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b(a)e(node)f Fm(i)j Fs(resides)d(in)i(se)n(v)o (eral)e(PEs)h(\(because)0 5244 y Fm(i)f Fs(is)f(a)g(v)o(erte)o(x)f(of)i (se)n(v)o(eral)d(elements)i(mapped)e(to)j(dif)n(ferent)f(PEs\),)g(the)g (v)n(alues)f Fm(x)2582 5258 y Ff(i)2634 5244 y Fs(and)g Fm(y)2834 5258 y Ff(i)2885 5244 y Fs(are)h(replicated)g(on)g(those)f (PEs.)0 5357 y(The)28 b(matrix)h Fi(K)g Fs(is)g(distrib)n(uted)g(so)f (that)h Fm(K)1410 5371 y Ff(ij)1499 5357 y Fs(resides)f(on)g(an)o(y)f (PE)i(on)f(which)g(nodes)f Fm(i)i Fs(and)f Fm(j)35 b Fs(both)28 b(reside.)50 b(Figure)28 b(2)p eop %%Page: 3 7 3 6 bop 1655 -228 a Fj(Mesh)21 b(properties)1608 b Fs(3)p 0 -191 3900 4 v 1213 1828 a @beginspecial 62 @llx 548 @lly 239 @urx 765 @ury 1770 @rwi @setspecial %%BeginDocument: cutmatrix.ps 50 dict begin /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { /patternGrayLevel idef patternGrayLevel -1 eq { /patternString idef } if false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont findfont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 0 descender sub printSize sub printFont /Courier ne printFont /Courier-Bold ne and { 1 add } if def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def %I Idraw 7 Grid 4 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.8 0 0 0.8 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Poly %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 1 SetP %I t [ 1 0 0 1 136 369 ] concat %I 4 107 483 98 448 53 448 53 493 4 Poly End Begin %I Poly %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 1 SetP %I t [ 1 0 0 1 136 369 ] concat %I 3 107 483 157 483 98 448 3 Poly End Begin %I MLine %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 1 SetP %I t [ 1 0 0 1 73 484 ] concat %I 3 170 368 220 368 126 433 3 MLine End Begin %I MLine %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 1 SetP %I t [ 1 0 0 1 43 484 ] concat %I 3 81 373 41 403 126 433 3 MLine End Begin %I MLine %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 1 SetP %I t [ 1 0 0 1 43 484 ] concat %I 3 71 333 41 403 81 373 3 MLine End Begin %I Poly %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 1 SetP %I t [ 1 0 0 1 73 484 ] concat %I 3 170 368 126 433 116 378 3 Poly End Begin %I Poly %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 1 SetP %I t [ 1 0 0 1 43 484 ] concat %I 3 126 433 116 378 81 373 3 Poly End Begin %I Poly %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 1 SetP %I t [ 1 0 0 1 43 484 ] concat %I 4 71 333 81 373 116 378 116 333 4 Poly End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 58 359 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 -47 429 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 112 394 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 -7 399 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 -17 359 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 102 359 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 68 459 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 58 404 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 162 394 ] concat %I 131 458 