* @note While this function is used in step-19, it is not an efficient
* function to use if the number of particles is large. That is because
* to find the particles that are located in one cell costs
- * ${\cal O)(\log N)$ where $N$ is the number of overall particles. Since
+ * ${\cal O}(\log N)$ where $N$ is the number of overall particles. Since
* you will likely do this for every cell, and assuming that the number
* of particles and the number of cells are roughly proportional,
- * you end up with an ${\cal O)(N \log N)$ algorithm. A better approach
+ * you end up with an ${\cal O}(N \log N)$ algorithm. A better approach
* is to use the fact that internally, particles are arranged in the
* order of the active cells they are in. In other words, if you iterate
* over all particles, you will encounter them in the same order as
* to the next cell, you increment the particle iterator as well until
* you find a particle located on that next cell. Counting how many
* steps this took will then give you the number you are looking for,
- * at a cost of ${\cal O)(\log N)$ when accumulated over all cells.
+ * at a cost of ${\cal O}(\log N)$ when accumulated over all cells.
* This is the approach used in step-70, for example. The approach is
* also detailed in the "Possibilities for extensions section"
* of step-19.
* @note While this function is used in step-19, it is not an efficient
* function to use if the number of particles is large. That is because
* to find the particles that are located in one cell costs
- * ${\cal O)(\log N)$ where $N$ is the number of overall particles. Since
+ * ${\cal O}(\log N)$ where $N$ is the number of overall particles. Since
* you will likely do this for every cell, and assuming that the number
* of particles and the number of cells are roughly proportional,
- * you end up with an ${\cal O)(N \log N)$ algorithm. A better approach
+ * you end up with an ${\cal O}(N \log N)$ algorithm. A better approach
* is to use the fact that internally, particles are arranged in the
* order of the active cells they are in. In other words, if you iterate
* over all particles, you will encounter them in the same order as
* to the next cell, you increment the particle iterator as well until
* you find a particle located on that next cell. This is the approach
* used in step-70, for example, and has an overall cost of
- * ${\cal O)(\log N)$ when accumulated over all cells. The approach is
+ * ${\cal O}(\log N)$ when accumulated over all cells. The approach is
* also detailed in the "Possibilities for extensions section"
* of step-19.
*/
* @note While this function is used in step-19, it is not an efficient
* function to use if the number of particles is large. That is because
* to find the particles that are located in one cell costs
- * ${\cal O)(\log N)$ where $N$ is the number of overall particles. Since
+ * ${\cal O}(\log N)$ where $N$ is the number of overall particles. Since
* you will likely do this for every cell, and assuming that the number
* of particles and the number of cells are roughly proportional,
- * you end up with an ${\cal O)(N \log N)$ algorithm. A better approach
+ * you end up with an ${\cal O}(N \log N)$ algorithm. A better approach
* is to use the fact that internally, particles are arranged in the
* order of the active cells they are in. In other words, if you iterate
* over all particles, you will encounter them in the same order as
* to the next cell, you increment the particle iterator as well until
* you find a particle located on that next cell. This is the approach
* used in step-70, for example, and has an overall cost of
- * ${\cal O)(\log N)$ when accumulated over all cells. The approach is
+ * ${\cal O}(\log N)$ when accumulated over all cells. The approach is
* also detailed in the "Possibilities for extensions section"
* of step-19.
*/
projects / dealii.git / commitdiff