Updated the documentation to reflect improved wording for introducing MGRIT from the Strand2D XBraid paper

Author: Jacob Schroder

docs/Abstract.md

@@ -20,23 +20,23 @@
   - Temple Place, Suite 330, Boston, MA 02111-1307 USA
  --> 
 
-This package implements an optimal-scaling multigrid solver for the linear
+This package implements an optimal-scaling multigrid solver for the (non)linear
 systems that arise from the discretization of problems with evolutionary
 behavior. Typically, solution algorithms for evolution equations are based on a
 time-marching approach, solving sequentially for one time step after the other.
 Parallelism in these traditional time-integration techniques is limited to
 spatial parallelism. However, current trends in computer architectures are
-leading towards systems with more, but not faster, processors. Therefore,
-faster compute speeds must come from greater parallelism. One approach to
-achieve parallelism in time is with multigrid, but extending classical
-multigrid methods for elliptic operators to this setting is a significant
-achievement. In this software, we implement a non-intrusive, optimal-scaling
-time-parallel method based on multigrid reduction techniques. The examples in
-the package demonstrate optimality of our multigrid-reduction-in-time algorithm
-(MGRIT) for solving a variety of equations in two and three spatial
-dimensions. These examples can also be used to show that MGRIT can achieve
-significant speedup in comparison to sequential time marching on modern
-architectures.
+leading towards systems with more, but not faster, processors, i.e., clock
+speeds are stagnate. Therefore, faster overall runtimes must come from greater
+parallelism. One approach to achieve parallelism in time is with multigrid, but
+extending classical multigrid methods for elliptic operators to this setting is
+a significant achievement. In this software, we implement a non-intrusive,
+optimal-scaling time-parallel method based on multigrid reduction techniques.
+The examples in the package demonstrate optimality of our
+multigrid-reduction-in-time algorithm (MGRIT) for solving a variety of
+equations in two and three spatial dimensions. These examples can also be used
+to show that MGRIT can achieve significant speedup in comparison to sequential
+time marching on modern architectures.
 
 It is **strongly recommended** that you also read [Parallel Time Integration
 with Multigrid](https://computation-rnd.llnl.gov/linear_solvers/pubs/mgritPaper-2013.pdf)

docs/Example.md

@@ -164,11 +164,11 @@ first argument to every function.
 
 6. **SpatialNorm**: This function tells XBraid how to take the norm 
    of a braid_Vector and is used for halting. This norm is only over 
-   space.  A common norm choice is the standard Eucliden norm, but 
+   space.  A common norm choice is the standard Euclidean norm, but 
    many other choices are possible, such as an L2-norm based on a 
    finite element space.  The norm choice should be based on what 
    makes sense for you problem.  How to accumulate spatial norm values
-   to obtain a global space-time residual norm for halting decsions is 
+   to obtain a global space-time residual norm for halting decisions is 
    controlled by [braid_SetTemporalNorm](@ref braid_SetTemporalNorm).
 
          int
@@ -188,14 +188,14 @@ first argument to every function.
    at time *t*.  This is most commonly used to print solution(s) to screen, file, etc... 
    The user defines what is appropriate output.  Notice how you are told the time value *t* of the 
    vector *u* and even more information in *astatus*.  This lets you tailor the output to only 
-   certain time values at certain XBraid iterations.  Querrying *astatus* for such information 
+   certain time values at certain XBraid iterations.  Querying *astatus* for such information 
    is done through _braid_AccessStatusGet**(..)_ routines.
    \latexonly \\ \endlatexonly
 
    The frequency of the calls to *access* is controlled through 
    [braid_SetAccessLevel](@ref braid_SetAccessLevel).  For instance, if access_level is 
    set to 2, then *access* is called every XBraid iteration and on every XBraid level.  In 
-   this case, querrying *astatus* to determine the current XBraid level and iteration will 
+   this case, querying *astatus* to determine the current XBraid level and iteration will 
    be useful. This scenario allows for even more detailed tracking of the simulation.
    \latexonly \\ \endlatexonly
 

docs/Introduction.md

@@ -176,7 +176,7 @@
 ~\\~\\~\\~\\~\\~\\~\\
 \begin{center}
    { \fontsize{40}{50}\selectfont XBraid }\\
-   { \large Time-Braid: Multigrid in Time Solvers}
+   { \large Parallel Multigrid in Time}
 \end{center}
 ~\\
 \begin{figure}[!ht]

docs/developer_manual_header.tex

@@ -176,7 +176,7 @@
 ~\\~\\~\\~\\~\\~\\~\\
 \begin{center}
    { \fontsize{40}{50}\selectfont XBraid }\\
-   { \large Time-Braid: Multigrid in Time Solvers}
+   { \large Parallel Multigrid in Time}
 \end{center}
 ~\\
 \begin{figure}[!ht]