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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 {13}GPU-Accelerated Envelope-Following Method}{289}}
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10 \@writefile{toc}{\contentsline {section}{\numberline {13.1}Introduction}{289}}
11 \newlabel{fig:ef1}{{13.1(a)}{291}}
12 \newlabel{sub@fig:ef1}{{(a)}{291}}
13 \newlabel{fig:ef2}{{13.1(b)}{291}}
14 \newlabel{sub@fig:ef2}{{(b)}{291}}
15 \@writefile{lof}{\contentsline {figure}{\numberline {13.1}{\ignorespaces Transient envelope-following analysis. (Both two figures reflect backward-Euler style envelope-following.)\relax }}{291}}
16 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Illustration of one envelope skip.}}}{291}}
17 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {The envelope changes in a slow time scale.}}}{291}}
18 \newlabel{fig:ef_intro}{{13.1}{291}}
19 \@writefile{toc}{\contentsline {section}{\numberline {13.2}The envelope-following method in a nutshell}{292}}
20 \newlabel{sec:ef}{{13.2}{292}}
21 \newlabel{eq:dae}{{13.1}{292}}
22 \newlabel{eq:Newton}{{13.2}{293}}
23 \newlabel{eq:A}{{13.3}{293}}
24 \@writefile{toc}{\contentsline {section}{\numberline {13.3}New parallel envelope-following method}{294}}
25 \newlabel{sec:gmres}{{13.3}{294}}
26 \@writefile{toc}{\contentsline {subsection}{\numberline {13.3.1}GMRES solver for Newton update equation}{294}}
27 \@writefile{lof}{\contentsline {figure}{\numberline {13.2}{\ignorespaces The flow of envelope-following method.\relax }}{295}}
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29 \@writefile{loa}{\contentsline {algocf}{\numberline {10}{\ignorespaces Standard GMRES algorithm.\relax }}{296}}
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31 \newlabel{line:mvp}{{5}{296}}
32 \newlabel{line:newnorm}{{11}{296}}
33 \@writefile{toc}{\contentsline {subsection}{\numberline {13.3.2}Parallelization on GPU platforms}{296}}
34 \newlabel{sec:gpu}{{13.3.2}{296}}
35 \@writefile{lof}{\contentsline {figure}{\numberline {13.3}{\ignorespaces GPU parallel solver for envelope-following update.\relax }}{297}}
36 \newlabel{fig:gmres}{{13.3}{297}}
37 \@writefile{toc}{\contentsline {subsection}{\numberline {13.3.3}Gear-2 based sensitivity calculation}{298}}
38 \newlabel{sec:gear}{{13.3.3}{298}}
39 \newlabel{eq:BE}{{13.4}{298}}
40 \newlabel{eq:sens1}{{13.5}{298}}
41 \newlabel{eq:Gear_t2}{{13.6}{299}}
42 \newlabel{eq:sens2}{{13.7}{299}}
43 \newlabel{eq:Gear_t3}{{13.8}{299}}
44 \newlabel{eq:sensM}{{13.9}{299}}
45 \@writefile{loa}{\contentsline {algocf}{\numberline {11}{\ignorespaces The matrix-free method for Krylov subspace construction.\relax }}{300}}
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47 \newlabel{line:mf_Gear_loop}{{4}{300}}
48 \newlabel{line:shift}{{8}{300}}
49 \@writefile{toc}{\contentsline {section}{\numberline {13.4}Numerical examples}{300}}
50 \newlabel{sec:exp}{{13.4}{300}}
51 \@writefile{lof}{\contentsline {figure}{\numberline {13.4}{\ignorespaces Diagram of a zero-voltage quasi-resonant flyback converter.\relax }}{301}}
52 \newlabel{fig:flyback}{{13.4}{301}}
53 \@writefile{lof}{\contentsline {figure}{\numberline {13.5}{\ignorespaces Illustration of power/ground network model.\relax }}{301}}
54 \newlabel{fig:pg}{{13.5}{301}}
55 \newlabel{fig:flybackWhole}{{13.6(a)}{302}}
56 \newlabel{sub@fig:flybackWhole}{{(a)}{302}}
57 \newlabel{fig:flybackZoom}{{13.6(b)}{302}}
58 \newlabel{sub@fig:flybackZoom}{{(b)}{302}}
59 \@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}}
60 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {The whole plot}}}{302}}
61 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Detail of one EF simulation period}}}{302}}
62 \newlabel{fig:flyback_wave}{{13.6}{302}}
63 \@writefile{lof}{\contentsline {figure}{\numberline {13.7}{\ignorespaces Buck converter solution calculated by envelope-following.\relax }}{303}}
64 \newlabel{fig:buck_wave}{{13.7}{303}}
65 \@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}}
66 \newlabel{table:circuit}{{13.1}{303}}
67 \@writefile{toc}{\contentsline {section}{\numberline {13.5}Summary}{304}}
68 \newlabel{sec:summary}{{13.5}{304}}
69 \@writefile{toc}{\contentsline {section}{\numberline {13.6}Glossary}{304}}
70 \@writefile{toc}{\contentsline {section}{Bibliography}{304}}
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