Domain Decomposition solvers (FETI) a random walk in history and some current trends Daniel J. Rixen Technische Universität München Institute of Applied Mechanics www.amm.mw.tum.de
[email protected] 8-10 October 2014 39th Woudschoten Conference, organised by the Werkgemeenschap Scientific Computing (WSC) 1 Divide et impera Center for Aerospace Structures CU, Boulder wikipedia When splitting the problem in parts and asking different cpu‘s (or threads) to take care of subproblems, will the problem be solved faster ? FETI, Primal Schur (Balancing) method around 1990 …….. basic methods, mesh decomposer technology 1990-2001 .…….. improvements •! preconditioners, coarse grids •! application to Helmholtz, dynamics, non-linear ... Here the concepts are outlined using some mechanical interpretation. For mathematical details, see lecture of Axel Klawonn. !"!! !"#$%&'()$&'(*+*',-%-.&$(*&$-%'#$%-'(*-/$0%1*()%-).1*,2%()'(%()$%,.,3$4*-($,+$% .5%'%-.6"(*.,%*&76*$-%'%6.2*+'6%+.,(8'0*+(*.,9%1)*6$%$,2*,$$#-%&*2)(%+.,-*0$#%'% ,"&$#*+'6%#$-"6(%'-%()$%.,6:%#$'-.,';6$%2.'6<%% ="+)%.,$%-*0$0%>*$1-%-$$&%(.%#$?$+(%)"&',%6*&*('(*.,-%#'()$#%()',%.;@$+(*>$%>'6"$-<%% A,%*(-$65%&'()$&'(*+-%*-%',%*,0*>*-*;6$%.#2',*-&%",*(*,2%()$.#$(*+'6%+.,($&76'(*.,% ',0%'+(*>$%'776*+'(*.,<%%%%% %%%%%%% R. Courant %B % in Variational! Methods for the solution of problems of equilibrium and vibrations Bulletin of American Mathematical Society, 49, pp.1-23, 1943 Here the concepts are outlined using some mechanical interpretation. For mathematical details, see lecture of Axel Klawonn. Content