Applying Newton's method to (4.13) and (4.14) one gets

_{x}^{ . }x + _{V}^{ . }V |
= | - f(x, V) |
(4.15) |

^{ . }x + ^{ . }V + G^{ . }V |
= | - I(x, V) - G^{ . }(V - V_{S}) . |
(4.16) |

Rearranging (4.15) yields

x = _{x}^{-1 . }
- f(x, V) - _{V}^{ . }V |
(4.17) |

which can be rewritten as

Substituting (4.18) in (4.16) yields

This equation can be rewritten as

with

G_{eq} |
= | - ^{ . }_{x}^{-1 . }_{V} + |
(4.22) |

I_{T} |
= | ^{ . }
+ I(x, V) . |
(4.23) |

Equation (4.21) is similar in form to that obtained by the two-level Newton algorithm. Hence, similar methods can be used to embed distributed devices into a circuit simulator and to provide a decoupling between both simulators even for this quasi full-Newton algorithm.

1999-05-31