📄 split.ps
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y(zero,)f(suc)o(h)g(that)g(ev)o(en)f(in)h(non-split)g(sc)o(hemes)e(in)o(terp)q(olation)i(to)g(collo)q(cation)g(p)q(oin)o(ts)h(has)f(to)h(b)q(e)78 1365 y(included)i(for)i(staggered)g(grid)f(metho)q(ds.)27b(When)18 b(splitting)g(the)g(w)o(a)o(v)o(e)g(op)q(erator,)h(one)g(has)g(to)78 1425 y(tak)o(e)e(care)h(of)g(prop)q(er)g(collo)q(cation)g(in)o(terp)q(olation)f(when)h(using)h(a)f(staggered)g(grid.)26b(Th)o(us)18 b(the)78 1485 y(in)o(terp)q(olation)e(issue)h(can)g(complicate)d(the)j(primary)e(goal)j(of)f(adapting)g(deriv)m(ativ)o(e)f(op)q(erators)78 1545 y(to)h(the)f(quan)o(tities.)44b(Splitting)16 b(of)g(the)h(w)o(a)o(v)o(e)e(op)q(erator)j(also)f(a\013ects)g(the)f(n)o(umerical)e(stabilit)o(y)78 1914y(Figure)36 b(0.1:)61 b(The)36 b(primary)e(grid)78 1962y(and)18 b(secondary)g(grid)g(as)g(usually)f(de-)78 2011y(\014ned)26 b(for)h(staggered)g(grid)g(applica-)78 2059y(tions)i(for)g(elastic)f(w)o(a)o(v)o(e)g(mo)q(deling.)782107 y(The)34 b(primary)e(cub)q(e)i(cen)o(ter)f(coin-)782155 y(cides)i(with)i(the)f(secondary)g(cub)q(e)78 2203y(edge.)70 b(The)33 b(p)q(ositions)g(of)g(stress,)782251 y(strain)g(and)h(sti\013ness)g(comp)q(onen)o(ts)782299 y(are)14 b(indicated)f(\(blac)o(k)g(triangles\),)g(to-)782348 y(gether)19 b(with)g(the)f(ev)m(aluation)i(p)q(oin)o(ts)782396 y(of)e(the)f(split)f(w)o(a)o(v)o(e)h(op)q(erator)h(sc)o(heme)782444 y(\(empt)o(y)c(b)q(o)o(xes\).)p 440 2408 158 2 v440 2463 2 55 v 57 w @beginspecial @setspecial @endspecialFa(stagsplit)p 596 2463 V 440 2465 158 2 v 28 w Fj([NR])8891701 y 16056010 14208860 2433925 11117117 36377313 40916254 startTexFig 889 1701 a%%BeginDocument: ././../split/Fig/stagsplit.ps.save/arrowhead {0 begintransform originalCTM itransform/taily exch def/tailx exch deftransform 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 defgsaveoriginalCTM setmatrixtipx tipy translateangle rotatenewpatharrowHeight neg arrowWidth 2 div moveto0 0 linetoarrowHeight neg arrowWidth 2 div neg linetopatternNone not {originalCTM setmatrix/padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mularrowWidth div def/padtail brushWidth 2 div deftipx tipy translateangle rotatepadtip 0 translatearrowHeight padtip add padtail add arrowHeight div dup scalearrowheadpathifill} ifbrushNone not {originalCTM setmatrixtipx tipy translateangle rotatearrowheadpathistroke} ifgrestoreend} dup 0 9 dict put def/arrowheadpath {newpatharrowHeight neg arrowWidth 2 div moveto0 0 linetoarrowHeight neg arrowWidth 2 div neg lineto} def/leftarrow {0 beginy exch get /taily exch defx exch get /tailx exch defy exch get /tipy exch defx exch get /tipx exch defbrushLeftArrow { tipx tipy tailx taily arrowhead } ifend} dup 0 4 dict put def/rightarrow {0 beginy exch get /tipy exch defx exch get /tipx exch defy exch get /taily exch defx exch get /tailx exch defbrushRightArrow { tipx tipy tailx taily arrowhead } ifend} dup 0 4 dict put def/arrowHeight 10 def/arrowWidth 5 def/IdrawDict 52 dict defIdrawDict begin/reencodeISO {dup dup findfont dup length dict begin{ 1 index /FID ne { def }{ pop pop } ifelse } forall/Encoding ISOLatin1Encoding defcurrentdict end definefont} def/ISOLatin1Encoding [/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/minus/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright/asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve/dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut/ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar/section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla/Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] def/Helvetica-Bold reencodeISO def/Symbol dup findfont def/none null def/numGraphicParameters 17 def/stringLimit 65535 def/Begin {savenumGraphicParameters dict begin} def/End {endrestore} def/SetB {dup type /nulltype eq {popfalse /brushRightArrow ideffalse /brushLeftArrow ideftrue /brushNone idef} {/brushDashOffset idef/brushDashArray idef0 ne /brushRightArrow idef0 ne /brushLeftArrow idef/brushWidth ideffalse /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} {dup -1 eq {/patternGrayLevel idef/patternString idef} {/patternGrayLevel idef} ifelsefalse /patternNone idef} ifelse} def/BSpl {0 beginstorexynnewpathn 1 gt {0 0 0 0 0 0 1 1 true subsplinen 2 gt {0 0 0 0 1 1 2 2 false subspline1 1 n 3 sub {/i exch defi 1 sub dup i dup i 1 add dup i 2 add dup false subspline} forn 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline} ifn 2 sub dup n 1 sub dup 2 copy 2 copy false subsplinepatternNone not brushLeftArrow not brushRightArrow not and and { ifill } ifbrushNone not { istroke } if0 0 1 1 leftarrown 2 sub dup n 1 sub dup rightarrow} ifend} dup 0 4 dict put def/Circ {newpath0 360 arcpatternNone not { ifill } ifbrushNone not { istroke } if} def/CBSpl {0 begindup 2 gt {storexynnewpathn 1 sub dup 0 0 1 1 2 2 true subspline
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