Results 1 to 10 of about 86 (69)
Computing Three-Dimensional Freeform Reflectors with a Scattering Surface [PDF]
EPJ Web of Conferences, 2023 We present a novel approach to computing reflectors with a scattering surface in illumination optics. A scattering model governed by a Fredholm integral equation is derived.
Kronberg Vì C.E. +3 more
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Advanced Nonlinear Studies, 2023 We consider the asymptotic behavior of solutions to the Monge-Ampère equations with slow convergence rate at infinity and fulfill previous results under faster convergence rate by Bao et al. [Monge-Ampère equation on exterior domains, Calc. Var PDE.
Liu Zixiao, Bao Jiguang
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Discrete Aleksandrov solutions of the Monge-Ampere equation
Electronic Journal of Differential Equations, 2022 We make two relaxations of the Oliker-Prussner method for the Dirichlet problem for the Monge-Ampere equation. First we relax the convexity requirement and consider mesh functions which are only discrete convex.
Gerard Awanou
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Design of optical surfaces conform the hyperbolic Monge-Ampère equation [PDF]
EPJ Web of Conferences, 2022 We present a method for designing freeform optical surfaces for illumination optics. By the laws of reflection, refraction and conservation of energy, a fully nonlinear PDE, the Monge-Ampere equation, is derived for the optical surface.
Bertens M.W.M.C. +3 more
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An adaptive least-squares algorithm for the elliptic Monge–Ampère equation
Comptes Rendus. Mécanique, 2023 We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach.
Caboussat, Alexandre +2 more
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Freeform design of a two-reflector system to collimate and shape a point source distribution [PDF]
EPJ Web of Conferences, 2021 We present a method to design a freeform two-reflector system to collimate and shape a beam from a point source. An important generalization compared to previous research is that the output beam can be in an arbitrary direction.
van Roosmalen A.H. +3 more
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Advances in Nonlinear Analysis, 2021 In this paper, we establish the second boundary behavior of the unique strictly convex solution to a singular Dirichlet problem for the Monge-Ampère ...
Wan Haitao, Shi Yongxiu, Liu Wei
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On some exact solutions of heavenly equations in four dimensions
AIP Advances, 2020 Some new classes of exact solutions (so-called functionally invariant solutions) of the elliptic and hyperbolic complex Monge–Ampère equations and of the second heavenly equation are found. Besides, non-invariance of the found classes of solutions of the
Ł. T. Stȩpień
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The connection between the phase problem in optics, focusing of radiation, and the Monge–Kantorovich problem [PDF]
Компьютерная оптика, 2018 We discuss the use of variational principles for solving the phase problem in optics. In this paper, we consider the connection between four fundamental problems: the phase problem in optics, the inverse problem of focusing coherent radiation, the Monge –
Nikolay Kazanskiy +3 more
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Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations
Advanced Nonlinear Studies, 2020 In this paper, we study the Cauchy problem of the parabolic Monge–Ampère ...
Dai Limei, Bao Jiguang
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