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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}{335}}
8 \@writefile{lof}{\addvspace {10\p@ }}
9 \@writefile{lot}{\addvspace {10\p@ }}
10 \@writefile{toc}{\contentsline {section}{\numberline {15.1}Introduction}{335}}
11 \newlabel{fig:ef1}{{15.1(a)}{337}}
12 \newlabel{sub@fig:ef1}{{(a)}{337}}
13 \newlabel{fig:ef2}{{15.1(b)}{337}}
14 \newlabel{sub@fig:ef2}{{(b)}{337}}
15 \@writefile{lof}{\contentsline {figure}{\numberline {15.1}{\ignorespaces Transient envelope-following analysis. (Both two figures reflect backward-Euler style envelope-following.)\relax }}{337}}
16 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Illustration of one envelope skip.}}}{337}}
17 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {The envelope changes in a slow time scale.}}}{337}}
18 \newlabel{fig:ef_intro}{{15.1}{337}}
19 \@writefile{toc}{\contentsline {section}{\numberline {15.2}The envelope-following method in a nutshell}{338}}
20 \newlabel{sec:ef}{{15.2}{338}}
21 \newlabel{eq:dae}{{15.1}{338}}
22 \newlabel{eq:Newton}{{15.2}{339}}
23 \newlabel{eq:A}{{15.3}{339}}
24 \@writefile{toc}{\contentsline {section}{\numberline {15.3}New parallel envelope-following method}{340}}
25 \newlabel{sec:gmres}{{15.3}{340}}
26 \@writefile{toc}{\contentsline {subsection}{\numberline {15.3.1}GMRES solver for Newton update equation}{340}}
27 \@writefile{lof}{\contentsline {figure}{\numberline {15.2}{\ignorespaces The flow of envelope-following method.\relax }}{341}}
28 \newlabel{fig:ef_flow}{{15.2}{341}}
29 \@writefile{loa}{\contentsline {algocf}{\numberline {14}{\ignorespaces Standard GMRES algorithm.\relax }}{342}}
30 \newlabel{alg:GMRES}{{14}{342}}
31 \newlabel{line:mvp}{{5}{342}}
32 \newlabel{line:newnorm}{{11}{342}}
33 \@writefile{toc}{\contentsline {subsection}{\numberline {15.3.2}Parallelization on GPU platforms}{342}}
34 \newlabel{sec:gpu}{{15.3.2}{342}}
35 \@writefile{lof}{\contentsline {figure}{\numberline {15.3}{\ignorespaces GPU parallel solver for envelope-following update.\relax }}{343}}
36 \newlabel{fig:gmres}{{15.3}{343}}
37 \@writefile{toc}{\contentsline {subsection}{\numberline {15.3.3}Gear-2 based sensitivity calculation}{344}}
38 \newlabel{sec:gear}{{15.3.3}{344}}
39 \newlabel{eq:BE}{{15.4}{344}}
40 \newlabel{eq:sens1}{{15.5}{344}}
41 \newlabel{eq:Gear_t2}{{15.6}{345}}
42 \newlabel{eq:sens2}{{15.7}{345}}
43 \newlabel{eq:Gear_t3}{{15.8}{345}}
44 \newlabel{eq:sensM}{{15.9}{345}}
45 \@writefile{loa}{\contentsline {algocf}{\numberline {15}{\ignorespaces The matrix-free method for Krylov subspace construction.\relax }}{346}}
46 \newlabel{alg:mf_Gear}{{15}{346}}
47 \newlabel{line:mf_Gear_loop}{{4}{346}}
48 \newlabel{line:shift}{{8}{346}}
49 \@writefile{toc}{\contentsline {section}{\numberline {15.4}Numerical examples}{346}}
50 \newlabel{sec:exp}{{15.4}{346}}
51 \@writefile{lof}{\contentsline {figure}{\numberline {15.4}{\ignorespaces Diagram of a zero-voltage quasi-resonant flyback converter.\relax }}{347}}
52 \newlabel{fig:flyback}{{15.4}{347}}
53 \@writefile{lof}{\contentsline {figure}{\numberline {15.5}{\ignorespaces Illustration of power/ground network model.\relax }}{347}}
54 \newlabel{fig:pg}{{15.5}{347}}
55 \newlabel{fig:flybackWhole}{{15.6(a)}{348}}
56 \newlabel{sub@fig:flybackWhole}{{(a)}{348}}
57 \newlabel{fig:flybackZoom}{{15.6(b)}{348}}
58 \newlabel{sub@fig:flybackZoom}{{(b)}{348}}
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 }}{348}}
60 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {The whole plot}}}{348}}
61 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Detail of one EF simulation period}}}{348}}
62 \newlabel{fig:flyback_wave}{{15.6}{348}}
63 \@writefile{lof}{\contentsline {figure}{\numberline {15.7}{\ignorespaces Buck converter solution calculated by envelope-following.\relax }}{349}}
64 \newlabel{fig:buck_wave}{{15.7}{349}}
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 }}{349}}
66 \newlabel{table:circuit}{{15.1}{349}}
67 \@writefile{toc}{\contentsline {section}{\numberline {15.5}Summary}{350}}
68 \newlabel{sec:summary}{{15.5}{350}}
69 \@writefile{toc}{\contentsline {section}{\numberline {15.6}Glossary}{350}}
70 \@writefile{toc}{\contentsline {section}{Bibliography}{350}}
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