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Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by...
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A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
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Two-dimensional fast marching for geometrical optics.

Amedeo Capozzoli, Claudio Curcio, Angelo Liseno

    Optics Express
    |November 18, 2014
    PubMed
    Summary

    This study presents a novel computational method for solving Maxwell

    Area of Science:

    • Computational electromagnetics
    • Wave propagation modeling
    • Numerical methods in physics

    Background:

    • Accurate solutions to Maxwell's equations are crucial for understanding wave phenomena.
    • Existing methods can be computationally intensive for complex geometries and inhomogeneous media.
    • Geometrical optics approximations offer efficiency but require careful implementation.

    Purpose of the Study:

    • To develop a fast and accurate method for determining geometrical optics solutions to Maxwell's equations.
    • To handle inhomogeneous 2D media and TM polarized electric fields efficiently.
    • To accurately discretize scatterer boundaries and computational domains.

    Main Methods:

    • Solving the eikonal equation using the fast marching method.

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  • Employing a computer graphics technique for direct and inverse ray tracing.
  • Solving the transport equation in its integral form.
  • Main Results:

    • The algorithm accurately determines geometrical optics solutions in complex scenarios.
    • It successfully models plane wave scattering from two perfectly conducting circular cylinders, accounting for multiple scattering.
    • It demonstrates the advantage of inverse ray tracing for Luneburg lens simulations.

    Conclusions:

    • The developed approach provides a fast and accurate method for geometrical optics solutions.
    • It effectively handles complex scattering phenomena and inhomogeneous media.
    • The choice between direct and inverse ray tracing depends on the specific application, with inverse tracing preferred for Luneburg lenses.