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Unconditionally stable algorithms to solve the time-dependent Maxwell equations.

J S Kole1, M T Figge, H De Raedt

  • 1Centre for Theoretical Physics and Materials Science Centre, University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands. j.s.kole@phys.rug.nl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
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We developed stable algorithms for solving Maxwell equations using the Suzuki product-formula approach. These methods are demonstrated for various dimensions and material properties, showing effective light propagation simulation.

Area of Science:

  • Computational physics
  • Electromagnetism
  • Numerical analysis

Background:

  • Solving time-dependent Maxwell equations is crucial for understanding electromagnetic phenomena.
  • Existing numerical methods may face stability challenges, especially for complex systems.
  • The Suzuki product-formula approach offers a potential avenue for stable algorithm development.

Purpose of the Study:

  • To construct a family of unconditionally stable algorithms for time-dependent Maxwell equations.
  • To implement and validate these algorithms in practical one-, two-, and three-dimensional systems.
  • To demonstrate the algorithms' capabilities through simulations of electromagnetic phenomena.

Main Methods:

  • Utilizing the Suzuki product-formula approach for algorithm construction.

Related Experiment Videos

  • Implementing algorithms for systems with spatially varying permittivity and permeability.
  • Applying algorithms to compute eigenmodes, density of states, and light propagation.

    • Main Results:

    • A family of unconditionally stable algorithms for time-dependent Maxwell equations was successfully constructed.
    • Practical implementations for 1D, 2D, and 3D systems were described.
    • Simulations accurately depicted light propagation in photonic band-gap materials and computed system eigenmodes.

    Conclusions:

    • The developed algorithms provide a robust and stable numerical tool for solving Maxwell's equations.
    • These methods are effective for systems with complex material properties and dimensions.
    • The approach facilitates accurate simulation of electromagnetic wave propagation and material properties.