new

[book_gpu.git] / BookGPU / Chapters / chapter13 / ch13.tex

diff --git a/BookGPU/Chapters/chapter13/ch13.tex b/BookGPU/Chapters/chapter13/ch13.tex
index ce2c7c281c5162b463f25a3dea8c0d23760a2937..db2ab78b8b97321189b32af7ee3d556ccd772cbe 100755 (executable)
--- a/BookGPU/Chapters/chapter13/ch13.tex
+++ b/BookGPU/Chapters/chapter13/ch13.tex
@@ -134,7 +134,7 @@ where $b=\{b_{1},b_{2},b_{3}\}$, $\|b\|_{2}$ denotes the Euclidean norm of $b$,
 $v=e^{-a}.u$ represents the general change of variables such that $a=\frac{b^{t}(x,y,z)}{2\eta}$.
 Consequently, the numerical resolution of the diffusion problem (the self-adjoint
 operator~(\ref{ch13:eq:04})) is done by optimization algorithms, in contrast to that
 $v=e^{-a}.u$ represents the general change of variables such that $a=\frac{b^{t}(x,y,z)}{2\eta}$.
 Consequently, the numerical resolution of the diffusion problem (the self-adjoint
 operator~(\ref{ch13:eq:04})) is done by optimization algorithms, in contrast to that

-of the convection-diffusion problem (non self-adjoint operator~(\ref{ch13:eq:03}))
+of the convection-diffusion problem (nonself-adjoint operator~(\ref{ch13:eq:03}))

 which is done by relaxation algorithms. In the case of our studied algorithm, the convergence\index{convergence}
 is ensured by M-matrix property; then, the performance is linked to the magnitude of
 the spectral radius of the iteration matrix, which is independent of the condition
 which is done by relaxation algorithms. In the case of our studied algorithm, the convergence\index{convergence}
 is ensured by M-matrix property; then, the performance is linked to the magnitude of
 the spectral radius of the iteration matrix, which is independent of the condition


@@ -747,7 +747,7 @@ consequently it also depends on the number of computing nodes.
 %%--------------------------%%
 \section{Red-black ordering technique}
 \label{ch13:sec:06}
 %%--------------------------%%
 \section{Red-black ordering technique}
 \label{ch13:sec:06}

-As is well-known, the Jacobi method\index{iterative method!Jacobi} is characterized
+As is well known, the Jacobi method\index{iterative method!Jacobi} is characterized

 by a slow convergence\index{convergence} rate compared to some iterative methods\index{iterative method}
 (for example, Gauss-Seidel method\index{iterative method!Gauss-Seidel}). So, in this
 section, we present some solutions to reduce the execution time and the number of
 by a slow convergence\index{convergence} rate compared to some iterative methods\index{iterative method}
 (for example, Gauss-Seidel method\index{iterative method!Gauss-Seidel}). So, in this
 section, we present some solutions to reduce the execution time and the number of