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\MyLogo{{\footnotesize Jeremi{\'c}, Manchester, Sept. 2003}}
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%\maketitle
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\vspace*{0.0truecm}
\begin{center}
{\huge \bf
%\vspace*{1.5truecm} \\
\rule[-3mm]{0cm}{1.3cm} The Plastic Domain Decomposition  \\
}
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%


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\vspace*{1.0truecm}


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\begin{large}
\begin{center}
{\bf Boris Jeremi{\' c}}
\end{center}
\end{large}

\vspace*{-0.50truecm}

\begin{small}
\begin{center}
{Department of Civil and Environmental Engineering }\\
{University of California, Davis}\\
\end{center}
\end{small}

%

%\vspace*{0.50truecm}
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\begin{small}
\begin{center}
{MRCCS/NSF Summer School} \\
{High Performance Computing in Finite Element Analysis}\\
{1st - 5th September 2003,}\\
{University of Manchester}\\
\end{center}
\end{small}
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\begin{small}

\begin{description}
%\item  Supported  in  part    by  the  NSF--PEER \#~EEC-9701568,
%Cal--EPA \#~99-01337V,
\item     Supported    in    part        by    the    NSF, PEER,
Caltrans, and Cal--EPA.

\item Collaborators:
Professors
Zhaohui Yang (UAA),
Sashi Kunnath (UCD),
%Bruce Kutter (UCD),
Gregory  Fenves  (UCB),
Jacobo Bielak (CMU),
%Bernd Hamann  (UCD),
Zhaojun  Bai  (UCD),
George Karypis (UMN),
Drs.
Francis  McKenna  (UCB),
Ingrid Hotz (UCD),
and
graduate  students
Xiaoyan Wu (UCD)
Ritu Jain (UCD),
Zhao Cheng (UCD),
Kallol Sett (UCD),
Qing Liu (UCD),
Jinxiu Liao (UCD).
Guanzhou Jie (UCD).
\end{description}

\end{small}
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\slide{Motivation}


\begin{large}


\begin{itemize}


\vspace*{1.0cm}
\item  Create  high  fidelity  models of constructed facilities
(bridges, buildings, port structures, dams...).

\vspace*{1.0cm}
\item Models will live concurrently  with  the  physical  system
they  represent.

\vspace*{1.0cm}
\item Models to provide  owners  and  operators  with  the
capabilities to assess operations and future performance.

\vspace*{1.0cm}
\item  Use  observed  performance  to update and validate models
through simulations.

\end{itemize}
\end{large}
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\slide{Large Scale Numerical Simulation Goal}
\begin{large}


\begin{itemize}

\vspace*{0.5cm}
\item  Scalable parallel finite element method for inelastic computations (solid
and structural elements)

\vspace*{0.5cm}
\item  Based on state of the art computational mechanics theories and implementation

\vspace*{0.5cm}
\item Available for a range of sequential and parallel machines, including
clusters, grids of machines and clusters (DMPs), and also multiprocessors (SMPs)


\vspace*{0.5cm}
\item  Public domain, portable platform.



\end{itemize}

\end{large}



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\slide{Incomplete Historical Background}

%\vspace*{-0.3cm}

\begin{large}


\begin{itemize}

\item Substructuring to achieve partitions (Noor et al. \cite{Noor1978}, Utku et
al.  \cite{Utku1982} and Storaasil and Bergan \cite{Storaasli1987})
%
\item  Techniques  to  account  for
different  types  of  elements  but  used  substructures  of  same element types
(non--balanced computations) (Fulton  and  Su  \cite{Fulton1992} ).
%

\item dynamic   analysis  of  framed  structures  with  the  objective  of  minimizing
communications (Hajjar  and  Abel  \cite{Hajjar1988})

\item
parallel computational techniques  for
elastic--plastic  problems but tied the algorithm to the specific multiprocessor
computers used (and specific network connectivity architecture) (Klaas et al. \cite{Klaas1994})

\item Greedy domain partitioning algorithm  good for topological DD but does not
redistributed the domains as a function of developed nonlinearities (Farhat  \cite{Farhat1987})


\end{itemize}

\end{large}



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\slide{Brief Methodology Background}

%\vspace*{-0.3cm}

\begin{large}

\begin{itemize}

\item    Static    domain  decomposition  will  lead to optimal parallel run for
many problems

    \begin{itemize}
      \item  equal number of mesh elements to each processor, this will balance
      computational load (CL) on parallel machine,
      \item  minimize  the size of subdomain boundaries, this will minimize  the
      inter-processor communications overhead,
    \end{itemize}


\item This can be done many ways, recently a set of good graphs partitioner were
developed (METIS family by Karypis et al.)

