Add an idea regarding precision to step-15. #15244
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examples/step-15/doc/results.dox
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| here is a different approach: Storing the system matrix (the "Jacobian") | ||
| in single-precision instead of double precision floating point numbers | ||
| (i.e., using `float` instead of `double` as the data type). This reduces | ||
| the amount of memory necessary by a factor of two, and consequently |
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This is not entirely correct, because the column indices in the matrix take the same space (4 bytes per entry) irrespective of the number type (4 or 8 bytes per entry). Thus, the saving is around a factor of 1.3-1.5. I agree we should not make the discussion here more complicated than necessary, so I suggest to add a short note towards the end of this paragraph that explains that a sparse matrix storage also consists of other terms. An interesting follow-up question would be to which extent one could compress the integer part of a sparse matrix more. There have been some papers in 2008-2009, but I never wanted to implement those because we would need them in Trilinos/PETSc and not in deal.II, and then matrix-free methods give even bigger gains.
examples/step-15/doc/results.dox
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| *as long as one stores the right hand side in double precision*. | ||
| A great overview of why this is so, along with numerical | ||
| experiments that also consider "half precision" floating point | ||
| numbers can be found in @cite Kelley2022 . |
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| numbers can be found in @cite Kelley2022 . | |
| numbers, can be found in @cite Kelley2022 . |
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Good point about the column indices. I've reworded this. |
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