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Reference documentation for deal.II version 9.6.0
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deal.II can be configured to use 64-bit indices for degrees of freedom, rather than the usual unsigned integers that default to 32-bit on most current systems. This is necessary since we want to be able to solve problems with more than 4 billion unknowns (the limit of what can be represented with 32-bit unsigned integers). At the same time, we do not want to indiscriminately replace all integers in deal.II with 64-bit versions, since this would increase memory use in many places where we represent quantities that will most definitely not be larger than 4 billion.
The data type we define for these indices to keep the bulk of the code base free of #ifdef
s is types::global_dof_index. If deal.II is configured as normal, this type is unsigned int
, but can be switched to unsigned long long int
if the right flag is provided (see the ReadMe file). This page is intended to clarify when types::global_dof_index must be used and when one can use a regular unsigned integer:
The number of blocks is an unsigned int because the number is expected to be low, i.e less than four billions. However, the size of the block is a types::global_dof_index because each block can be arbitrary large.
The ID of cell is not unique: Cells with different levels of refinement and/or on different processors can have the same ID. Thus, all the data associated to cells can be unsigned int because on a single processor, one one mesh level, there will definitely not be more than 4 billion cells.
The ID of each degree of freedom is unique in a parallel computation. Therefore, degrees of freedom are types::global_dof_index.
The numbers of row and column are types::global_dof_index even if it is not expected that someone will create a FullMatrix with so many entries. However, some methods of the AffineConstraints class are templated on the matrix type and thus, the size of a FullMatrix has to be of the same type than the size of SparseMatrix.
The size of SparseMatrix can be arbitrary large and it is conceivable that with sufficient memory on a single node, one may generate a matrix with more than 4 billion rows or columns. Therefore, types::global_dof_index is used. However, even for a large complex problem we can solve now, it is not reasonable to expect the number of non-zero entries in a sparse matrix to go over four billion. Thus, we still use unsigned int for, e.g., SparsityPattern::row_lengths and similar functions.