\item    This    is  indeed  good for problems where the computational domain or
discretization does not change.

\item  For  inelastic  computations using finite element method, the change will
occur in internal state determination.


\end{itemize}


\end{large}

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\slide{Inelastic Parallel Problem}


\begin{large}


\begin{itemize}

%\vspace*{0.2truecm}
\item Presence of elastic and inelastic (plasticity, damage) computational domains.

%\vspace*{0.2truecm}
\item   Difference  in  computational  load  for  elastic  and  inelastic  state
determination leads to computational load imbalance


%\vspace*{0.2truecm}
\item    This  leads  to imbalanced computations, very inefficient, not much gain
from using parallelization

%\vspace*{0.2truecm}
\item  Internal state determination can take as much as 80\% of CL


\end{itemize}


%
\begin{figure}[!htb]
%\vspace*{1.1cm}
\begin{center}
{\includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2003/ParallelManchester/sii.pdf}}
\end{center}
\vspace*{-0.3cm}
\end{figure}
\noindent




\end{large}

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\slide{Inelastic Computational Load Balancing Challenge:
\\
Adaptive Computations}


\begin{large}



  \begin{itemize}
    \item  Dynamic  computations,  structure  of  elastic  and  elastic--plastic
    domains changes dynamically and unpredictably
    \item  Periodic  computational
load-balancing is required during the course of the computation
    \item Computational load balancing cost similar to static DD (balance   the
    mesh elements and minimize the inter-processor communications
    \item It also requires that the
cost associated with redistributing the data in order to balance
the  computational  load  is  minimized

  \end{itemize}





\end{large}

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\slide{Inelastic Computational Load Balancing Challenge:
\\
Multi-phase Computation }


\begin{large}



  \begin{itemize}
\vspace*{0.7truecm}
    \item  Elastic--plastic  computations  follow  up  the
elastic  computations, there is a synchronization step between

\vspace*{0.7truecm}
    \item    Each  phase  needs to be separately computational load balanced
    \begin{itemize}
     \item Elastic phase computations (topological DD might be OK)
     \item Elastic--plastic phase computations (PDD)
    \end{itemize}

\vspace*{0.7truecm}
    \item  System of equations needs to be CL balanced as well

  \end{itemize}



\end{large}

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\slide{Elastic Computations}


\begin{large}



%
\begin{samepage}
\begin{eqnarray*}
{}^{(m)}\! K_{IacJ}
=
\int_{V^{m} }  H_{I,b} \; E_{abcd} \; H_{J,d} \;  dV^{m}
\label{FED20}
\end{eqnarray*}
\end{samepage}
%
%
%
\begin{samepage}
\begin{eqnarray*}
E_{ijkl} = \lambda \delta_{ij} \delta_{kl}
   + \mu \left( \delta_{ik} \delta_{jl} + \delta_{il} \delta_{jk} \right)
\label{elast06}
\end{eqnarray*}
\end{samepage}
%
%

\noindent
{\em  Lam{\'e} (elastic)  coefficients}:
%
%
\begin{samepage}
\begin{eqnarray*}
\lambda = \frac{\nu E}{\left( 1+\nu \right) \left( 1-2\nu \right)}
\;\;\;\;\;
;
\;\;\;\;\;
\mu = \frac{E}{ 2 \left( 1+\nu \right) }
 \label{elast07}
\end{eqnarray*}
\end{samepage}
%
%
%
Applies to linear and nonlinear elasticity



\end{large}




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\slide{Elastic--Plastic Computations}


\begin{large}


\begin{itemize}

\vspace*{0.4truecm}
  \item Integration of constitutive equations at each integration point:
    \begin{itemize}
      \item Explicit integration  (Forward Euler (FE) algorithm)
      \item Implicit integration  (Backward Euler (BE) algorithm)
      \item Mid--point integration (Crank--Nickolson (CN) algorithm)
    \end{itemize}

