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1 \relax 
2 \@writefile{toc}{\author{X.-X. Liu}{}}
3 \@writefile{toc}{\author{S. X.-D. Tan}{}}
4 \@writefile{toc}{\author{H. Wang}{}}
5 \@writefile{toc}{\author{H. Yu}{}}
6 \@writefile{loa}{\addvspace {10\p@ }}
7 \@writefile{toc}{\contentsline {chapter}{\numberline {15}GPU-Accelerated Envelope-Following Method}{341}}
8 \@writefile{lof}{\addvspace {10\p@ }}
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10 \@writefile{toc}{\contentsline {section}{\numberline {15.1}Introduction}{341}}
11 \newlabel{fig:ef1}{{15.1(a)}{343}}
12 \newlabel{sub@fig:ef1}{{(a)}{343}}
13 \newlabel{fig:ef2}{{15.1(b)}{343}}
14 \newlabel{sub@fig:ef2}{{(b)}{343}}
15 \@writefile{lof}{\contentsline {figure}{\numberline {15.1}{\ignorespaces Transient envelope-following analysis. (Both two figures reflect backward-Euler style envelope-following.)\relax }}{343}}
16 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Illustration of one envelope skip.}}}{343}}
17 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {The envelope changes in a slow time scale.}}}{343}}
18 \newlabel{fig:ef_intro}{{15.1}{343}}
19 \@writefile{toc}{\contentsline {section}{\numberline {15.2}The envelope-following method in a nutshell}{344}}
20 \newlabel{sec:ef}{{15.2}{344}}
21 \newlabel{eq:dae}{{15.1}{344}}
22 \newlabel{eq:Newton}{{15.2}{345}}
23 \newlabel{eq:A}{{15.3}{345}}
24 \@writefile{toc}{\contentsline {section}{\numberline {15.3}New parallel envelope-following method}{346}}
25 \newlabel{sec:gmres}{{15.3}{346}}
26 \@writefile{toc}{\contentsline {subsection}{\numberline {15.3.1}GMRES solver for Newton update equation}{346}}
27 \@writefile{lof}{\contentsline {figure}{\numberline {15.2}{\ignorespaces The flow of envelope-following method.\relax }}{347}}
28 \newlabel{fig:ef_flow}{{15.2}{347}}
29 \@writefile{loa}{\contentsline {algocf}{\numberline {14}{\ignorespaces Standard GMRES algorithm.\relax }}{348}}
30 \newlabel{alg:GMRES}{{14}{348}}
31 \newlabel{line:mvp}{{5}{348}}
32 \newlabel{line:newnorm}{{11}{348}}
33 \@writefile{toc}{\contentsline {subsection}{\numberline {15.3.2}Parallelization on GPU platforms}{348}}
34 \newlabel{sec:gpu}{{15.3.2}{348}}
35 \@writefile{lof}{\contentsline {figure}{\numberline {15.3}{\ignorespaces GPU parallel solver for envelope-following update.\relax }}{349}}
36 \newlabel{fig:gmres}{{15.3}{349}}
37 \@writefile{toc}{\contentsline {subsection}{\numberline {15.3.3}Gear-2 based sensitivity calculation}{350}}
38 \newlabel{sec:gear}{{15.3.3}{350}}
39 \newlabel{eq:BE}{{15.4}{350}}
40 \newlabel{eq:sens1}{{15.5}{350}}
41 \newlabel{eq:Gear_t2}{{15.6}{351}}
42 \newlabel{eq:sens2}{{15.7}{351}}
43 \newlabel{eq:Gear_t3}{{15.8}{351}}
44 \newlabel{eq:sensM}{{15.9}{351}}
45 \@writefile{loa}{\contentsline {algocf}{\numberline {15}{\ignorespaces The matrix-free method for Krylov subspace construction.\relax }}{352}}
46 \newlabel{alg:mf_Gear}{{15}{352}}
47 \newlabel{line:mf_Gear_loop}{{4}{352}}
48 \newlabel{line:shift}{{8}{352}}
49 \@writefile{toc}{\contentsline {section}{\numberline {15.4}Numerical examples}{352}}
50 \newlabel{sec:exp}{{15.4}{352}}
51 \@writefile{lof}{\contentsline {figure}{\numberline {15.4}{\ignorespaces Diagram of a zero-voltage quasi-resonant flyback converter.\relax }}{353}}
52 \newlabel{fig:flyback}{{15.4}{353}}
53 \@writefile{lof}{\contentsline {figure}{\numberline {15.5}{\ignorespaces Illustration of power/ground network model.\relax }}{353}}
54 \newlabel{fig:pg}{{15.5}{353}}
55 \newlabel{fig:flybackWhole}{{15.6(a)}{354}}
56 \newlabel{sub@fig:flybackWhole}{{(a)}{354}}
57 \newlabel{fig:flybackZoom}{{15.6(b)}{354}}
58 \newlabel{sub@fig:flybackZoom}{{(b)}{354}}
59 \@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 }}{354}}
60 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {The whole plot}}}{354}}
61 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Detail of one EF simulation period}}}{354}}
62 \newlabel{fig:flyback_wave}{{15.6}{354}}
63 \@writefile{lof}{\contentsline {figure}{\numberline {15.7}{\ignorespaces Buck converter solution calculated by envelope-following.\relax }}{355}}
64 \newlabel{fig:buck_wave}{{15.7}{355}}
65 \@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 }}{355}}
66 \newlabel{table:circuit}{{15.1}{355}}
67 \@writefile{toc}{\contentsline {section}{\numberline {15.5}Summary}{356}}
68 \newlabel{sec:summary}{{15.5}{356}}
69 \@writefile{toc}{\contentsline {section}{\numberline {15.6}Glossary}{356}}
70 \@writefile{toc}{\contentsline {section}{Bibliography}{356}}
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