Least squares spectral element method for 2d maxwell equations in the frequency domain

We propose a high order numerical method for the first order Maxwell equations in the frequency domain, defined in media with arbitrary complex shape. Our approach is based on the combination of the least squares approach with the spectral element method. The former frees the solution from spurious modes, that can be found sometimes in classical finite element simulations. Many examples of such non physical solutions exist in literature, and elimination of these spurious effects is a subject of great interest. Spectral elements are a numerical technique for solving partial differential equations which can be regarded as an extension of finite elements: they merge the flexibility of finite elements in dealing with complex geometries, and the better accuracy of spectral methods. Convergence to exact solution is improved by increasing (at run time) the polynomial degree, with no changes on the computational grid: this provides a significant advantage in respect to low order finite element, which necessarily have to resort to grid refinement. In the authors opinion this approach can be successfully used for the treatment of large scale electromagnetic problems or, alternatively, for applications where higher precision is required. We present a few numerical experiments which prove the capability of the method in object.

@Article{MMP04a,
  author       = {Maggio, F. and Mazzarella, G. and Pitzianti, C.},
  title        = {Least squares spectral element method for 2d maxwell equations in the frequency domain},
  journal      = {International Journal of Numerical Modelling: Electronic Networks, Devices and Fields},
  number       = {6},
  volume       = {17},
  pages        = {509--522},
  year         = {2004},
  note         = {idxproject: TAMC},
  keywords     = {Spectral elements; least squares; spurious modes; Maxwell equations},
  url          = {https://publications.crs4.it/pubdocs/2004/MMP04a},
}