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A comparision

There are many numerical methods to solve optical problems. Besides the Finite Element Method (FEM), these are

 

  • Finite Difference Time Domain (FDTD) methods
  • Finite Difference Frequency Domain (FDFD) methods
  • Mode Matching methods
  • Rigorous Coupled Wave Analysis (RCWA)
  • Boundary Element methods (BEM)
  • Beam Propagation Methods
  • Method of Lines (MoL)

and many more. Each method has its pros and cons. For each method applications are known, where this method is superior to the other ones.

Some of the following key features of the Finite Element Method belong also to some of the other methods, but there is no competing method which covers all of them:

  • Exact and easy treatment of complicated geometries
  • Rigourous treatment of full Maxwell's equations
  • Rigorous treatment of wave propagation on unbounded and possibly inhomogeneous domains available
  • Rigorous treatment of optical sources from plane waves and Gaussian beams to point sources available
  • Arbitrary high-order methods for fast convergence available
  • Error control available
  • Automatic adaptive mesh refinement available

The Finite Element Method provides a general, rigorous, versatile, and very fast method to the solution of scientific and technological challenges.