoh, T.; Machi, Y.; Mittra, R.; Richter, K. R.; Vanbiaricum, G. F.

doi:10.1109/tmtt.1969.1126969

Cited by 2 publications

(3 citation statements)

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“…A two-conductor waveguide presents an interesting setup for the application of the point-matching technique. This technique has been widely used to solve eigenvalue problems in many areas of engineering science [27]. The boundary conditions are imposed at a finite number of points around the periphery of both conductors.…”

Section: Point-matching Numerical Approachmentioning

confidence: 99%

“…In this paper, we explore a new numerical approach to compute the Casimir interaction energy in a two conductor waveguide for arbitrary cross section. The idea is to combine a well known method for computing eigenvalues of the Helmholtz equation, the point-matching technique [27], with the argument theorem to compute explicitly the sum over eigenfrequencies. Our technique is first tested for geometries with known solutions and then is applied to new geometries.…”

Section: Introductionmentioning

confidence: 99%

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Computing the Casimir energy using the point-matching method

et al. 2009

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We use a point-matching approach to numerically compute the Casimir interaction energy for a two perfect-conductor waveguide of arbitrary section. We present the method and describe the procedure used to obtain the numerical results. At first, our technique is tested for geometries with known solutions, such as concentric and eccentric cylinders. Then, we apply the point-matching technique to compute the Casimir interaction energy for new geometries such as concentric corrugated cylinders and cylinders inside conductors with focal lines.Comment: 11 pages, 18 figure

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Section: Point-matching Numerical Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computing the Casimir energy using the point-matching method

et al. 2009

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“…This technique has been widely used to solve eigenvalue problems in many areas of engineering science. 2 The boundary conditions are imposed at a finite number of points around the periphery of both media. For the sake of concreteness, we will bear in mind the situation in which one perfect conductor encloses two dielectric media, as shown in Fig.1, although the method could be applied to more general cases.…”

Section: Point-matching Numerical Approachmentioning

confidence: 99%

Using Boundary Methods to Compute the Casimir Energy

Lombardo

Mazzitelli

Villar

2010

Quantum Field Theory Under the Influence of External Conditions (QFEXT09)

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We discuss new approaches to compute numerically the Casimir interaction energy for waveguides of arbitrary section, based on the boundary methods traditionally used to compute eigenvalues of the 2D Helmholtz equation. These methods are combined with the Cauchy's theorem in order to perform the sum over modes. As an illustration, we describe a point-matching technique to compute the vacuum energy for waveguides containing media with different permittivities. We present explicit numerical evaluations for perfect conducting surfaces in the case of concentric corrugated cylinders and a circular cylinder inside an elliptic one.

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Cited by 2 publications

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Computing the Casimir energy using the point-matching method

Computing the Casimir energy using the point-matching method

Using Boundary Methods to Compute the Casimir Energy

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