Theory and applications of domain decomposition with characteristic mixed finite element of three-dimensional semiconductor transient problem of heat conduction.

*(English)*Zbl 1332.82090Summary: A type of domain decomposition combined with mixed finite element is discussed in this paper to simulate three-dimensional semiconductor transient problem of heat conduction. The potential equation is solved by mixed finite element, and the concentration equations of electron and hole and the heat conduction equation are computed by domain decomposition with characteristic finite element in parallel. An optimal error estimate in \(L^2\) norm is derived for the coupled problem by using some techniques such as variation, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, prior estimates theory and other techniques of partial differential equations. Experimental examples whose numerical data are consistent with theoretical convergence rate are given and computation efficiency is great. Therefore, numerical method of this type can successfully solve this kind of international problems.

##### MSC:

82D37 | Statistical mechanical studies of semiconductors |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

65N06 | Finite difference methods for boundary value problems involving PDEs |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

65N15 | Error bounds for boundary value problems involving PDEs |

65Y05 | Parallel numerical computation |

65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |

65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |