[cig-commits] commit: Very minor edits based on review 2.
Mercurial
hg at geodynamics.org
Mon May 6 16:32:50 PDT 2013
changeset: 175:9162e3d712fc
tag: tip
user: Brad Aagaard <baagaard at usgs.gov>
date: Mon May 06 16:32:45 2013 -0700
files: faultRup.tex response_jgr2.tex
description:
Very minor edits based on review 2.
diff -r b045f86bf618 -r 9162e3d712fc faultRup.tex
--- a/faultRup.tex Mon Feb 11 08:32:42 2013 -0800
+++ b/faultRup.tex Mon May 06 16:32:45 2013 -0700
@@ -16,7 +16,7 @@
% :SUBMIT:
% Extract figures and captions from PDF file.
-% gs -dBATCH -dNOPAUSE -q -sDEVICE=pdfwrite -dFirstPage=50 -dLastPage=64 -sOUTPUTFILE=figures.pdf faultRup.pdf
+% gs -dBATCH -dNOPAUSE -q -sDEVICE=pdfwrite -dFirstPage=56 -dLastPage=70 -sOUTPUTFILE=figures.pdf faultRup.pdf
% ======================================================================
@@ -349,16 +349,16 @@ with fault slip (sometimes called the ``
with fault slip (sometimes called the ``stress-free strain''
\citep{Aki:Richards:2002}). The total strain is the superposition of
this effective plastic strain and the elastic strain. The fault
-tractions are associated with the total strain, not the effective
-plastic strain. This illustrates a key difference between this
-approach and the domain decomposition approach in which the Lagrange
-multipliers and the constraint equation directly relate the fault slip
-to the fault tractions (Lagrange multipliers). One implication of this
-difference is that when using double couple point forces, the body
-forces driving slip depend on the elastic modulii and will differ
-across a fault surface with a contrast in the elastic modulii, whereas
-the fault tractions (Lagrange multipliers) in the domain decomposition
-approach will be equal in magnitude across the fault.
+tractions are associated with the elastic strain. This illustrates a
+key difference between this approach and the domain decomposition
+approach in which the Lagrange multipliers and the constraint equation
+directly relate the fault slip to the fault tractions (Lagrange
+multipliers). One implication of this difference is that when using
+double couple point forces, the body forces driving slip depend on the
+elastic modulii and will differ across a fault surface with a contrast
+in the elastic modulii, whereas the fault tractions (Lagrange
+multipliers) in the domain decomposition approach will be equal in
+magnitude across the fault.
We express the weighting function $\pmb{\phi}$, trial solution
$\bm{u}$, Lagrange multipliers $\bm{l}$, and fault slip $\bm{d}$ as
@@ -559,12 +559,12 @@ The matrix $\bm{L}$ defined in
The matrix $\bm{L}$ defined in
equation~(\ref{eqn:jacobian:constraint}) is spectrally equivalent to
the identity, because it involves integration of products of the basis
-functions. This makes the traditional LBB stability criterion
-\citep{Brenner:Scott:2008} trivial to satisfy by choosing the space of
-Lagrange multipliers to be exactly the space of displacements,
-restricted to the fault. This means we simply need to know the distance
-between any pair of vertices spanning the fault, which can be
-expressed as a relative displacement, i.e., fault slip.
+functions. This makes the traditional Ladyzhenskaya-Babuska-Brezzi
+(LBB) stability criterion \citep{Brenner:Scott:2008} trivial to satisfy by
+choosing the space of Lagrange multipliers to be exactly the space of
+displacements, restricted to the fault. This means we simply need to
+know the distance between any pair of vertices spanning the fault,
+which can be expressed as a relative displacement, i.e., fault slip.
% ------------------------------------------------------------------
\subsection{Dynamic Simulations}
@@ -1316,7 +1316,7 @@ weighting the cohesive cells the same as
weighting the cohesive cells the same as conventional bulk cells while
partitioning. In this performance benchmark matrix-vector
multiplication (the PETSc \texttt{MatMult} function) has a load
-imbalance of up to 20\% on 96 cores The cell partition balances
+imbalance of up to 20\% on 96 cores. The cell partition balances
the number of cells across the processes using ParMetis
\citep{Karypis:etal:1999} to achieve good balance for the
finite element integration. This does not take into account a
@@ -1508,6 +1508,10 @@ include inertial terms and time stepping
include inertial terms and time stepping is done via a series of
static problems so that the temporal accuracy depends only on the
temporal variation of the boundary conditions and constitutive models.
+These benchmarks simulations can be run on a laptop or desktop
+computer. For example, the high resolution benchmarks took 46 min
+(hexahedral cells) and 36 min (tetrahedral cells) using four processes
+on a dual quad core desktop computer with Intel Xeon E5630 processors.
Figure~\ref{fig:savage:prescott:profiles} compares the numerical
results extracted on the ground surface along the center of the model
@@ -1586,19 +1590,25 @@ include fluid pressure, we instead formu
include fluid pressure, we instead formulate the simulation parameters
in terms of effective stresses.
+The TPV13-2D simulations require a small fraction of the computational
+resources needed for the TPV13 3-D simulations and run quickly on a
+laptop or desktop computer. The 50 m resolution cases took 62 s
+(triangular cells) and 120 s (quadrilateral cells) using 8 processes
+on a dual quad core desktop computer with Intel Xeon E5630 processors.
Figure~\ref{fig:tpv13-2d:stress:slip}(b) displays the final slip
distribution in the TPV13-2D simulation with triangular cells at a
resolution of 100 m. The large dynamic stress drop and supershear
rupture generate 20 m of slip at a depth of about 7
-km. Figure~\ref{fig:tpv13-2d:slip:rate}(a)--(d) demonstrates the convergence
-of the solution as the discretization size decreases as evident in
-the normal faulting component of fault slip rate time histories. For a
-resolution of 200 m on the fault, the solution contains some
-high-frequency oscillation due to insufficient resolution of the
-cohesive zone \citep{Rice:1993}. The finer meshes provide sufficient
-resolution of the cohesive zone so there is very little high-frequency
-oscillation in the slip rate time histories. The triangular cells
-generate less oscillation compared with quadrilateral cells.
+km. Figure~\ref{fig:tpv13-2d:slip:rate}(a)--(d) demonstrates the
+convergence of the solution as the discretization size decreases as
+evident in the normal faulting component of fault slip rate time
+histories. For a resolution of 200 m on the fault, the solution
+contains some high-frequency oscillation due to insufficient
+resolution of the cohesive zone \citep{Rice:1993}. The finer meshes
+provide sufficient resolution of the cohesive zone so there is very
+little high-frequency oscillation in the slip rate time histories. The
+triangular cells generate less oscillation compared with quadrilateral
+cells.
In this benchmark without an analytical solution, as in all of the
exercises in the SCEC spontaneous rupture benchmark suite, we rely on
@@ -1614,11 +1624,15 @@ variations in the amount of numerical da
variations in the amount of numerical damping used in the various
codes.
-The results for the 3-D version of the TPV13 benchmark yield
-similar results. Figure~\ref{fig:tpv13:rupture:time}(a) shows the same
-trends in rupture speed with discretization size that we observed in
-the 2-D version. In both cases models with insufficient resolution to
-resolve the cohesive zone propagate slightly slower than models with
+The 3-D version of the TPV13 benchmark yields similar results but
+requires greater computational resources. The simulations with a
+discretization size of 100 m took 2.5 hours using 64 processes (8
+compute nodes with 8 processes per dual quad core compute node) on a
+cluster with Intel Xeon E5620 processors.
+Figure~\ref{fig:tpv13:rupture:time}(a) shows the same trends in
+rupture speed with discretization size that we observed in the 2-D
+version. In both cases models with insufficient resolution to resolve
+the cohesive zone propagate slightly slower than models with
sufficient resolution. In this case the differences between the
rupture times for the 200 m and 100 m resolution tetrahedral meshes
are less than 0.1 seconds over the entire fault surface. Comparing the
@@ -1736,9 +1750,424 @@ rupture propagation.
% ------------------------------------------------------------------
% :SUBMIT: comment out
-\bibliography{references}
-\bibliographystyle{agufull08}
+%\bibliography{references}
+%\bibliographystyle{agufull08}
% paste .bbl file HERE.
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+
% ------------------------------------------------------------------
% FIGURES
@@ -1966,7 +2395,7 @@ rupture propagation.
% TABLES
% ------------------------------------------------------------------
\begin{table}
-%\scriptsize % :SUBMIT:
+\scriptsize % :SUBMIT:
\caption{Example Preconditioners for the Saddle Point Problem in
Equation~(\ref{eqn:saddle:point})\tablenotemark{a}}
\label{tab:preconditioner:options}
@@ -2089,7 +2518,7 @@ rupture propagation.
\begin{table}
-%\scriptsize % :SUBMIT:
+\scriptsize % :SUBMIT:
\caption{Performance Benchmark Memory System Evaluation\tablenotemark{a}}
\label{tab:solvertest:memory:events}
\centering
diff -r b045f86bf618 -r 9162e3d712fc response_jgr2.tex
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/response_jgr2.tex Mon May 06 16:32:45 2013 -0700
@@ -0,0 +1,97 @@
+%-*- TeX -*-
+%
+% ----------------------------------------------------------------------
+%
+% Brad T. Aagaard
+% U.S. Geological Survey
+%
+% ----------------------------------------------------------------------
+%
+
+\documentclass{reviewresponse}
+
+% ==================================================================
+\begin{document}
+
+\maketitle
+
+% ----------------------------------------------------------------------
+\reviewer{Associate Editor}
+
+\comment{%
+ Item 1 -- L 288: abbreviation LBB not defined previously; please add
+ here
+}{%
+ Expanded LBB to Ladyzhenskaya-Babuska-Brezzi.
+}%
+
+\comment{%
+ Suggestion 1 -- in Section 6, add a sentence or two on the
+ computational demands for the test cases shown. I.e. how long did
+ the runs take in 6.1, 6.2 on which architecture, and what were the
+ computational requirements. I envision that many research groups
+ may be interested in using the PyLith package, perhaps even in an
+ almost ``black-box'' mode, but not everyone has access to very-large
+ HPC systems. So some information on what is takes to run the cases
+ in 6.1 and 6.2 may be of interest to many who contemplate to install
+ and run the package on their compute system.
+
+}{%
+ Added some sentences on the run-time and computational resources used
+ for each of the benchmarks in section 6 (lines 796--799, 850--853,
+ 873--875). We chose to give the information for the highest
+ resolution runs, which take the longest and use more computational
+ resources.
+}%
+
+\comment{%
+ Suggestion 2 -- Upon reading the manuscript once more, I found
+ Section 5 quite technical, and sort of distracting from the main
+ theme ... namely to solve a geo-physical problem with some (new)
+ code. Many readers may skip this section, I suppose ... so I wonder
+ if it could be moved into an Appendix, and hence making the main
+ body or the paper more concise and ``user friendly''. My Suggestion 1
+ could then also be dealt with in this Appendix.
+}{%
+ The choice of the preconditioners and parallel performance can
+ significantly affect run-time, which users care about. Consequently,
+ we prefer to keep the performance benchmark section in the main body
+ rather than move it to an appendix. We have also found that many
+ users know very little about selecting proper preconditioners, so
+ exposure to this information is useful. The section headers
+ clearly separate the sections, so readers can easily move onto the
+ next section if they are not interested in the details.
+}%
+
+% ----------------------------------------------------------------------
+\reviewer{Reviewer \#1: Sylvain Barbot}
+
+\comment{%
+ ``The fault tractions are associated with the total strain, not the
+ effective plastic strain'' should be ``The fault tractions are
+ associated with the elastic strain, not the effective plastic
+ strain'', because the total strain is the sum of the elastic and
+ inelastic strains: $\epsilon = \epsilon^e+\epsilon^i$ and with the
+ stress being due to elastic strain alone $\sigma = C : \epsilon^e$,
+ we obtain $\sigma = C : (\epsilon-\epsilon^i).$ Then the traction is
+ just $\sigma\cdot\hat{n}$. So either the traction depends on total
+ strain and inelastic strain or it depends on elastic strain alone.
+}{%
+ This is correct. Updated text to ``The fault tractions are
+ associated with the elastic strain.''
+}%
+
+\comment{%
+ There's alone a mission period page 33 after "96 cores".
+}{%
+ The period appears to have been away on a mission of some sort. In
+ any case, it has returned and now sits at its appropriate place
+ (line 668).
+}%
+
+
+
+% ==================================================================
+\end{document}
+
+% End of file
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