last version

[book_gpu.git] / BookGPU / Chapters / chapter16 / gpu.tex

diff --git a/BookGPU/Chapters/chapter16/gpu.tex b/BookGPU/Chapters/chapter16/gpu.tex
index 26bd53674cd48fabdbf69200b36618decf3ac9ea..4d4d6ef365353105617ca6b9bde55f864738f997 100644 (file)
--- a/BookGPU/Chapters/chapter16/gpu.tex
+++ b/BookGPU/Chapters/chapter16/gpu.tex
@@ -5,7 +5,7 @@ In this section, we explain how to efficiently
 use matrix-free GMRES to solve
 the Newton update problems with implicit sensitivity calculation,
 i.e., the steps enclosed by the double dashed block
 use matrix-free GMRES to solve
 the Newton update problems with implicit sensitivity calculation,
 i.e., the steps enclosed by the double dashed block

-in Fig.~\ref{fig:ef_flow}.
+in Figure~\ref{fig:ef_flow}.

 Then implementation issues of GPU acceleration
 will be discussed in detail. 
 Finally,  the Gear-2 integration is briefly introduced.
 Then implementation issues of GPU acceleration
 will be discussed in detail. 
 Finally,  the Gear-2 integration is briefly introduced.


@@ -78,7 +78,7 @@ a preset tolerance~\cite{Golub:Book'96}.
 %% \end{algorithm}
 
 \begin{algorithm}
 %% \end{algorithm}
 
 \begin{algorithm}

-\caption{Standard GMRES\index{iterative method!GMRES} algorithm.} \label{alg:GMRES}
+\caption{standard GMRES\index{iterative method!GMRES} algorithm} \label{alg:GMRES}

   \KwIn{ $ A \in \mathbb{R}^{N \times N}$, $b \in \mathbb{R}^N$,
       and initial guess $x_0 \in \mathbb{R}^N$}
   \KwOut{ $x \in \mathbb{R}^N$: $\| b - A x\|_2 < tol$}
   \KwIn{ $ A \in \mathbb{R}^{N \times N}$, $b \in \mathbb{R}^N$,
       and initial guess $x_0 \in \mathbb{R}^N$}
   \KwOut{ $x \in \mathbb{R}^N$: $\| b - A x\|_2 < tol$}


@@ -160,7 +160,7 @@ period in order to solve a Newton update.
 At each time step, SPICE\index{SPICE} has
 to linearize device models, stamp matrix elements
 into MNA (short for modified nodal analysis\index{modified nodal analysis, or MNA}) matrices,
 At each time step, SPICE\index{SPICE} has
 to linearize device models, stamp matrix elements
 into MNA (short for modified nodal analysis\index{modified nodal analysis, or MNA}) matrices,

-and solve circuit equations in its inner Newton iteration\index{Newton iteration}.
+and solve circuit equations in its inner Newton iteration\index{iterative method!Newton iteration}.

 When convergence is attained,
 circuit states are saved and then next time step begins.
 This is also the time when we store the needed matrices
 When convergence is attained,
 circuit states are saved and then next time step begins.
 This is also the time when we store the needed matrices


@@ -225,7 +225,7 @@ Hence, in consideration of the serial nature of the trianularization,
 the small size of Hessenberg matrix,
 and the frequent inspection of values by host, it is
 preferable to allocate $\tilde{H}$ in CPU (host) memory.
 the small size of Hessenberg matrix,
 and the frequent inspection of values by host, it is
 preferable to allocate $\tilde{H}$ in CPU (host) memory.

-As shown in Fig.~\ref{fig:gmres}, the memory copy from device to host
+As shown in Figure~\ref{fig:gmres}, the memory copy from device to host

 is called each time when Arnoldi iteration generates a new vector
 and the orthogonalization produces the vector $h$.
 
 is called each time when Arnoldi iteration generates a new vector
 and the orthogonalization produces the vector $h$.