-\@writefile{toc}{\contentsline {section}{\numberline {15.1}Introduction}{343}}
-\newlabel{fig:ef1}{{15.1(a)}{345}}
-\newlabel{sub@fig:ef1}{{(a)}{345}}
-\newlabel{fig:ef2}{{15.1(b)}{345}}
-\newlabel{sub@fig:ef2}{{(b)}{345}}
-\@writefile{lof}{\contentsline {figure}{\numberline {15.1}{\ignorespaces Transient envelope-following analysis. (Both two figures reflect backward-Euler style envelope-following.)\relax }}{345}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Illustration of one envelope skip.}}}{345}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {The envelope changes in a slow time scale.}}}{345}}
-\newlabel{fig:ef_intro}{{15.1}{345}}
-\@writefile{toc}{\contentsline {section}{\numberline {15.2}The envelope-following method in a nutshell}{346}}
-\newlabel{sec:ef}{{15.2}{346}}
-\newlabel{eq:dae}{{15.1}{346}}
-\newlabel{eq:Newton}{{15.2}{347}}
-\newlabel{eq:A}{{15.3}{347}}
-\@writefile{toc}{\contentsline {section}{\numberline {15.3}New parallel envelope-following method}{348}}
-\newlabel{sec:gmres}{{15.3}{348}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {15.3.1}GMRES solver for Newton update equation}{348}}
-\@writefile{lof}{\contentsline {figure}{\numberline {15.2}{\ignorespaces The flow of envelope-following method.\relax }}{349}}
-\newlabel{fig:ef_flow}{{15.2}{349}}
-\@writefile{loa}{\contentsline {algocf}{\numberline {14}{\ignorespaces Standard GMRES algorithm.\relax }}{350}}
-\newlabel{alg:GMRES}{{14}{350}}
-\newlabel{line:mvp}{{5}{350}}
-\newlabel{line:newnorm}{{11}{350}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {15.3.2}Parallelization on GPU platforms}{350}}
-\newlabel{sec:gpu}{{15.3.2}{350}}
-\@writefile{lof}{\contentsline {figure}{\numberline {15.3}{\ignorespaces GPU parallel solver for envelope-following update.\relax }}{351}}
-\newlabel{fig:gmres}{{15.3}{351}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {15.3.3}Gear-2 based sensitivity calculation}{352}}
-\newlabel{sec:gear}{{15.3.3}{352}}
-\newlabel{eq:BE}{{15.4}{352}}
-\newlabel{eq:sens1}{{15.5}{352}}
-\newlabel{eq:Gear_t2}{{15.6}{353}}
-\newlabel{eq:sens2}{{15.7}{353}}
-\newlabel{eq:Gear_t3}{{15.8}{353}}
-\newlabel{eq:sensM}{{15.9}{353}}
-\@writefile{loa}{\contentsline {algocf}{\numberline {15}{\ignorespaces The matrix-free method for Krylov subspace construction.\relax }}{354}}
-\newlabel{alg:mf_Gear}{{15}{354}}
-\newlabel{line:mf_Gear_loop}{{4}{354}}
-\newlabel{line:shift}{{8}{354}}
-\@writefile{toc}{\contentsline {section}{\numberline {15.4}Numerical examples}{354}}
-\newlabel{sec:exp}{{15.4}{354}}
-\@writefile{lof}{\contentsline {figure}{\numberline {15.4}{\ignorespaces Diagram of a zero-voltage quasi-resonant flyback converter.\relax }}{355}}
-\newlabel{fig:flyback}{{15.4}{355}}
-\@writefile{lof}{\contentsline {figure}{\numberline {15.5}{\ignorespaces Illustration of power/ground network model.\relax }}{355}}
-\newlabel{fig:pg}{{15.5}{355}}
-\newlabel{fig:flybackWhole}{{15.6(a)}{356}}
-\newlabel{sub@fig:flybackWhole}{{(a)}{356}}
-\newlabel{fig:flybackZoom}{{15.6(b)}{356}}
-\newlabel{sub@fig:flybackZoom}{{(b)}{356}}
-\@writefile{lof}{\contentsline {figure}{\numberline {15.6}{\ignorespaces Flyback converter solution calculated by envelope-following. The red curve is traditional SPICE simulation result, and the back curve is the envelope-following output with simulation points marked.\relax }}{356}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {The whole plot}}}{356}}
-\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Detail of one EF simulation period}}}{356}}
-\newlabel{fig:flyback_wave}{{15.6}{356}}
-\@writefile{lof}{\contentsline {figure}{\numberline {15.7}{\ignorespaces Buck converter solution calculated by envelope-following.\relax }}{357}}
-\newlabel{fig:buck_wave}{{15.7}{357}}
-\@writefile{lot}{\contentsline {table}{\numberline {15.1}{\ignorespaces CPU and GPU time comparisons (in seconds) for solving Newton update equation with the proposed Gear-2 sensitivity. \relax }}{357}}
-\newlabel{table:circuit}{{15.1}{357}}
-\@writefile{toc}{\contentsline {section}{\numberline {15.5}Summary}{358}}
-\newlabel{sec:summary}{{15.5}{358}}
-\@writefile{toc}{\contentsline {section}{\numberline {15.6}Glossary}{358}}
-\@writefile{toc}{\contentsline {section}{Bibliography}{358}}