\vspace*{0.4truecm}
   \item Single step  (FE) and iterative algorithms (BE, CN)

\vspace*{0.4truecm}
   \item  Elastic  computations,  computational  load   per element (integration
   point) known a priori


\vspace*{0.4truecm}
   \item Elastic--Plastic computations,  computational  load  much larger

\vspace*{0.4truecm}
   \item  Computations Load  is not known a priori (the extent of plastic zone is not
   known prior to analysis)



\end{itemize}
%
%


\end{large}




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\slide{Implicit Constitutive Integration}


\begin{large}



Iterative procedure, unknown number of steps
%
\begin{eqnarray*}
& &  \Delta  \sigma_{mn} =
- (
{}^{old} \! r_{ij} +
\\
& &
\frac { {}^{n+1} \! F^{old}
-
 {}^{n+1} \! n_{mn} \; {}^{old} \! r_{ij}  {}^{n+1}\!T_{ijmn}^{-1} }
{ {}^{n+1} \! n_{mn} E_{ijkl} \; {}^{n+1} \!H_{kl} {}^{n+1}\!T_{ijmn}^{-1}
 -
 {}^{n+1} \! \xi_{\ast} \; h_{\ast} }
\; E_{ijkl} \; {}^{n+1} \!H_{kl}
)
{}^{n+1}\!T_{ijmn}^{-1}
\end{eqnarray*}
%

\begin{eqnarray*}
  \Delta q_{\ast} =
\left(
\frac { {}^{n+1} \! F^{old}
-
{}^{n+1} \! n_{mn} \; {}^{old} \! r_{ij} {}^{n+1}\!T_{ijmn}^{-1} }
{ {}^{n+1} \! n_{mn} E_{ijkl} \; {}^{n+1} \!H_{kl} {}^{n+1}\!T_{ijmn}^{-1}
- {}^{n+1} \! \xi_{\ast} \; h_{\ast} }
\right)
h_{\ast}
\end{eqnarray*}
%
%
%
\begin{small}
%
\begin{samepage}
\begin{eqnarray*}
{}^{n+1} \!T_{ijmn} =
\delta_{im} \delta_{nj} +
\lambda \; E_{ijkl} \;
\left.  % just because of the \right|
\frac{ \partial m_{kl} }{\partial \sigma_{mn}} \right|_{n+1}
\;\; \mbox{;} \;\;
 {}^{n+1} \!H_{kl}  =
{}^{n+1} \!m_{kl}
+
\left.  % just because of the =right|
\lambda \frac{ \partial m_{kl} }{\partial q_{\ast}} \right|_{n+1} \! h_{\ast}
\\
n_{ij} = \frac{\partial F}{\partial \sigma_{ij}}
\;\; \mbox{;} \;\;
m_{ij} = \frac{\partial Q}{\partial \sigma_{ij}}
\;\; \mbox{;} \;\;
\xi_{\ast} = \frac{\partial F}{\partial q_{\ast}}
\end{eqnarray*}
\end{samepage}
\end{small}







\end{large}




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\slide{Computational Load Varies}


\begin{large}

\begin{itemize}

  \item  Load  per integration point for each iteration/increment (4 CPU cycles
  (CPUc) for addition, 6 CPUc for multiplication, 13 CPUc for division...):
    \begin{itemize}
      \item Elastic computation: approx. $3600$ CPUc
      \item Forward Euler single step: approx. $7000$ CPUc
      \item  Backward Euler single step: approx. $12000 + n \times 15000 $ CPUc
    \end{itemize}

  \item Example \#1: say 5 iteration steps $\rightarrow$ $87000 $ CPUc (24 times more CPU load)

  \item Example \#2: say 25 iteration steps $\rightarrow$ $387000 $ CPUc (108 times more CPU load)

  \item This is all load per one integration point!

