2-FFT PPPM, also called analytic differentiation or ad PPPM, uses 2 FFTs -instead of the 4 FFTs used by the default ik differentiation PPPM. However, -2-FFT PPPM also requires a slightly larger mesh size to achieve the same accuracy -as 4-FFT PPPM. For problems where the FFT cost is the performance bottleneck (typically -large problems running on many processors), 2-FFT PPPM may be faster than 4-FFT PPPM. +
2-FFT PPPM, also called analytic differentiation or ad PPPM, uses +2 FFTs instead of the 4 FFTs used by the default ik differentiation +PPPM. However, 2-FFT PPPM also requires a slightly larger mesh size to +achieve the same accuracy as 4-FFT PPPM. For problems where the FFT +cost is the performance bottleneck (typically large problems running +on many processors), 2-FFT PPPM may be faster than 4-FFT PPPM.
-Staggered PPPM performs calculations using two different meshes, one shifted slightly with -respect to the other. This can reduce force aliasing errors and increase the accuracy of the -method, but also doubles the amount of work required. For high relative accuracy, using staggered -PPPM allows one to half the mesh size in each dimension as compared to regular PPPM, -which can give around a 4x speedup in the kspace time. However, for low relative -accuracy, using staggered PPPM gives little benefit and can be up to 2x slower in the -kspace time. For example, the rhodopsin benchmark was run on a single processor, -and results for kspace time vs. relative accuracy for the different methods are shown -in the figure below. For this system, staggered PPPM (using ik differentiation) -becomes useful when using a relative accuracy of slightly greater than 1e-5 and above. +
Staggered PPPM performs calculations using two different meshes, one +shifted slightly with respect to the other. This can reduce force +aliasing errors and increase the accuracy of the method, but also +doubles the amount of work required. For high relative accuracy, using +staggered PPPM allows one to half the mesh size in each dimension as +compared to regular PPPM, which can give around a 4x speedup in the +kspace time. However, for low relative accuracy, using staggered PPPM +gives little benefit and can be up to 2x slower in the kspace +time. For example, the rhodopsin benchmark was run on a single +processor, and results for kspace time vs. relative accuracy for the +different methods are shown in the figure below. For this system, +staggered PPPM (using ik differentiation) becomes useful when using a +relative accuracy of slightly greater than 1e-5 and above.
IMPORTANT NOTE: Using staggered PPPM may not give the same increase in accuracy of energy and pressure -as it does in forces, so some caution must be used if energy and/or pressure are quantities of interest, such -as when using a barostat. +
IMPORTANT NOTE: Using staggered PPPM may not give the same increase in +accuracy of energy and pressure as it does in forces, so some caution +must be used if energy and/or pressure are quantities of interest, +such as when using a barostat.
diff --git a/doc/Section_accelerate.txt b/doc/Section_accelerate.txt index bc35e25faa..66bc2dcd43 100644 --- a/doc/Section_accelerate.txt +++ b/doc/Section_accelerate.txt @@ -97,28 +97,33 @@ load-balancing: balance and fix balance processor command for layout OMP when lots of cores :ul -2-FFT PPPM, also called {analytic differentiation} or {ad} PPPM, uses 2 FFTs -instead of the 4 FFTs used by the default {ik differentiation} PPPM. However, -2-FFT PPPM also requires a slightly larger mesh size to achieve the same accuracy -as 4-FFT PPPM. For problems where the FFT cost is the performance bottleneck (typically -large problems running on many processors), 2-FFT PPPM may be faster than 4-FFT PPPM. +2-FFT PPPM, also called {analytic differentiation} or {ad} PPPM, uses +2 FFTs instead of the 4 FFTs used by the default {ik differentiation} +PPPM. However, 2-FFT PPPM also requires a slightly larger mesh size to +achieve the same accuracy as 4-FFT PPPM. For problems where the FFT +cost is the performance bottleneck (typically large problems running +on many processors), 2-FFT PPPM may be faster than 4-FFT PPPM. -Staggered PPPM performs calculations using two different meshes, one shifted slightly with -respect to the other. This can reduce force aliasing errors and increase the accuracy of the -method, but also doubles the amount of work required. For high relative accuracy, using staggered -PPPM allows one to half the mesh size in each dimension as compared to regular PPPM, -which can give around a 4x speedup in the kspace time. However, for low relative -accuracy, using staggered PPPM gives little benefit and can be up to 2x slower in the -kspace time. For example, the rhodopsin benchmark was run on a single processor, -and results for kspace time vs. relative accuracy for the different methods are shown -in the figure below. For this system, staggered PPPM (using ik differentiation) -becomes useful when using a relative accuracy of slightly greater than 1e-5 and above. +Staggered PPPM performs calculations using two different meshes, one +shifted slightly with respect to the other. This can reduce force +aliasing errors and increase the accuracy of the method, but also +doubles the amount of work required. For high relative accuracy, using +staggered PPPM allows one to half the mesh size in each dimension as +compared to regular PPPM, which can give around a 4x speedup in the +kspace time. However, for low relative accuracy, using staggered PPPM +gives little benefit and can be up to 2x slower in the kspace +time. For example, the rhodopsin benchmark was run on a single +processor, and results for kspace time vs. relative accuracy for the +different methods are shown in the figure below. For this system, +staggered PPPM (using ik differentiation) becomes useful when using a +relative accuracy of slightly greater than 1e-5 and above. :c,image(JPG/rhodo_staggered.jpg) -IMPORTANT NOTE: Using staggered PPPM may not give the same increase in accuracy of energy and pressure -as it does in forces, so some caution must be used if energy and/or pressure are quantities of interest, such -as when using a barostat. +IMPORTANT NOTE: Using staggered PPPM may not give the same increase in +accuracy of energy and pressure as it does in forces, so some caution +must be used if energy and/or pressure are quantities of interest, +such as when using a barostat. :line