2 2 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 120 891 ] concat %I [ (a) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 148 882 ] concat %I [ (b) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 206 882 ] concat %I [ (c) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 237 880 ] concat %I [ (d) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 105 856 ] concat %I [ (e) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 137 840 ] concat %I [ (f) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 211 842 ] concat %I [ (g) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 253 843 ] concat %I [ (h) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 81 901 ] concat %I [ (1) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 127 855 ] concat %I [ (2) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 111 811 ] concat %I [ (3) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 174 925 ] concat %I [ (4) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 162 857 ] concat %I [ (5) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 155 811 ] concat %I [ (6) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 244 865 ] concat %I [ (7) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 229 811 ] concat %I [ (8) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 290 847 ] concat %I [ (9) ] Text End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 28 359 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 28 404 ] concat %I 131 458 2 2 Elli End Begin %I Elli %I b 65535 1 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg %I p 0 SetP %I t [ 1 0 0 1 38 458 ] concat %I 131 458 2 2 Elli End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 204 925 ] concat %I [ (4) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 192 857 ] concat %I [ (5) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 185 811 ] concat %I [ (6) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 105 792 ] concat %I [ (1) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 115 792 ] concat %I [ (2) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 125 792 ] concat %I [ (3) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 135 792 ] concat %I [ (4) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 145 792 ] concat %I [ (5) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 154 792 ] concat %I [ (6) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 105 777 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 115 777 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 125 777 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 135 777 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 105 767 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 115 767 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 125 767 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 135 767 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 145 767 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 154 767 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 105 757 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 115 757 