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
-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.
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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