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[Krylov_multi.git] / krylov_multi.tex

diff --git a/krylov_multi.tex b/krylov_multi.tex
index 963ce3e0fb614c59f12eabcee07b3120bf055798..40380d0f50678f162ca474373e64278fbf915124 100644 (file)
--- a/krylov_multi.tex
+++ b/krylov_multi.tex
@@ -108,15 +108,15 @@ Jacobi method.
 A general framework  for studying parallel multisplitting has  been presented in
 \cite{o1985multi} by O'Leary and White. Convergence conditions are given for the
 most general case.  Many authors improved multisplitting algorithms by proposing
 A general framework  for studying parallel multisplitting has  been presented in
 \cite{o1985multi} by O'Leary and White. Convergence conditions are given for the
 most general case.  Many authors improved multisplitting algorithms by proposing

-for  example  a  asynchronous  version  \cite{bru1995parallel}  and  convergence
-condition  \cite{bai1999block,bahi2000asynchronous}   in  this  case   or  other
-two-stage algorithms~\cite{frommer1992h,bru1995parallel}
+for  example  an  asynchronous  version  \cite{bru1995parallel}  and  convergence
+conditions  \cite{bai1999block,bahi2000asynchronous}   in  this  case   or  other
+two-stage algorithms~\cite{frommer1992h,bru1995parallel}.

 
 In  \cite{huang1993krylov},  the  authors  proposed  a  parallel  multisplitting
 algorithm in which all the tasks except  one are devoted to solve a sub-block of
 the splitting  and to send their  local solution to  the first task which  is in
 charge to  combine the vectors at  each iteration.  These vectors  form a Krylov
 
 In  \cite{huang1993krylov},  the  authors  proposed  a  parallel  multisplitting
 algorithm in which all the tasks except  one are devoted to solve a sub-block of
 the splitting  and to send their  local solution to  the first task which  is in
 charge to  combine the vectors at  each iteration.  These vectors  form a Krylov

-basis for  which the first tasks minimize  the error function over  the basis to
+basis for  which the first task minimizes  the error function over  the basis to

 increase the convergence, then the other tasks receive the update solution until
 convergence of the global system. 
 
 increase the convergence, then the other tasks receive the update solution until
 convergence of the global system. 
 


@@ -127,7 +127,11 @@ of multisplitting algorithms that take benefit from multisplitting algorithms to
 solve large scale linear systems. Inner  solvers could be based on scalar direct
 method with the LU method or scalar iterative one with GMRES.
 
 solve large scale linear systems. Inner  solvers could be based on scalar direct
 method with the LU method or scalar iterative one with GMRES.
 

-
+In~\cite{prace-multi},  the  authors  have  proposed a  parallel  multisplitting
+algorithm in which large block are solved using a GMRES solver. The authors have
+performed large scale experimentations upto  32.768 cores and they conclude that
+asynchronous  multisplitting algorithm  could more  efficient  than traditionnal
+solvers on exascale architecture with hunders of thousands of cores.

 
 
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