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 125 757 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 145 757 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 154 757 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 105 747 ] concat %I [ (X) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-courier-bold-r-*-120-* /Courier-Bold 12 SetF %I t [ 1 0 0 1 115 747 ] concat %I [ (X) ] Text End Begin %I Text 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b(communication)i(pr)n(operties)0 4859 y Fs(Figure)32 b(12)h(sho)n(ws)e(the)h(total)i(v)n(olume)e(of)h (data)f(transferred)h(by)f(all)h(PEs)f(during)h(the)g(communication)e (phase)g(of)i(an)0 4972 y(SMVP)24 b(operation.)36 b(The)23 b(total)h(communication)f(v)n(olume)g(is)h(related)g(to,)g(b)n(ut)g (not)g(identical)g(to,)g(the)g(global)g(number)f(of)0 5085 y(interf)o(ace)f(nodes.)31 b(The)22 b(reason)f(the)o(y)h(are)g (not)h(identical)f(is)h(that)g(a)f(node)g(might)g(be)h(shared)e(by)h (multiple)h(subdomains.)141 5247 y(Figure)34 b(13)g(sho)n(ws)e(the)i (bisection)f(v)n(olume)h Fm(V)54 b Fs(for)35 b(the)f(Quak)o(e)f(SMVP)h (operations,)h(where)f(bisection)f(v)n(olume)0 5360 y(is)e(de\002ned)e (as)h(follo)n(ws.)58 b(W)-7 b(e)30 b(are)h(gi)n(v)o(en)e(a)i(symmetric) g Fm(p)24 b Fg(\002)h Fm(p)31 b Fs(matrix)g Fm(m)g Fs(such)f(that)h Fm(m)2934 5374 y Ff(ij)3026 5360 y Fs(is)g(the)f(number)g(of)i(w)o (ords)p eop %%Page: 7 11 7 10 bop 1462 -228 a Fj(Communication)21 b(properties)1415 b Fs(7)p 0 -191 3900 4 v 247 123 3407 4 v 245 222 4 100 v 741 222 V 758 222 V 1026 193 a Fp(sf10)p 1434 222 V 1451 222 V 569 w(sf5)p 2126 222 V 2143 222 V 611 w(sf2)p 2860 222 V 2877 222 V 653 w(sf1)p 3635 222 V 3652 222 V 247 226 3407 4 v 245 325 4 100 v 297 296 a(subdomains)p 741 325 V 758 325 V 133 w(total)p 1044 325 V 119 w(interf)o(ace)p 1434 325 V 1451 325 V 134 w(total)p 1737 325 V 119 w(interf)o(ace)p 2126 325 V 2143 325 V 155 w(total)p 2470 325 V 140 w(interf)o(ace)p 2860 325 V 2877 325 V 176 w(total)p 3246 325 V 160 w(interf)o(ace)p 3635 325 V 3652 325 V 247 329 3407 4 v 247 349 V 245 448 4 100 v 469 448 V 521 418 a(min)p 741 448 V 758 448 V 159 w(1,947)p 1044 448 V 262 w(211)p 1434 448 V 1451 448 V 115 w(7,828)p 1737 448 V 262 w(432)p 2126 448 V 2143 448 V 115 w(96,123)p 2470 448 V 200 w(3,765)p 2860 448 V 2877 448 V 114 w(614,564)p 3246 448 V 174 w(13,621)p 3652 448 V 245 548 V 338 518 a(4)p 469 548 V 141 w(a)n(vg)p 741 548 V 758 548 V 170 w(1,970)p 1044 548 V 262 w(287)p 1434 548 V 1451 548 V 115 w(7,968)p 1737 548 V 262 w(847)p 2126 548 V 2143 548 V 115 w(97,572)p 2470 548 V 200 w(5,760)p 2860 548 V 2877 548 V 114 w(624,583)p 3246 548 V 174 w(18,297)p 3652 548 V 245 648 V 469 648 V 521 618 a(max)p 741 648 V 758 648 V 145 w(1,997)p 1044 648 V 262 w(366)p 1434 648 V 1451 648 V 115 w(8,207)p 1737 648 V 200 w(1,274)p 2126 648 V 2143 648 V 114 w(99,613)p 2470 648 V 200 w(9,185)p 2860 648 V 2877 648 V 114 w(630,394)p 3246 648 V 174 w(30,944)p 3652 648 V 247 651 3407 4 v 245 751 4 100 v 469 751 V 521 721 a(min)p 741 751 V 758 751 V 159 w(1,025)p 1044 751 V 262 w(181)p 1434 751 V 1451 751 V 115 w(3,971)p 