  \item Standard 20 node brick element should have at least 27 integration points ($3 \times 3 \times 3)$



\end{itemize}


\end{large}

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\slide{Computational Load Imbalance}

%

\begin{large}


\begin{itemize}
%\vspace{0.5cm}
%\item Domain decomposition (DD) technique (substructuring)

\vspace{0.5cm}
\item Existing parallel computational algorithms: topological(preprocessing)  DD
into substructures with equal number of elements

\vspace{0.5cm}
\item Topological DD assumes equal computational load per element

\vspace{0.5cm}
\item Topological DD performed during a pre--processing phase


\vspace{0.5cm}
\item  No  provisions  for  variation  of  computational load per element or for
variation in connectivity speed (latency and bandwidth)


\vspace{0.5cm}
\item  Separate  problem  for  internal  state  determination  (elastic--plastic
computations on the element level) and for the system of equations solution


\end{itemize}





\end{large}

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\slide{Possible Solutions}
%

\begin{large}


\begin{itemize}
%\item Domain decomposition (DD) technique (substructuring)

%\vspace{0.2cm}
\item Perform pre--processing stage DD, topological DD (
equal computational load per element, pre--processing
phase,    no   provisions  for:  variation  of  computational load per element, 
connectivity speed, latency and bandwidth)



%\vspace{0.2cm}
\item  Distribute small subdomains to processor as they become idle, feed hungry
CPUs (dynamic CL by design, expensive as it sends a lot of "small" data packets,
internal  state  determination  and  system solution phases are totally separate,
 a lot of data moving around)


\item    Element  by  element  family  of  methods in conjunction with iterative
equation solvers

%\vspace{0.2cm}
\item Dynamic CL balancing $\rightarrow$ Plastic Domain Decomposition (currently
being implemented into OpenSees)


\end{itemize}





\end{large}

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\slide{Feed Hungry CPUs}

%
\begin{large}

\begin{itemize}

\item Distribute computations of element  matrices to parallel nodes in small groups


\item Solve the system in parallel using  MP\_SOLVE

\item Both phases separate

\end{itemize}
%\vspace{0.5cm}
%\item Relatively slow network hinders performance for 2 nodes

%
\begin{figure}[!htb]
\vspace*{1.1cm}
\begin{center}
{\includegraphics[width=10.2cm]{/home/jeremic/tex/works/Conferences/2000/ASCE-EM_Austin/SSI/Present/plab_pdf.jpg}}
\hfill
{\includegraphics[width=10.2cm]{/home/jeremic/tex/works/Conferences/2000/ASCE-EM_Austin/SSI/Present/plabMPS_pdf.jpg}}
\end{center}
\vspace*{-0.3cm}
\end{figure}
\noindent
 stiffness matrix formations   \hspace*{4.5cm} system solution





\end{large}





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\slide{Development of the Plastic Domain Decomposition}

%
\begin{large}

\begin{itemize}

\item Based on work of Karypis et al.

\item Multilevel  Graph Partitioning
  \begin{itemize}
    \item graph coarsening
    \item initial partitioning
    \item multilevel refinement
  \end{itemize}

\item Par--METIS system

\item Weighted graphs edges and \\ graph nodes

\item Zoltan framework used as an \\
      interface layer for extensibility

\end{itemize}


\begin{figure}[!htb]
\vspace*{-18.1cm}
\hspace*{12cm}
{\includegraphics[width=13.2cm]{/home/jeremic/tex/works/Proposals/2002/Parallel01/gp.pdf}}
\vspace*{-0.3cm}
\end{figure}



\end{large}





% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \slide{Adaptive Graph Partitioning}
%
% %
% \begin{large}
%
% \begin{itemize}
%
% \item  Dynamic    computational  load-balancing    algorithms,    based  on  the
% multilevel graph partitioning paradigm
%
% \item Attempt to minimize the data redistribution costs
%
%   \begin{itemize}
%     \item  compute  a  new partitioning from scratch and then intelligently map
%     this  back  to  the  original partitioning (tends to result in partitionings
%     that  do  very  well at minimizing the inter-processor communications costs,
%     because when a new partitioning is computed from scratch, we can
% use   a  state-of-the-art  partitioning  method  to do so, however it results in
% higher data redistribution costs compared to other methods,
% especially when the partitioning is only slightly imbalanced. This is because it
% is  often  the  case  that  the  newly  computed  partitioning  is substantially
% different  from  the  original partitioning, so even a good remapping of
% the  new  partitioning  can  still  incur  large  data  redistribution costs)
%
%     \item Perturb the original partitioning just enough so as
% to  balance  the  computational  load (extremely low data
% redistribution  costs, however result in higher inter-processor
% communications  costs for highly imbalanced
% partitionings, because during the process of balancing the partitioning,
% locally  optimum  selections  are  made and the more that partitioning needs to be
% perturbed  in order to balance it, the greater the likelihood that the effect of
% the  locally optimum decisions that are made to balance the partitioning will be
% globally         sub-optimal)
%
%   \end{itemize}
%
%
%
% \end{itemize}
%
%
% \end{large}
%



