The PML absorbing boundary condition was introduced in the early 1990s when the computers were not as powerful as they are today. At the time, solving the Maxwell equations in an unbounded space with such numerical methods as FDTD or FEM was a challenging problem. In comparison to previously used ABCs, the PML provided the users with such possibilities as increasing the dynamic range in the FDTD domain, solving problems of larger size, or using a finer discretization. However, a critical question was the optimisation of the parameters of the PML because of the numerical reflection produced by the PML in the discretized space of numerical methods. This chapter discusses the impact of the considerable increase of the power of computers as time has elapsed, from which the question of the optimisation of PMLs can be revisited.  A  simple semi-empirical method is presented for the optimisation of the PML parameters, requiring a small number of experiments, and not too much dependent on the type of application.

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Using the PML in the Context of Modern Computers

  • Jean-Pierre Bérenger

摘要

The PML absorbing boundary condition was introduced in the early 1990s when the computers were not as powerful as they are today. At the time, solving the Maxwell equations in an unbounded space with such numerical methods as FDTD or FEM was a challenging problem. In comparison to previously used ABCs, the PML provided the users with such possibilities as increasing the dynamic range in the FDTD domain, solving problems of larger size, or using a finer discretization. However, a critical question was the optimisation of the parameters of the PML because of the numerical reflection produced by the PML in the discretized space of numerical methods. This chapter discusses the impact of the considerable increase of the power of computers as time has elapsed, from which the question of the optimisation of PMLs can be revisited.  A  simple semi-empirical method is presented for the optimisation of the PML parameters, requiring a small number of experiments, and not too much dependent on the type of application.