1737 751 V 262 w(521)p 2126 751 V 2143 751 V 115 w(48,046)p 2470 751 V 200 w(2,368)p 2860 751 V 2877 751 V 114 w(306,611)p 3246 751 V 216 w(9,974)p 3652 751 V 245 850 V 338 820 a(8)p 469 850 V 141 w(a)n(vg)p 741 850 V 758 850 V 170 w(1,061)p 1044 850 V 262 w(288)p 1434 850 V 1451 850 V 115 w(4,164)p 1737 850 V 262 w(772)p 2126 850 V 2143 850 V 115 w(49,559)p 2470 850 V 200 w(4,397)p 2860 850 V 2877 850 V 114 w(315,659)p 3246 850 V 174 w(15,814)p 3652 850 V 245 950 V 469 950 V 521 920 a(max)p 741 950 V 758 950 V 145 w(1,081)p 1044 950 V 262 w(373)p 1434 950 V 1451 950 V 115 w(4,280)p 1737 950 V 200 w(1,102)p 2126 950 V 2143 950 V 114 w(50,990)p 2470 950 V 200 w(5,676)p 2860 950 V 2877 950 V 114 w(323,728)p 3246 950 V 174 w(24,650)p 3652 950 V 247 953 3407 4 v 245 1053 4 100 v 469 1053 V 521 1023 a(min)p 741 1053 V 758 1053 V 221 w(542)p 1044 1053 V 263 w(148)p 1434 1053 V 1451 1053 V 115 w(2,081)p 1737 1053 V 262 w(324)p 2126 1053 V 2143 1053 V 115 w(24,213)p 2470 1053 V 200 w(1,911)p 2860 1053 V 2877 1053 V 114 w(155,093)p 3246 1053 V 216 w(7,656)p 3652 1053 V 245 1152 V 317 1122 a(16)p 469 1152 V 120 w(a)n(vg)p 741 1152 V 758 1152 V 232 w(575)p 1044 1152 V 263 w(225)p 1434 1152 V 1451 1152 V 115 w(2,182)p 1737 1152 V 262 w(571)p 2126 1152 V 2143 1152 V 115 w(25,367)p 2470 1152 V 200 w(3,331)p 2860 1152 V 2877 1152 V 114 w(160,383)p 3246 1152 V 174 w(12,922)p 3652 1152 V 245 1252 V 469 1252 V 521 1222 a(max)p 741 1252 V 758 1252 V 207 w(620)p 1044 1252 V 263 w(285)p 1434 1252 V 1451 1252 V 115 w(2,273)p 1737 1252 V 262 w(767)p 2126 1252 V 2143 1252 V 115 w(26,278)p 2470 1252 V 200 w(4,471)p 2860 1252 V 2877 1252 V 114 w(165,556)p 3246 1252 V 174 w(19,254)p 3652 1252 V 247 1255 3407 4 v 245 1355 4 100 v 469 1355 V 521 1325 a(min)p 741 1355 V 758 1355 V 221 w(295)p 1044 1355 V 263 w(103)p 1434 1355 V 1451 1355 V 115 w(1,115)p 1737 1355 V 262 w(276)p 2126 1355 V 2143 1355 V 115 w(12,366)p 2470 1355 V 200 w(1,471)p 2860 1355 V 2877 1355 V 155 w(78,918)p 3246 1355 V 217 w(4,202)p 3652 1355 V 245 1455 V 317 1425 a(32)p 469 1455 V 120 w(a)n(vg)p 741 1455 V 758 1455 V 232 w(321)p 1044 1455 V 263 w(169)p 1434 1455 V 1451 1455 V 115 w(1,167)p 1737 1455 V 262 w(422)p 2126 1455 V 2143 1455 V 115 w(13,120)p 2470 1455 V 200 w(2,501)p 2860 1455 V 2877 1455 V 155 w(81,675)p 3246 1455 V 217 w(9,360)p 3652 1455 V 245 1554 V 469 1554 V 521 1524 a(max)p 741 1554 V 758 1554 V 207 w(349)p 1044 1554 V 263 w(246)p 1434 1554 V 1451 1554 V 115 w(1,245)p 1737 1554 V 262 w(617)p 2126 1554 V 2143 1554 V 115 w(13,788)p 2470 1554 V 200 w(3,551)p 2860 1554 V 2877 1554 V 155 w(85,963)p 3246 1554 V 175 w(13,779)p 3652 1554 V 247 1557 3407 4 v 245 1657 4 100 v 469 1657 V 521 1627 a(min)p 741 1657 V 758 1657 V 221 w(162)p 1044 1657 V 305 w(66)p 1434 1657 V 1451 1657 V 177 w(583)p 1737 1657 V 263 w(145)p 2126 1657 V 2143 1657 V 157 w(6,441)p 2470 1657 V 262 w(988)p 2860 1657 V 2877 1657 V 156 w(40,405)p 3246 1657 V 217 w(2,751)p 3652 1657 V 245 1757 V 317 1727 a(64)p 469 1757 V 120 w(a)n(vg)p 741 1757 V 758 1757 V 232 w(184)p 1044 1757 V 263 w(123)p 1434 1757 V 1451 1757 V 177 w(637)p 1737 1757 