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\slide{Adaptive Graph Partitioning}

%
\begin{large}

\begin{itemize}

\vspace*{1.0cm}
\item  Dynamic    computational  load-balancing    algorithms,    based  on  the
multilevel graph partitioning paradigm

\vspace*{1.0cm}
\item Attempt to minimize the data redistribution costs using one of
the two methods:

  \begin{itemize}
    \item  compute  a  new partitioning from scratch and then intelligently map
    this  back  to  the  original partitioning


    \item Perturb the original partitioning just enough so as
to  balance  the  computational  load

  \end{itemize}



\end{itemize}


\end{large}


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\slide{Adaptive Graph Partitioning I}

%
\begin{large}

Compute  a  new partitioning from scratch and then intelligently map
    this  back  to  the  original partitioning:

\begin{itemize}

    \item  result in partitioning
    that  do  very  well at minimizing the inter-processor communications costs,

    \item because when a new partitioning is computed from scratch, we can
use   a  state-of-the-art  partitioning  method  to do so,

    \item results in
higher data redistribution costs compared to other methods,

    \item especially when the partitioning is only slightly imbalanced

    \item because it
is  often  the  case  that  the  newly  computed  partitioning  is substantially
different  from  the  original partitioning

    \item  so even a good remapping of
the  new  partitioning  can  still  incur  large  data  redistribution costs


\end{itemize}


\end{large}


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\slide{Adaptive Graph Partitioning II}

\begin{large}


Perturb the original partitioning just enough so as
to  balance  the  computational  load:


\begin{itemize}

    \item extremely low data
redistribution  costs,

    \item result in higher inter-processor
communications  costs for highly imbalanced
partitioning,

\item because during the process of balancing the partitioning, locally  optimum
selections  are  made  and  the  more that partitioning needs to be perturbed in
order  to  balance it, the greater the likelihood that the effect of the locally
optimum  decisions  that  are  made to balance the partitioning will be globally
sub-optimal


%  \item

\end{itemize}


\end{large}





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\slide{Multi-phase  Graph  Partitioning}

\begin{large}

\begin{itemize}

  \item Traditional graph partitioners CL balance only single phase

  \item Other phases might be seriously imbalanced

  \item Generalized formulation of the graph partitioning problem that is able to
  balance   multiple   phases   simultaneously,   while  also  minimizing  the
  inter-processor communications costs


  \item  Think    of  adaptive  partitioning  as  a multi-objective optimization
  problem, that is minimize  both  the  inter-processor communications, the data
  redistribution  costs  and  create  good  partitions (CL balanced with minimal
  boundary)

  \item Unified adaptive partitioning--repartitioning algorithms

  \item  Compute decompositions that take into account the relative  costs of
  performing inter-processor communications and data redistributions


\end{itemize}


\end{large}

\vspace*{-3.5cm}





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\slide{Plastic Domain Decomposition}

\begin{large}

\begin{itemize}

\vspace*{0.5cm}
  \item Take into the account:

    \begin{itemize}
      \item heterogeneous element loads that change in each iteration

      \item heterogeneous processor performance (multiple generations nodes)

      \item inter-processor communications 

      \item data redistribution costs


    \end{itemize}
  
  
\vspace*{0.5cm}
      \item  Perform  global  optimization for both internal state determination
      and system solution phases

\vspace*{0.5cm}
      \item  Available  for  all  elements  (solid, structural) that provide the
      interface (sendSelf, RecvSelf, timer or CL weight estimate)