+\@writefile{toc}{\contentsline {section}{\numberline {14.1}Introduction}{299}}
+\newlabel{fig:ef1}{{14.1(a)}{301}}
+\newlabel{sub@fig:ef1}{{(a)}{301}}
+\newlabel{fig:ef2}{{14.1(b)}{301}}
+\newlabel{sub@fig:ef2}{{(b)}{301}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14.1}{\ignorespaces Transient envelope-following analysis. (Both two figures reflect backward-Euler style envelope-following.)\relax }}{301}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Illustration of one envelope skip.}}}{301}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {The envelope changes in a slow time scale.}}}{301}}
+\newlabel{fig:ef_intro}{{14.1}{301}}
+\@writefile{toc}{\contentsline {section}{\numberline {14.2}The envelope-following method in a nutshell}{302}}
+\newlabel{sec:ef}{{14.2}{302}}
+\newlabel{eq:dae}{{14.1}{302}}
+\newlabel{eq:Newton}{{14.2}{303}}
+\newlabel{eq:A}{{14.3}{303}}
+\@writefile{toc}{\contentsline {section}{\numberline {14.3}New parallel envelope-following method}{304}}
+\newlabel{sec:gmres}{{14.3}{304}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {14.3.1}GMRES solver for Newton update equation}{304}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14.2}{\ignorespaces The flow of envelope-following method.\relax }}{305}}
+\newlabel{fig:ef_flow}{{14.2}{305}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {14}{\ignorespaces Standard GMRES algorithm.\relax }}{306}}
+\newlabel{alg:GMRES}{{14}{306}}
+\newlabel{line:mvp}{{5}{306}}
+\newlabel{line:newnorm}{{11}{306}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {14.3.2}Parallelization on GPU platforms}{306}}
+\newlabel{sec:gpu}{{14.3.2}{306}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14.3}{\ignorespaces GPU parallel solver for envelope-following update.\relax }}{307}}
+\newlabel{fig:gmres}{{14.3}{307}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {14.3.3}Gear-2 based sensitivity calculation}{308}}
+\newlabel{sec:gear}{{14.3.3}{308}}
+\newlabel{eq:BE}{{14.4}{308}}
+\newlabel{eq:sens1}{{14.5}{308}}
+\newlabel{eq:Gear_t2}{{14.6}{309}}
+\newlabel{eq:sens2}{{14.7}{309}}
+\newlabel{eq:Gear_t3}{{14.8}{309}}
+\newlabel{eq:sensM}{{14.9}{309}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {15}{\ignorespaces The matrix-free method for Krylov subspace construction.\relax }}{310}}
+\newlabel{alg:mf_Gear}{{15}{310}}
+\newlabel{line:mf_Gear_loop}{{4}{310}}
+\newlabel{line:shift}{{8}{310}}
+\@writefile{toc}{\contentsline {section}{\numberline {14.4}Numerical examples}{310}}
+\newlabel{sec:exp}{{14.4}{310}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14.4}{\ignorespaces Diagram of a zero-voltage quasi-resonant flyback converter.\relax }}{311}}
+\newlabel{fig:flyback}{{14.4}{311}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14.5}{\ignorespaces Illustration of power/ground network model.\relax }}{311}}
+\newlabel{fig:pg}{{14.5}{311}}
+\newlabel{fig:flybackWhole}{{14.6(a)}{312}}
+\newlabel{sub@fig:flybackWhole}{{(a)}{312}}
+\newlabel{fig:flybackZoom}{{14.6(b)}{312}}
+\newlabel{sub@fig:flybackZoom}{{(b)}{312}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14.6}{\ignorespaces Flyback converter solution calculated by envelope-following. The red curve is traditional SPICE simulation result, and the back curve is the envelope-following output with simulation points marked.\relax }}{312}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {The whole plot}}}{312}}
+\@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Detail of one EF simulation period}}}{312}}
+\newlabel{fig:flyback_wave}{{14.6}{312}}
+\@writefile{lof}{\contentsline {figure}{\numberline {14.7}{\ignorespaces Buck converter solution calculated by envelope-following.\relax }}{313}}
+\newlabel{fig:buck_wave}{{14.7}{313}}
+\@writefile{lot}{\contentsline {table}{\numberline {14.1}{\ignorespaces CPU and GPU time comparisons (in seconds) for solving Newton update equation with the proposed Gear-2 sensitivity. \relax }}{313}}
+\newlabel{table:circuit}{{14.1}{313}}
+\@writefile{toc}{\contentsline {section}{\numberline {14.5}Summary}{314}}
+\newlabel{sec:summary}{{14.5}{314}}
+\@writefile{toc}{\contentsline {section}{\numberline {14.6}Glossary}{314}}
+\@writefile{toc}{\contentsline {section}{Bibliography}{314}}
