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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 {17}GPU-Accelerated Envelope-Following Method}{397}}
8 \@writefile{lof}{\addvspace {10\p@ }}
9 \@writefile{lot}{\addvspace {10\p@ }}
10 \@writefile{toc}{\contentsline {section}{\numberline {17.1}Introduction}{397}}
11 \newlabel{fig:ef1}{{17.1(a)}{399}}
12 \newlabel{sub@fig:ef1}{{(a)}{399}}
13 \newlabel{fig:ef2}{{17.1(b)}{399}}
14 \newlabel{sub@fig:ef2}{{(b)}{399}}
15 \@writefile{lof}{\contentsline {figure}{\numberline {17.1}{\ignorespaces Transient envelope-following analysis. (Both two figures reflect backward-Euler style envelope-following.)\relax }}{399}}
16 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Illustration of one envelope skip.}}}{399}}
17 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {The envelope changes in a slow time scale.}}}{399}}
18 \newlabel{fig:ef_intro}{{17.1}{399}}
19 \@writefile{toc}{\contentsline {section}{\numberline {17.2}The envelope-following method in a nutshell}{400}}
20 \newlabel{sec:ef}{{17.2}{400}}
21 \newlabel{eq:dae}{{17.1}{400}}
22 \newlabel{eq:Newton}{{17.2}{401}}
23 \newlabel{eq:A}{{17.3}{401}}
24 \@writefile{toc}{\contentsline {section}{\numberline {17.3}New parallel envelope-following method}{402}}
25 \newlabel{sec:gmres}{{17.3}{402}}
26 \@writefile{toc}{\contentsline {subsection}{\numberline {17.3.1}GMRES solver for Newton update equation}{402}}
27 \@writefile{lof}{\contentsline {figure}{\numberline {17.2}{\ignorespaces The flow of envelope-following method.\relax }}{403}}
28 \newlabel{fig:ef_flow}{{17.2}{403}}
29 \@writefile{loa}{\contentsline {algocf}{\numberline {20}{\ignorespaces Standard GMRES algorithm.\relax }}{404}}
30 \newlabel{alg:GMRES}{{20}{404}}
31 \newlabel{line:mvp}{{5}{404}}
32 \newlabel{line:newnorm}{{11}{404}}
33 \@writefile{toc}{\contentsline {subsection}{\numberline {17.3.2}Parallelization on GPU platforms}{404}}
34 \newlabel{sec:gpu}{{17.3.2}{404}}
35 \@writefile{lof}{\contentsline {figure}{\numberline {17.3}{\ignorespaces GPU parallel solver for envelope-following update.\relax }}{405}}
36 \newlabel{fig:gmres}{{17.3}{405}}
37 \@writefile{toc}{\contentsline {subsection}{\numberline {17.3.3}Gear-2 based sensitivity calculation}{406}}
38 \newlabel{sec:gear}{{17.3.3}{406}}
39 \newlabel{eq:BE}{{17.4}{406}}
40 \newlabel{eq:sens1}{{17.5}{406}}
41 \newlabel{eq:Gear_t2}{{17.6}{407}}
42 \newlabel{eq:sens2}{{17.7}{407}}
43 \newlabel{eq:Gear_t3}{{17.8}{407}}
44 \newlabel{eq:sensM}{{17.9}{407}}
45 \@writefile{loa}{\contentsline {algocf}{\numberline {21}{\ignorespaces The matrix-free method for Krylov subspace construction.\relax }}{408}}
46 \newlabel{alg:mf_Gear}{{21}{408}}
47 \newlabel{line:mf_Gear_loop}{{4}{408}}
48 \newlabel{line:shift}{{8}{408}}
49 \@writefile{toc}{\contentsline {section}{\numberline {17.4}Numerical examples}{408}}
50 \newlabel{sec:exp}{{17.4}{408}}
51 \@writefile{lof}{\contentsline {figure}{\numberline {17.4}{\ignorespaces Diagram of a zero-voltage quasi-resonant flyback converter.\relax }}{409}}
52 \newlabel{fig:flyback}{{17.4}{409}}
53 \@writefile{lof}{\contentsline {figure}{\numberline {17.5}{\ignorespaces Illustration of power/ground network model.\relax }}{409}}
54 \newlabel{fig:pg}{{17.5}{409}}
55 \newlabel{fig:flybackWhole}{{17.6(a)}{410}}
56 \newlabel{sub@fig:flybackWhole}{{(a)}{410}}
57 \newlabel{fig:flybackZoom}{{17.6(b)}{410}}
58 \newlabel{sub@fig:flybackZoom}{{(b)}{410}}
59 \@writefile{lof}{\contentsline {figure}{\numberline {17.6}{\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 }}{410}}
60 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {The whole plot}}}{410}}
61 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Detail of one EF simulation period}}}{410}}
62 \newlabel{fig:flyback_wave}{{17.6}{410}}
63 \@writefile{lof}{\contentsline {figure}{\numberline {17.7}{\ignorespaces Buck converter solution calculated by envelope-following.\relax }}{411}}
64 \newlabel{fig:buck_wave}{{17.7}{411}}
65 \@writefile{lot}{\contentsline {table}{\numberline {17.1}{\ignorespaces CPU and GPU time comparisons (in seconds) for solving Newton update equation with the proposed Gear-2 sensitivity. \relax }}{411}}
66 \newlabel{table:circuit}{{17.1}{411}}
67 \@writefile{toc}{\contentsline {section}{\numberline {17.5}Summary}{412}}
68 \newlabel{sec:summary}{{17.5}{412}}
69 \@writefile{toc}{\contentsline {section}{\numberline {17.6}Glossary}{412}}
70 \@writefile{toc}{\contentsline {section}{Bibliography}{412}}
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