\vspace*{0.5cm}
  \item Able to handle SMPs, local clusters, grids of computers

     
%  \item

\end{itemize}


\end{large}



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\slide{PDD Implementation}

\begin{large}

\begin{itemize}

  \item  Internal state determination:
    \begin{itemize}
      \item  Use  lightweight  measurement  of each element performance (or provided
      information on CL)

      \item    Use    lightweight  measurement  of network latency and bandwidth
      (including local are and wide area networks)
  
      \item  Use information from previous incremental step to make PDD decisions

      \item    Question:  do  we  perform  PDD  for  each  iteration  (or  after few
  iterations) or for each increment (or after few increments)
    \end{itemize}


  
  
      \item  System of equations solution (SES):

    \begin{itemize}
      \item Use previous decomposition as much as possible

      \item might be somewhat imbalanced but it is OK if SES takes only 20\% of time
  
    \end{itemize}



%  \item

\end{itemize}


\end{large}



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\slide{PDD Goals: SFSI}

\begin{figure}[!h]
\vspace*{-0.6cm}
\begin{center}
{\includegraphics[width=16cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/soilmeshDEEP02.jpg}}
\hspace*{7cm}
\\
\vspace*{-4cm}
{\includegraphics[width=11cm]{/home/jeremic/tex/works/Presentation/2003/PEER-Site-Visit/I880_system.jpg}}
\hfill
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Presentation/2002/SFBayComputingDay/I-880_02.jpg}}
\vspace*{-4cm}
\end{center}
\end{figure}


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\slide{PDD Working Example}


\begin{large}

Pile, column and a mass on top

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\begin{figure}[!htb]
\vspace*{-2.0cm}
\hspace*{14.0cm}
{\includegraphics[width=10cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/model3.jpg}}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!h]
\begin{center}
\vspace*{-5.0cm}
{\includegraphics[width=11.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Eq_P/P_T_DL_NS.pdf}}
\hspace{-1.8cm}
{\includegraphics[width=11.5cm]{/home/jeremic/tex/works/Thesis/JinxiuLiao/newthesis/figures/Eq_P/P_S_DL_NS.pdf}}
\vspace*{-4.2cm}
\end{center}
\end{figure}

 \hspace*{4cm} Stiff soil   \hspace*{8cm}  Soft soil
\end{large}



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\slide{PDD: Elastic Decomposition}

\begin{large}

\begin{itemize}

  \item 16 subdomains, 
  \item approx. equal number of elastic elements per domain, 
  \item   minimized inter--domain boundary

  \item OpenSees $\Rightarrow$ Zoltan $\Rightarrow$ Par--METIS

%  \item

\end{itemize}


\end{large}

%\vspace*{-3.5cm}



%\vspace*{-3.5cm}


\begin{figure}[htb]
%\vspace*{-15.5cm}
\begin{center}
{\includegraphics[height=10.0cm]{/home/jeremic/tex/works/Thesis/RituJain/noweight.jpg}}
%{\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Thesis/RituJain/10weight.jpg}}
%{\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Thesis/RituJain/1000weight.jpg}}
\end{center}
\vspace{-9.5cm}
%\vspace*{-0.5cm}
\end{figure}
%




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\slide{PDD: Mild Plasticity}

\begin{large}

\begin{itemize}

  \item Small amount of plastic elements close to the pile


  \item Note smaller domain close to the pile

  \item Note also somewhat increased inter--domain boundary

\end{itemize}


\end{large}

%\vspace*{-3.5cm}



%\vspace*{-3.5cm}


\begin{figure}[htb]
%\vspace*{-15.5cm}
\begin{center}
%{\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Thesis/RituJain/noweight.jpg}}
{\includegraphics[height=10.0cm]{/home/jeremic/tex/works/Thesis/RituJain/10weight.jpg}}
%{\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Thesis/RituJain/1000weight.jpg}}
\end{center}
\vspace{-9.5cm}
%\vspace*{-0.5cm}
\end{figure}
%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\slide{PDD: Severe Plasticity}

\begin{large}

\begin{itemize}

  \item Note small number of elements per CL heavy domains

  \item Note also two large, mostly elastic, subdomains 

  \item Good DD for internal state determination, but bad for SES

  \item Use graph--partitioner to optimize SES phase using info on imbalance and network speed

