X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/4932967a1c684dc3f7ed04c19144101278b79972..b231a0489d9378f3ea1c2014902e9e55966907ff:/BookGPU/Chapters/chapter16/intro.tex?ds=sidebyside diff --git a/BookGPU/Chapters/chapter16/intro.tex b/BookGPU/Chapters/chapter16/intro.tex index cbed054..875093f 100644 --- a/BookGPU/Chapters/chapter16/intro.tex +++ b/BookGPU/Chapters/chapter16/intro.tex @@ -11,7 +11,7 @@ switching power converters. The new method first exploits the parallelisim in the envelope-following method and parallelize the Newton update solving part, which is the most computational expensive, in GPU platforms to boost the simulation performance. To further -speed up the iterative GMRES\index{GMRES} solving for Newton update equation in the +speed up the iterative GMRES\index{iterative method!GMRES} solving for Newton update equation in the envelope-following method, we apply the matrix-free\index{matrix-free} Krylov subspace\index{Krylov subspace} basis generation technique, which was previously used for RF simulation. @@ -42,7 +42,7 @@ In those switching power converters, it is the envelope, which is the power voltage delivered, not the fast switching waves in every cycle, that is of interest to the designers. -As shown in Fig.~\ref{fig:ef1}, the solid line is +As shown in Figure~\ref{fig:ef1}, the solid line is the waveform of the output node in a Buck converter~\cite{Krein:book'97}, the dots are the simulation points of SPICE\index{SPICE}, and the appended dash line is the envelope. @@ -54,7 +54,7 @@ clock cycle to get the accurate details of the carrier. For switching power converters, the waveform of the carrier in consequent cycles does not change much, envelope-following method is an approximation analysis method, which skips over several -cycles (the dash line in Fig.~\ref{fig:ef2}), the so called +cycles (the dash line in Figure~\ref{fig:ef2}), the so called envelope step, without simulating them, and then carries out a correction, which usually contains a sensitivity-based Newton iteration or shooting until convergence, in order to begin the @@ -75,14 +75,14 @@ next envelope step. \subfigure[The envelope changes in a slow time scale.] {\resizebox{.9\textwidth}{!}{\input{./Chapters/chapter16/figures/envelope.pdf_t}} \label{fig:ef2} } - \caption{Transient envelope-following\index{envelope-following} analysis. - (Both two figures reflect backward-Euler\index{backward-Euler} style envelope-following.)} + \caption[Transient envelope-following\index{envelope-following} analysis.]{Transient envelope-following\index{envelope-following} analysis. + (Both two figures reflect backward Euler\index{Euler!backward Euler} style envelope-following.)} \label{fig:ef_intro} \end{figure} %\IEEEpubidadjcol -Also, iterative GMRES\index{GMRES} solver is typically used in the +Also, iterative GMRES\index{iterative method!GMRES} solver is typically used in the envelope-following method to compute the solution of Newton update due to its efficiency compared to direct LU\index{LU} method. However, as the Jacobian matrix\index{Jacobian matrix}