V 263 w(303)p 2126 1757 V 2143 1757 V 157 w(6,870)p 2470 1757 V 200 w(1,832)p 2860 1757 V 2877 1757 V 155 w(41,994)p 3246 1757 V 217 w(6,908)p 3652 1757 V 245 1856 V 469 1856 V 521 1826 a(max)p 741 1856 V 758 1856 V 207 w(222)p 1044 1856 V 263 w(184)p 1434 1856 V 1451 1856 V 177 w(760)p 1737 1856 V 263 w(479)p 2126 1856 V 2143 1856 V 157 w(7,199)p 2470 1856 V 200 w(2,869)p 2860 1856 V 2877 1856 V 155 w(44,132)p 3246 1856 V 175 w(11,146)p 3652 1856 V 247 1860 3407 4 v 245 1959 4 100 v 469 1959 V 521 1929 a(min)p 741 1959 V 758 1959 V 262 w(91)p 1044 1959 V 306 w(51)p 1434 1959 V 1451 1959 V 177 w(314)p 1737 1959 V 305 w(95)p 2126 1959 V 2143 1959 V 157 w(3,408)p 2470 1959 V 262 w(523)p 2860 1959 V 2877 1959 V 156 w(20,803)p 3246 1959 V 217 w(2,110)p 3652 1959 V 245 2059 V 297 2029 a(128)p 469 2059 V 98 w(a)n(vg)p 741 2059 V 758 2059 V 232 w(107)p 1044 2059 V 305 w(84)p 1434 2059 V 1451 2059 V 177 w(353)p 1737 2059 V 263 w(209)p 2126 2059 V 2143 2059 V 157 w(3,622)p 2470 2059 V 200 w(1,253)p 2860 2059 V 2877 2059 V 155 w(21,632)p 3246 2059 V 217 w(4,652)p 3652 2059 V 245 2159 V 469 2159 V 521 2129 a(max)p 741 2159 V 758 2159 V 207 w(133)p 1044 2159 V 263 w(125)p 1434 2159 V 1451 2159 V 177 w(406)p 1737 2159 V 263 w(324)p 2126 2159 V 2143 2159 V 157 w(3,997)p 2470 2159 V 200 w(2,232)p 2860 2159 V 2877 2159 V 155 w(22,683)p 3246 2159 V 217 w(7,579)p 3652 2159 V 247 2162 3407 4 v 886 2414 a Fs(Figure)23 b(10:)32 b(T)-7 b(otal)23 b(nodes)d(and)i(interf)o(ace)h(nodes)d(per)j(subdomain)p 153 2637 3594 4 v 151 2736 4 100 v 648 2736 V 665 2736 V 953 2707 a Fp(sf10)p 1382 2736 V 1399 2736 V 611 w(sf5)p 2116 2736 V 2133 2736 V 652 w(sf2)p 2891 2736 V 2908 2736 V 705 w(sf1)p 3728 2736 V 3745 2736 V 153 2740 3594 4 v 151 2839 4 100 v 203 2809 a(subdomains)p 648 2839 V 665 2839 V 154 w(total)p 993 2839 V 140 w(interf)o(ace)p 1382 2839 V 1399 2839 V 155 w(total)p 1726 2839 V 140 w(interf)o(ace)p 2116 2839 V 2133 2839 V 176 w(total)p 2502 2839 V 160 w(interf)o(ace)p 2891 2839 V 2908 2839 V 207 w(total)p 3339 2839 V 192 w(interf)o(ace)p 3728 2839 V 3745 2839 V 153 2843 3594 4 v 153 2863 V 151 2962 4 100 v 376 2962 V 427 2932 a(min)p 648 2962 V 665 2962 V 159 w(11,548)p 993 2962 V 262 w(565)p 1382 2962 V 1399 2962 V 115 w(48,378)p 1726 2962 V 200 w(1,193)p 2116 2962 V 2133 2962 V 114 w(631,492)p 2502 2962 V 157 w(10,974)p 2891 2962 V 2908 2962 V 114 w(4,169,622)p 3339 2962 V 173 w(40,262)p 3745 2962 V 151 3062 V 245 3032 a(4)p 376 3062 V 140 w(a)n(vg)p 648 3062 V 665 3062 V 170 w(11,624)p 993 3062 V 262 w(781)p 1382 3062 V 1399 3062 V 115 w(48,777)p 1726 3062 V 200 w(2,361)p 2116 3062 V 2133 3062 V 114 w(635,662)p 2502 3062 V 157 w(16,782)p 2891 3062 V 2908 3062 V 114 w(4,198,043)p 3339 3062 V 173 w(54,008)p 3745 3062 V 151 3161 V 376 3161 V 427 3132 a(max)p 648 3161 V 665 3161 V 145 w(11,703)p 993 3161 V 200 w(1,000)p 1382 3161 V 1399 3161 V 114 w(49,464)p 1726 3161 V 200 w(3,537)p 2116 3161 V 2133 3161 V 114 w(641,529)p 2502 3161 V 157 w(26,799)p 2891 3161 V 2908 3161 V 114 w(4,213,857)p 3339 3161 V 173 w(91,207)p 3745 3161 V 153 3165 3594 4 v 151 3264 4 100 v 376 3264 V 427 