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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 {14}GPU-Accelerated Envelope-Following Method}{317}}
8 \@writefile{lof}{\addvspace {10\p@ }}
9 \@writefile{lot}{\addvspace {10\p@ }}
10 \@writefile{toc}{\contentsline {section}{\numberline {14.1}Introduction}{317}}
11 \newlabel{fig:ef1}{{14.1(a)}{319}}
12 \newlabel{sub@fig:ef1}{{(a)}{319}}
13 \newlabel{fig:ef2}{{14.1(b)}{319}}
14 \newlabel{sub@fig:ef2}{{(b)}{319}}
15 \@writefile{lof}{\contentsline {figure}{\numberline {14.1}{\ignorespaces Transient envelope-following analysis. (Both two figures reflect backward-Euler style envelope-following.)\relax }}{319}}
16 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {Illustration of one envelope skip.}}}{319}}
17 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {The envelope changes in a slow time scale.}}}{319}}
18 \newlabel{fig:ef_intro}{{14.1}{319}}
19 \@writefile{toc}{\contentsline {section}{\numberline {14.2}The envelope-following method in a nutshell}{320}}
20 \newlabel{sec:ef}{{14.2}{320}}
21 \newlabel{eq:dae}{{14.1}{320}}
22 \newlabel{eq:Newton}{{14.2}{321}}
23 \newlabel{eq:A}{{14.3}{321}}
24 \@writefile{toc}{\contentsline {section}{\numberline {14.3}New parallel envelope-following method}{322}}
25 \newlabel{sec:gmres}{{14.3}{322}}
26 \@writefile{toc}{\contentsline {subsection}{\numberline {14.3.1}GMRES solver for Newton update equation}{322}}
27 \@writefile{lof}{\contentsline {figure}{\numberline {14.2}{\ignorespaces The flow of envelope-following method.\relax }}{323}}
28 \newlabel{fig:ef_flow}{{14.2}{323}}
29 \@writefile{loa}{\contentsline {algocf}{\numberline {12}{\ignorespaces Standard GMRES algorithm.\relax }}{324}}
30 \newlabel{alg:GMRES}{{12}{324}}
31 \newlabel{line:mvp}{{5}{324}}
32 \newlabel{line:newnorm}{{11}{324}}
33 \@writefile{toc}{\contentsline {subsection}{\numberline {14.3.2}Parallelization on GPU platforms}{324}}
34 \newlabel{sec:gpu}{{14.3.2}{324}}
35 \@writefile{lof}{\contentsline {figure}{\numberline {14.3}{\ignorespaces GPU parallel solver for envelope-following update.\relax }}{325}}
36 \newlabel{fig:gmres}{{14.3}{325}}
37 \@writefile{toc}{\contentsline {subsection}{\numberline {14.3.3}Gear-2 based sensitivity calculation}{326}}
38 \newlabel{sec:gear}{{14.3.3}{326}}
39 \newlabel{eq:BE}{{14.4}{326}}
40 \newlabel{eq:sens1}{{14.5}{326}}
41 \newlabel{eq:Gear_t2}{{14.6}{327}}
42 \newlabel{eq:sens2}{{14.7}{327}}
43 \newlabel{eq:Gear_t3}{{14.8}{327}}
44 \newlabel{eq:sensM}{{14.9}{327}}
45 \@writefile{loa}{\contentsline {algocf}{\numberline {13}{\ignorespaces The matrix-free method for Krylov subspace construction.\relax }}{328}}
46 \newlabel{alg:mf_Gear}{{13}{328}}
47 \newlabel{line:mf_Gear_loop}{{4}{328}}
48 \newlabel{line:shift}{{8}{328}}
49 \@writefile{toc}{\contentsline {section}{\numberline {14.4}Numerical examples}{328}}
50 \newlabel{sec:exp}{{14.4}{328}}
51 \@writefile{lof}{\contentsline {figure}{\numberline {14.4}{\ignorespaces Diagram of a zero-voltage quasi-resonant flyback converter.\relax }}{329}}
52 \newlabel{fig:flyback}{{14.4}{329}}
53 \@writefile{lof}{\contentsline {figure}{\numberline {14.5}{\ignorespaces Illustration of power/ground network model.\relax }}{329}}
54 \newlabel{fig:pg}{{14.5}{329}}
55 \newlabel{fig:flybackWhole}{{14.6(a)}{330}}
56 \newlabel{sub@fig:flybackWhole}{{(a)}{330}}
57 \newlabel{fig:flybackZoom}{{14.6(b)}{330}}
58 \newlabel{sub@fig:flybackZoom}{{(b)}{330}}
59 \@writefile{lof}{\contentsline {figure}{\numberline {14.6}{\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 }}{330}}
60 \@writefile{lof}{\contentsline {subfigure}{\numberline{(a)}{\ignorespaces {The whole plot}}}{330}}
61 \@writefile{lof}{\contentsline {subfigure}{\numberline{(b)}{\ignorespaces {Detail of one EF simulation period}}}{330}}
62 \newlabel{fig:flyback_wave}{{14.6}{330}}
63 \@writefile{lof}{\contentsline {figure}{\numberline {14.7}{\ignorespaces Buck converter solution calculated by envelope-following.\relax }}{331}}
64 \newlabel{fig:buck_wave}{{14.7}{331}}
65 \@writefile{lot}{\contentsline {table}{\numberline {14.1}{\ignorespaces CPU and GPU time comparisons (in seconds) for solving Newton update equation with the proposed Gear-2 sensitivity. \relax }}{331}}
66 \newlabel{table:circuit}{{14.1}{331}}
67 \@writefile{toc}{\contentsline {section}{\numberline {14.5}Summary}{332}}
68 \newlabel{sec:summary}{{14.5}{332}}
69 \@writefile{toc}{\contentsline {section}{\numberline {14.6}Glossary}{332}}
70 \@writefile{toc}{\contentsline {section}{Bibliography}{332}}
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