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hppp [2016/11/04 20:49] – sbshppp [2022/03/22 11:54] (current) – sbs
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 \begin{eqnarray} \begin{eqnarray}
     \label{eq:num:pos}     \label{eq:num:pos}
-    \overset{\tiny k+1}{p_i} &=& \overset{k}{p_i} + \overset{k+1}{v_i} dt \\+    \overset{\tiny k+1}{p_i} &=& \overset{k}{p_i} + \overset{k}{v_i} dt \\
     \label{eq:num:vel}     \label{eq:num:vel}
-    \overset{k+1}{v_i} &=& \overset{k}{v_i} + \overset{k+1}{a_i} dt \\+    \overset{k+1}{v_i} &=& \overset{k}{v_i} + \overset{k}{a_i} dt \\
     \label{eq:num:acc}     \label{eq:num:acc}
     \overset{k+1}{a_i} &=& \sum\limits_{j \neq i}^{n}     \overset{k+1}{a_i} &=& \sum\limits_{j \neq i}^{n}
-                         \dfrac{m_j (\overset{k}{p_j} - \overset{k}{p_i})} +                         \dfrac{m_j (\overset{k+1}{p_j} - \overset{k+1}{p_i})} 
-                               {\left|\overset{k}{p_j} - \overset{k}{p_i} \right|^3}+                               {\left|\overset{k+1}{p_j} - \overset{k+1}{p_i} \right|^3}
 \end{eqnarray} \end{eqnarray}
  
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 </code> </code>
 Note here, that $k$ is mapped into the actual compute time and that $i$ in the first two assignments as well as the 3D nature of all positions, velocities and accelerations are implicitly derived by the compiler! Note here, that $k$ is mapped into the actual compute time and that $i$ in the first two assignments as well as the 3D nature of all positions, velocities and accelerations are implicitly derived by the compiler!
-More details as well as further examples can be found in our [[cases|case studies]].+More details as well as further examples can be found in our [[about:cases|case studies]].
 </panel> </panel>
  
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 abstract SAC programs into performance-tuned C-code, CUDA-code or similar, depending on the chosen target machine. abstract SAC programs into performance-tuned C-code, CUDA-code or similar, depending on the chosen target machine.
  
-Examples and performance figures can be found in our [[cases|case studies]] as well as in our [[publications#apps|application-related publications]].+Examples and performance figures can be found in our [[about:cases|case studies]] as well as in our [[publications#apps|application-related publications]].
 </panel> </panel>