3235 a(min)p 648 3264 V 665 3264 V 201 w(5,912)p 993 3264 V 262 w(479)p 1382 3264 V 1399 3264 V 115 w(24,319)p 1726 3264 V 200 w(1,442)p 2116 3264 V 2133 3264 V 114 w(315,794)p 2502 3264 V 199 w(6,829)p 2891 3264 V 2908 3264 V 114 w(2,083,537)p 3339 3264 V 173 w(29,454)p 3745 3264 V 151 3364 V 245 3334 a(8)p 376 3364 V 140 w(a)n(vg)p 648 3364 V 665 3364 V 212 w(6,013)p 993 3364 V 262 w(788)p 1382 3364 V 1399 3364 V 115 w(24,882)p 1726 3364 V 200 w(2,158)p 2116 3364 V 2133 3364 V 114 w(320,054)p 2502 3364 V 157 w(12,809)p 2891 3364 V 2908 3364 V 114 w(2,108,905)p 3339 3364 V 173 w(46,704)p 3745 3364 V 151 3464 V 376 3464 V 427 3434 a(max)p 648 3464 V 665 3464 V 187 w(6,072)p 993 3464 V 200 w(1,018)p 1382 3464 V 1399 3464 V 114 w(25,230)p 1726 3464 V 200 w(3,095)p 2116 3464 V 2133 3464 V 114 w(324,028)p 2502 3464 V 157 w(16,557)p 2891 3464 V 2908 3464 V 114 w(2,131,610)p 3339 3464 V 173 w(72,806)p 3745 3464 V 153 3467 3594 4 v 151 3567 4 100 v 376 3567 V 427 3537 a(min)p 648 3567 V 665 3567 V 201 w(3,033)p 993 3567 V 262 w(393)p 1382 3567 V 1399 3567 V 115 w(12,423)p 1726 3567 V 262 w(889)p 2116 3567 V 2133 3567 V 115 w(158,507)p 2502 3567 V 199 w(5,561)p 2891 3567 V 2908 3567 V 114 w(1,047,039)p 3339 3567 V 173 w(22,444)p 3745 3567 V 151 3666 V 224 3636 a(16)p 376 3666 V 119 w(a)n(vg)p 648 3666 V 665 3666 V 212 w(3,122)p 993 3666 V 262 w(616)p 1382 3666 V 1399 3666 V 115 w(12,710)p 1726 3666 V 200 w(1,603)p 2116 3666 V 2133 3666 V 114 w(161,708)p 2502 3666 V 199 w(9,724)p 2891 3666 V 2908 3666 V 114 w(1,061,930)p 3339 3666 V 173 w(38,216)p 3745 3666 V 151 3766 V 376 3766 V 427 3736 a(max)p 648 3766 V 665 3766 V 187 w(3,244)p 993 3766 V 262 w(811)p 1382 3766 V 1399 3766 V 115 w(12,977)p 1726 3766 V 200 w(2,161)p 2116 3766 V 2133 3766 V 114 w(164,204)p 2502 3766 V 157 w(13,120)p 2891 3766 V 2908 3766 V 114 w(1,076,253)p 3339 3766 V 173 w(57,141)p 3745 3766 V 153 3769 3594 4 v 151 3869 4 100 v 376 3869 V 427 3839 a(min)p 648 3869 V 665 3869 V 201 w(1,576)p 993 3869 V 262 w(274)p 1382 3869 V 1399 3869 V 156 w(6,419)p 1726 3869 V 263 w(752)p 2116 3869 V 2133 3869 V 156 w(79,986)p 2502 3869 V 200 w(4,243)p 2891 3869 V 2908 3869 V 176 w(527,572)p 3339 3869 V 174 w(12,258)p 3745 3869 V 151 3968 V 224 3939 a(32)p 376 3968 V 119 w(a)n(vg)p 648 3968 V 665 3968 V 212 w(1,645)p 993 3968 V 262 w(466)p 1382 3968 V 1399 3968 V 156 w(6,556)p 1726 3968 V 201 w(1,188)p 2116 3968 V 2133 3968 V 155 w(82,091)p 2502 3968 V 200 w(7,299)p 2891 3968 V 2908 3968 V 176 w(535,294)p 3339 3968 V 174 w(27,698)p 3745 3968 V 151 4068 V 376 4068 V 427 4038 a(max)p 648 4068 V 665 4068 V 187 w(1,719)p 993 4068 V 262 w(706)p 1382 4068 V 1399 4068 V 156 w(6,783)p 1726 4068 V 201 w(1,768)p 2116 4068 V 2133 4068 V 155 w(83,863)p 2502 4068 V 158 w(10,462)p 2891 4068 V 2908 4068 V 176 w(547,042)p 3339 4068 V 174 w(41,060)p 3745 4068 V 153 4071 3594 4 v 151 4171 4 100 v 376 4171 V 427 4141 a(min)p 648 4171 V 665 4171 V 263 w(822)p 993 4171 V 263 w(171)p 1382 4171 V 1399 4171 V 156 w(3,270)p 1726 4171 V 263 w(392)p 2116 4171 V 2133 4171 V 156 w(40,731)p 2502 4171 V 200 w(2,836)p 2891 4171 V 2908 4171 V 176 