\relax \@writefile{toc}{\author{X.-X. Liu}{}} \@writefile{toc}{\author{S. X.-D. Tan}{}} \@writefile{toc}{\author{H. Wang}{}} \@writefile{toc}{\author{H. Yu}{}} \@writefile{loa}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {chapter}{\numberline {13}GPU-Accelerated Envelope-Following Method}{289}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {13.1}Introduction}{289}} \newlabel{fig:ef1}{{13.1(a)}{291}} \newlabel{sub@fig:ef1}{{(a)}{291}} \newlabel{fig:ef2}{{13.1(b)}{291}} \newlabel{sub@fig:ef2}{{(b)}{291}} \@writefile{lof}{\contentsline {figure}{\numberline {13.1}{\ignorespaces Transient envelope-following analysis. (Both two figures reflect backward-Euler style envelope-following.)\relax }}{291}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Illustration of one envelope skip.}}}{291}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {The envelope changes in a slow time scale.}}}{291}} \newlabel{fig:ef_intro}{{13.1}{291}} \@writefile{toc}{\contentsline {section}{\numberline {13.2}The envelope-following method in a nutshell}{292}} \newlabel{sec:ef}{{13.2}{292}} \newlabel{eq:dae}{{13.1}{292}} \newlabel{eq:Newton}{{13.2}{293}} \newlabel{eq:A}{{13.3}{293}} \@writefile{toc}{\contentsline {section}{\numberline {13.3}New parallel envelope-following method}{294}} \newlabel{sec:gmres}{{13.3}{294}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.3.1}GMRES solver for Newton update equation}{294}} \@writefile{lof}{\contentsline {figure}{\numberline {13.2}{\ignorespaces The flow of envelope-following method.\relax }}{295}} \newlabel{fig:ef_flow}{{13.2}{295}} \@writefile{loa}{\contentsline {algocf}{\numberline {10}{\ignorespaces Standard GMRES algorithm.\relax }}{296}} \newlabel{alg:GMRES}{{10}{296}} \newlabel{line:mvp}{{5}{296}} \newlabel{line:newnorm}{{11}{296}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.3.2}Parallelization on GPU platforms}{296}} \newlabel{sec:gpu}{{13.3.2}{296}} \@writefile{lof}{\contentsline {figure}{\numberline {13.3}{\ignorespaces GPU parallel solver for envelope-following update.\relax }}{297}} \newlabel{fig:gmres}{{13.3}{297}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.3.3}Gear-2 based sensitivity calculation}{298}} \newlabel{sec:gear}{{13.3.3}{298}} \newlabel{eq:BE}{{13.4}{298}} \newlabel{eq:sens1}{{13.5}{298}} \newlabel{eq:Gear_t2}{{13.6}{299}} \newlabel{eq:sens2}{{13.7}{299}} \newlabel{eq:Gear_t3}{{13.8}{299}} \newlabel{eq:sensM}{{13.9}{299}} \@writefile{loa}{\contentsline {algocf}{\numberline {11}{\ignorespaces The matrix-free method for Krylov subspace construction.\relax }}{300}} \newlabel{alg:mf_Gear}{{11}{300}} \newlabel{line:mf_Gear_loop}{{4}{300}} \newlabel{line:shift}{{8}{300}} \@writefile{toc}{\contentsline {section}{\numberline {13.4}Numerical examples}{300}} \newlabel{sec:exp}{{13.4}{300}} \@writefile{lof}{\contentsline {figure}{\numberline {13.4}{\ignorespaces Diagram of a zero-voltage quasi-resonant flyback converter.\relax }}{301}} \newlabel{fig:flyback}{{13.4}{301}} \@writefile{lof}{\contentsline {figure}{\numberline {13.5}{\ignorespaces Illustration of power/ground network model.\relax }}{301}} \newlabel{fig:pg}{{13.5}{301}} \newlabel{fig:flybackWhole}{{13.6(a)}{302}} \newlabel{sub@fig:flybackWhole}{{(a)}{302}} \newlabel{fig:flybackZoom}{{13.6(b)}{302}} \newlabel{sub@fig:flybackZoom}{{(b)}{302}} \@writefile{lof}{\contentsline {figure}{\numberline {13.6}{\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 }}{302}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {The whole plot}}}{302}} \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Detail of one EF simulation period}}}{302}} \newlabel{fig:flyback_wave}{{13.6}{302}} \@writefile{lof}{\contentsline {figure}{\numberline {13.7}{\ignorespaces Buck converter solution calculated by envelope-following.\relax }}{303}} \newlabel{fig:buck_wave}{{13.7}{303}} \@writefile{lot}{\contentsline {table}{\numberline {13.1}{\ignorespaces CPU and GPU time comparisons (in seconds) for solving Newton update equation with the proposed Gear-2 sensitivity. \relax }}{303}} \newlabel{table:circuit}{{13.1}{303}} \@writefile{toc}{\contentsline {section}{\numberline {13.5}Summary}{304}} \newlabel{sec:summary}{{13.5}{304}} \@writefile{toc}{\contentsline {section}{\numberline {13.6}Glossary}{304}} \@writefile{toc}{\contentsline {section}{Bibliography}{304}} \@setckpt{Chapters/chapter16/ch16}{ \setcounter{page}{306} \setcounter{equation}{9} \setcounter{enumi}{2} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{22} \setcounter{footnote}{0} \setcounter{mpfootnote}{0} \setcounter{part}{1} \setcounter{chapter}{13} \setcounter{section}{6} \setcounter{subsection}{0} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{7} \setcounter{table}{1} \setcounter{numauthors}{0} \setcounter{parentequation}{4} \setcounter{subfigure}{0} \setcounter{lofdepth}{1} \setcounter{subtable}{0} \setcounter{lotdepth}{1} \setcounter{lstnumber}{9} \setcounter{ContinuedFloat}{0} \setcounter{AlgoLine}{8} \setcounter{algocfline}{11} \setcounter{algocfproc}{11} \setcounter{algocf}{11} \setcounter{proposition}{1} \setcounter{theorem}{0} \setcounter{exercise}{0} \setcounter{example}{0} \setcounter{definition}{0} \setcounter{proof}{1} \setcounter{lstlisting}{0} }