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

In this paper we propose a high order numerical method for the first order Maxwell equations in the frequency domain, where equations are 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 least squares approach preserves the solution from spurious modes, that can be found sometimes in classical finite element solutions. Many examples of such non physical solutions exist in literature, and elimination of these spurious effects is a subject of great interest. Spectral elements is a numerical technique for solving partial differential equations which can be regarded as an extension of the finite elements technique: it merges 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 can prove the capability of the method here proposed.

@TechReport{MMP03a,
  author       = {Maggio, F. and Mazzarella, G. and Pitzianti, C.},
  title        = {Least squares spectral element method for 2d maxwell equations in the frequency domain},
  institution  = {CRS4, Center for Advanced Studies, Research and Development in Sardinia},
  number       = {03/46},
  month        = {september},
  year         = {2003},
  address      = {Cagliari, Italy},
  type         = {techreport},
  keywords     = {Maxwell equations, spurious modes, spectral elements},
  url          = {https://publications.crs4.it/pubdocs/2003/MMP03a},
}