w(266,474)p 3339 4171 V 216 w(7,987)p 3745 4171 V 151 4271 V 224 4241 a(64)p 376 4271 V 119 w(a)n(vg)p 648 4271 V 665 4271 V 274 w(879)p 993 4271 V 263 w(338)p 1382 4271 V 1399 4271 V 156 w(3,415)p 1726 4271 V 263 w(855)p 2116 4271 V 2133 4271 V 156 w(41,918)p 2502 4271 V 200 w(5,356)p 2891 4271 V 2908 4271 V 176 w(270,992)p 3339 4271 V 174 w(20,454)p 3745 4271 V 151 4370 V 376 4370 V 427 4340 a(max)p 648 4370 V 665 4370 V 249 w(968)p 993 4370 V 263 w(518)p 1382 4370 V 1399 4370 V 156 w(3,736)p 1726 4370 V 201 w(1,381)p 2116 4370 V 2133 4370 V 155 w(42,807)p 2502 4370 V 200 w(8,601)p 2891 4370 V 2908 4370 V 176 w(276,949)p 3339 4370 V 174 w(33,471)p 3745 4370 V 153 4374 3594 4 v 151 4473 4 100 v 376 4473 V 427 4443 a(min)p 648 4473 V 665 4473 V 263 w(438)p 993 4473 V 263 w(130)p 1382 4473 V 1399 4473 V 156 w(1,691)p 1726 4473 V 263 w(249)p 2116 4473 V 2133 4473 V 156 w(20,904)p 2502 4473 V 200 w(1,479)p 2891 4473 V 2908 4473 V 176 w(134,982)p 3339 4473 V 216 w(6,122)p 3745 4473 V 151 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2976 V 1448 2946 a(min)p 1668 2976 V 1685 2976 V 218 w(43)p 1928 2976 V 99 w(401)p 2152 2976 V 98 w(2,206)p 2438 2976 V 98 w(5,692)p 2725 2976 V 1172 3075 V 1265 3045 a(4)p 1396 3075 V 141 w(a)n(vg)p 1668 3075 V 1685 3075 V 229 w(88)p 1928 3075 V 99 w(415)p 2152 3075 V 98 w(2,280)p 2438 3075 V 98 w(6,582)p 2725 3075 V 1172 3175 V 1396 3175 V 1448 3145 a(max)p 1668 3175 V 1685 3175 V 163 w(189)p 1928 3175 V 98 w(429)p 2152 3175 V 98 w(2,354)p 2438 3175 V 98 w(8,012)p 2725 3175 V 1174 3178 1553 4 v 1172 3278 4 100 v 1396 3278 V 1448 3248 a(min)p 1668 3278 V 1685 3278 V 260 w(1)p 1928 3278 V 182 w(4)p 2152 3278 V 161 w(733)p 2438 3278 V 161 w(173)p 2725 3278 V 1172 3377 V 1265 3347 a(8)p 1396 3377 V 141 w(a)n(vg)p 1668 3377 V 1685 3377 V 229 w(61)p 1928 3377 V 99 w(181)p 2152 3377 V 98 w(1,166)p 2438 3377 V 98 w(3,365)p 2725 3377 V 1172 3477 V 1396 3477 V 1448 3447 a(max)p 1668 3477 V 1685 3477 V 163 w(134)p 1928 3477 V 98 w(385)p 2152 3477 V 98 w(1,953)p 2438 3477 V 98 w(5,214)p 2725 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b(a)f(sparse)f(local)i(matrix)0 1216 y(is)37 b(constructed)e(on)h(each) g(PE.)g(Figure)g(24)h(sho)n(ws)e(the)h(number)g(of)h(nonzero)f(matrix)h (entries)f(per)h(subdomain.)73 b(If)0 1329 y(the)29 b(simulation)h(has) e Fm(k)33 b Fs(dof,)e(then)e(each)f(nonzero)g(entry)i(requires)e(2)p Fm(k)2309 1296 y Fd(2)2376 1329 y Fs(\003oating)h(point)h(operations)e (during)h(the)g(local)0 1441 y(computation)c(phase)f(of)j(the)e(SMVP) -10 b(.)26 b(Notice)g(that)g(the)g(computation)f(is)h(reasonably)e (well)j(balanced)d(across)g(the)i(PEs,)0 1554 y(with)d(only)f(a)h(fe)n (w)f(percent)g(dif)n(ference)g(between)f(the)h(maximum)g(and)g(minimum) h(number)f(of)h(nonzeros.)p 913 1777 2074 4 v 911 1876 4 100 v 963 1847 a Fp(subdomains)p 1408 1876 V 1425 1876 V 157 w(sf10)p 1752 1876 V 225 w(sf5)p 2122 1876 V 299 w(sf2)p 2553 1876 V 329 w(sf1)p 2985 1876 V 913 1880 2074 4 v 913 1900 V 911 1999 4 100 v 1136 1999 V 1187 1969 a(min)p 1408 1999 V 1425 1999 V 159 w(25,043)p 1752 1999 V 97 w(104,584)p 2122 1999 V 