X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/17bff40b83bcdcc39769f9e59c70ffae1c525b72..b4a21f0b9226126a2c50f54a5518be5ef7c60749:/BookGPU/Chapters/chapter7/ch7.tex?ds=sidebyside diff --git a/BookGPU/Chapters/chapter7/ch7.tex b/BookGPU/Chapters/chapter7/ch7.tex index f9f7fd4..53cbae2 100644 --- a/BookGPU/Chapters/chapter7/ch7.tex +++ b/BookGPU/Chapters/chapter7/ch7.tex @@ -359,7 +359,7 @@ Subtracting $g^n$ in \eqref{ch7:eq:discreteupdate} and dividing by a pseudo time \frac{g^{*,n+1}-g^n}{\tau} =\frac{(1-\Gamma)}{\tau} (g_e^n-g^n). \end{align} % -The first term is similar to a first-order accurate Forward Euler\index{forward Euler} approximation of a rate of change term. This motivates an {\em embedded penalty forcing technique} based on adding a correction term of the form +The first term is similar to a first-order accurate Forward Euler\index{Euler!forward Euler} approximation of a rate of change term. This motivates an {\em embedded penalty forcing technique} based on adding a correction term of the form % \begin{align}\label{ch7:eq:penalty} \partial_t g = \mathcal{N}(g) + \frac{1-\Gamma(x)}{\tau} (g_e(t,x)-g(t,x)), \quad {\bf x}\in\Omega_\Gamma,