On the numerical performance of a domain decomposition method for conformal mapping

Papamichael, N.; Stylianopoulos, Nikos

doi:10.1007/bfb0087905

Cited by 10 publications

(4 citation statements)

References 13 publications

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“…(iii) The results of several numerical examples that confirm the theory of [-9] and support the conjectures made in [10] (cf. (iv) An estimate for the error in the DDM approximation to re(Q), which (unlike our estimate in [9]) is derived without imposing any conditions on the boundary segments Yl, V2, other than requiring that they are Jordan arcs.…”

Section: Introductionsupporting

confidence: 83%

“…(iv) An estimate for the error in the DDM approximation to re(Q), which (unlike our estimate in [9]) is derived without imposing any conditions on the boundary segments Yl, V2, other than requiring that they are Jordan arcs. (This proves one of the conjectures made in [10].) (v) Certain other estimates that connect the contbrmal modules of the quadrilaterals involved in the decomposition with the conformal radii of certain curves associated with the arcs Vl, ~2.…”

Section: Introductionmentioning

confidence: 68%

“…In this paper we consider again the problem of computing approximations to re(Q), and investigate the possibility of extending the application of the DDM to a wider class of quadrilaterals than that studied in [2,3,9,10]. Our main objective is to show that the method does, indeed, have much wider applicability and, for each new application, to derive an estimate of the error in the resulting DDM approximation to re(Q).…”

Section: Introductionmentioning

confidence: 97%

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A domain decomposition method for approximating the conformal modules of long quadrilaterals

Papamichael

Stylianopoulos

1992

Numer. Math.

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Summary. This paper is concerned with the study of a domain decomposition method for approximating the conformal modules of long quadrilaterals. The method has been studied already by us and also by D. Gaier and W.K. Hayman, but only in connection with a special class of quadrilaterals, viz. quadrilaterals where: (a) the defining domain is bounded by two parallel straight lines and two Jordan arcs, and (b) the four specified boundary points are the four corners where the arcs meet the straight lines.Our main purpose here is to explain how the method may be extended to a wider class of quadrilaterals than that indicated above. Mathematics Subject Classification (1991): 30C30, 65E05

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Section: Introductionsupporting

confidence: 83%

Section: Introductionmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 97%

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A domain decomposition method for approximating the conformal modules of long quadrilaterals

Papamichael

Stylianopoulos

1992

Numer. Math.

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“…If all quadrilaterals have the same conformal module, they are conformally equivalent [ 37 ]. The conformal module ( M ) is the rectangle’s aspect ratio in the intermediate space.…”

Section: Design Methodsmentioning

confidence: 99%

Design of a Low-Reflection Flat Lens Antenna Based on Conformal Transformation Optics

Nazarzadeh

Heidari

2023

Micromachines

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In this paper, a wideband flat lens antenna with low reflection and good performance is presented based on conformal transformation optics (CTO). Physical space optimization is applied to eliminate singular refractive index values. Furthermore, we employ the optical path rescaling method to enhance the sub-unity refractive indices and to reduce reflection. Therefore, an implementable all-dielectric isotropic medium is obtained. The final flat lens profile comprises six layers with a constant permittivity value in each layer. Simulation results of the three-dimensional structure indicate that the designed flat lens operates in a wide frequency bandwidth. The flat lens antenna has an S11 value of less than −15 dB in the frequency range of 13 to 30 GHz. The proposed lens was designed and simulated using COMSOL Multiphysics, and radiation performance results were validated using the CST Studio Suite. The simulated radiation pattern shows that the side lobe level is less than −16.5 dB in two simulation software programs, and the half-power beam width varies from 5.6° to 2.7° with increasing frequency. Moreover, the simulated antenna gain is about 28.3–35.5 dBi in the 13–30 GHz frequency range.

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Conformal mapping of long quadrilaterals and thick doubly connected domains

Laugesen

1994

Constr. Approx

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Abstract. In this paper we investigate theoretically an approximation technique for avoiding the crowding phenomenon in numerical conformal mapping. The method applies to conformal maps from rectangles to "long quadrilaterals," i.e., Jordan domains bounded by two parallel straight lines and two Jordan arcs, where the two arcs are far apart. We require that these maps take the four corners of the rectangle to the four corners of the quadrilateral.Our main theorem tackles a conformal mapping problem for doubly connected domains, and we derive from this our results for quadrilaterals. As a corollary, we extend the "domain decomposition" mapping technique of Papamichael and Stylianopoulos.Similar results hold for the inverse maps, from quadrilaterals to rectangles.

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On the numerical performance of a domain decomposition method for conformal mapping

Cited by 10 publications

References 13 publications

A domain decomposition method for approximating the conformal modules of long quadrilaterals

A domain decomposition method for approximating the conformal modules of long quadrilaterals

Design of a Low-Reflection Flat Lens Antenna Based on Conformal Transformation Optics

Conformal mapping of long quadrilaterals and thick doubly connected domains

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