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2074 4 v 911 2604 4 100 v 1136 2604 V 1187 2574 a(min)p 1408 2604 V 1425 2604 V 200 w(6,608)p 1752 2604 V 139 w(26,927)p 2122 2604 V 160 w(341,227)p 2553 2604 V 96 w(2,249,171)p 2985 2604 V 911 2703 V 984 2674 a(16)p 1136 2703 V 119 w(a)n(vg)p 1408 2703 V 1425 2703 V 211 w(6,819)p 1752 2703 V 139 w(27,604)p 2122 2703 V 160 w(348,782)p 2553 2703 V 96 w(2,284,243)p 2985 2703 V 911 2803 V 1136 2803 V 1187 2773 a(max)p 1408 2803 V 1425 2803 V 186 w(7,108)p 1752 2803 V 139 w(28,227)p 2122 2803 V 160 w(354,686)p 2553 2803 V 96 w(2,318,062)p 2985 2803 V 913 2806 2074 4 v 911 2906 4 100 v 1136 2906 V 1187 2876 a(min)p 1408 2906 V 1425 2906 V 200 w(3,447)p 1752 2906 V 139 w(13,953)p 2122 2906 V 160 w(172,338)p 2553 2906 V 96 w(1,134,062)p 2985 2906 V 911 3006 V 984 2976 a(32)p 1136 3006 V 119 w(a)n(vg)p 1408 3006 V 1425 3006 V 211 w(3,610)p 1752 3006 V 139 w(14,278)p 2122 3006 V 160 w(177,302)p 2553 3006 V 96 w(1,152,263)p 2985 3006 V 911 3105 V 1136 3105 V 1187 3075 a(max)p 1408 3105 V 1425 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w(46,568)p 2553 3610 V 159 w(296,267)p 2985 3610 V 911 3710 V 1136 3710 V 1187 3680 a(max)p 1408 3710 V 1425 3710 V 186 w(1,208)p 1752 3710 V 181 w(4,278)p 2122 3710 V 201 w(49,047)p 2553 3710 V 159 w(302,947)p 2985 3710 V 913 3713 2074 4 v 151 3965 a Fs(Figure)f(24:)33 b(Nonzero)21 b(matrix)i(entries)f(per)h(subdomain)d(per)j(dof)g Fg(\002)f Fs(dof)h(\(assuming)e(nonsymmetric)g(storage\))141 4228 y(Figure)16 b(25)g(sho)n(ws)e(the)i(number)f(of)i(nonzero)d (entries)i(per)g(ro)n(w)g(for)h(the)f(PE)g(with)g(the)g(fe)n(west)g(a)n (v)o(erage)e(entries)h(per)h(ro)n(w)-6 b(.)0 4341 y(These)18 b(are)i(interesting)f(numbers)g(because)e(the)o(y)i(sho)n(w)g(ho)n(w)g (e)o(xtremely)g(sparse)f(the)i(matrices)f(are.)32 b(The)19 b(implication)h(is)0 4454 y(that)h(the)g(inner)h(loops)e(of)h(the)g (SMVP)h(will)g(tend)f(to)g(be)g(short)g(and)f(we)h(can)f(e)o(xpect)g (dif)n(\002culty)h(in)g(amortizing)g(the)g(startup)0 4566 y(costs)g(of)i(these)f(loops.)141 4729 y(The)j(ratio)i(of)f (computation)f(to)h(communication)f(on)h(a)f(PE)h(can)f(pro)o(vide)g (some)g(insight)h(into)g(the)g(relati)n(v)o(e)g(cost)f(of)0 4842 y(communication)30 b(at)h(runtime.)59 b(Generally)-6 b(,)33 b(high)e(computation/communication)e(ratios)i(are)g(desirable.) 58 b(Figure)31 b(26)0 4955 y(sho)n(ws)17 b(the)h (computation/communication)e(ratios)i(for)h(the)f(SPMV)g(operations)g (from)h(the)f(Quak)o(e)f(simulations.)30 b(F)o(or)18 b(the)0 5068 y(SMVP)-10 b(,)21 b(the)f(\003oating)h(point)g(operation)f (is)h(a)g(useful)f(measure)g(of)h(w)o(ork.)32 b(Thus,)20 b(each)g(ratio)h(\(denoted)f(fp/comm)h(ratio)h(in)0 5181 y(the)k(\002gure\))g(is)h(computed)d(by)i(the)g(di)n(viding)g(the)g(a)n (v)o(erage)e(number)i(of)g(\003oating)g(point)g(operations)f(per)h(PE)g (during)g(the)0 5294 y(computation)21 b(phase)g(by)h(the)h(a)n(v)o (erage)d(number)i(of)h(w)o(ords)f(transferred)h(per)f(PE)g(during)h (the)f(communication)f(phase.)p eop %%Page: 16 20 16 19 bop 0 -228 a Fs(16)867 b Fj(Da)n(vid)22 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