%  \item

\end{itemize}


\end{large}

%\vspace*{-3.5cm}



%\vspace*{-3.5cm}


\begin{figure}[htb]
\vspace*{-2.0cm}
\begin{center}
%{\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Thesis/RituJain/noweight.jpg}}
%{\includegraphics[height=6.0cm]{/home/jeremic/tex/works/Thesis/RituJain/10weight.jpg}}
{\includegraphics[height=10.0cm]{/home/jeremic/tex/works/Thesis/RituJain/1000weight.jpg}}
\end{center}
\vspace{-8.9cm}
%\vspace*{-0.5cm}
\end{figure}
%




%
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\slide{Current Grid Resources}

\begin{figure}[!htbp]
\begin{center}
{\includegraphics[width=21truecm]{/home/jeremic/tex/works/Conferences/2003/ParallelManchester/Grid05.pdf}}
\end{center}
\vspace*{-1cm}
%\vspace*{-0.3cm}
\end{figure}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\slide{Stress Field Visualization}
%
\begin{figure}[!htb]
\begin{center}
{\includegraphics[height=8.0truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic15.pdf}}
{\includegraphics[height=8.0truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic27.pdf}}
\\
\vspace*{0.2cm}
{\includegraphics[height=8.0truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic28.pdf}}
{\includegraphics[height=8.0truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic38.pdf}}
\vspace*{-1cm}
\end{center}
\end{figure}
%
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\slide{Pile Group Visualization}
%
\begin{figure}[!htb]
\begin{center}
{\includegraphics[height=6truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic71.pdf}}
{\includegraphics[height=6truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic70.pdf}}
{\includegraphics[height=6truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic62.pdf}}
\\
\vspace*{0.2cm}
{\includegraphics[height=9truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic33.pdf}}
{\includegraphics[height=9truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic80.pdf}}
\end{center}
\vspace*{-1cm}
\end{figure}
%
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\slide{Constitutive    Integration   \\   Visual
Debugging}
%
\begin{figure}[!htb]
\begin{center}
{\includegraphics[width=10cm]{/home/jeremic/oofep/mathematica/BModel/BEBtest.pdf}}
{\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/1999/LineSearch/Erratic02.pdf}}
\vspace*{-1cm}
\end{center}
\end{figure}
%
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\slide{Conclusions}

\begin{large}


\begin{itemize}

\vspace*{1.0cm}
\item Plastic Domain Decomposition for tightly and loosely connected processors


\vspace*{1.0cm}
\item Can handle both computational load imbalance, heterogeneous processors and
heterogeneous connectivity speeds

\vspace*{1.0cm}
\item Use of Par--METIS, Zoltan (and all that interfaces with Zoltan), Super--LU, MP\_SOLVE

\vspace*{1.0cm}
\item Public domain within OpenSees framework


%\vspace*{1.0cm}
%\item


\end{itemize}

\end{large}

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%
%    \newpage
%  \begin{center}
%  \includegraphics[height=5.5truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/PileGroups/Plastified_3X3pg_skewCOLOR.jpg}
%  \includegraphics[height=5.5truecm]{/home/jeremic/public_html/GeoWulf/GeoWulf_01_Nov2001a.jpg}
%  \includegraphics[height=5.5truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic30.jpg}
%  \includegraphics[height=5.5truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic71.jpg}
%  \\
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Papers/2001/Visualization/pic80.jpg}
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/SinglePiles/MQP_sand_wsfclay_UFmid2hdp0.pdf}
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Reports/2001/PEER/FinalReport/sp2_stress_pile_isoSmall.jpg}
% % \includegraphics[height=5.0truecm]{/home/jeremic/tex/works/Reports/2001/PEER/FinalReport/sp2_MQP_pile.jpg}
%  \\
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cubic_el_05.jpg}
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Thesis/ZhaohuiYang/Cube/Cubic_pl_05.jpg}
%  \includegraphics[height=6.0truecm]{/home/jeremic/tex/works/Conferences/2002/WCCM/Keynote/Present/p-version_slope.jpg}
%  \end{center}
%



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