parallelisim in the envelope-following method and parallelize the
Newton update solving part, which is the most computational expensive,
in GPU platforms to boost the simulation performance. To further
-speed up the iterative GMRES\index{GMRES} solving for Newton update equation in the
+speed up the iterative GMRES\index{iterative method!GMRES} solving for Newton update equation in the
envelope-following method, we apply the matrix-free\index{matrix-free}
Krylov subspace\index{Krylov subspace} basis
generation technique, which was previously used for RF simulation.
which is the power voltage delivered,
not the fast switching waves in every cycle,
that is of interest to the designers.
-As shown in Fig.~\ref{fig:ef1}, the solid line is
+As shown in Figure~\ref{fig:ef1}, the solid line is
the waveform of the output node in a Buck
converter~\cite{Krein:book'97}, the dots are the simulation points
of SPICE\index{SPICE}, and the appended dash line is the envelope.
switching power converters, the waveform of the carrier in
consequent cycles does not change much, envelope-following method
is an approximation analysis method, which skips over several
-cycles (the dash line in Fig.~\ref{fig:ef2}), the so called
+cycles (the dash line in Figure~\ref{fig:ef2}), the so called
envelope step, without simulating them, and then carries out a
correction, which usually contains a sensitivity-based Newton
iteration or shooting until convergence, in order to begin the
\subfigure[The envelope changes in a slow time scale.]
{\resizebox{.9\textwidth}{!}{\input{./Chapters/chapter16/figures/envelope.pdf_t}}
\label{fig:ef2} }
- \caption{Transient envelope-following\index{envelope-following} analysis.
- (Both two figures reflect backward-Euler\index{backward-Euler} style envelope-following.)}
+ \caption[Transient envelope-following\index{envelope-following} analysis.]{Transient envelope-following\index{envelope-following} analysis.
+ (Both figures reflect backward Euler\index{Euler!backward Euler} style envelope-following.)}
\label{fig:ef_intro}
\end{figure}
%\IEEEpubidadjcol
-Also, iterative GMRES\index{GMRES} solver is typically used in the
+Also, iterative GMRES\index{iterative method!GMRES} solver is typically used in the
envelope-following method to compute the solution of Newton update
due to its efficiency compared to direct LU\index{LU} method.
However, as the Jacobian matrix\index{Jacobian matrix}
