Integration takes more time:

*To*: mathgroup at smc.vnet.net*Subject*: [mg91504] Integration takes more time:*From*: Gopinath Venkatesan <gopinathv at ou.edu>*Date*: Sun, 24 Aug 2008 07:06:42 -0400 (EDT)

Hello Mathematica Friends This notebook takes more time to evaluate one integral. Any suggestions to improve the speed? Actually I found the Timing[] for intfactor[1,0.5] which comes to be 7.5 sec. So the integration could take around 7.5*240 sec = 30 min. But it took nearly 50 minutes. But still I am wondering if we could improve the solution time here, even less than 30 min, as it looked odd for me. May be something wrong here? Thanks, Gopinath University of Oklahoma (* code starts here *) mperl = 2303; (* previously was 4000 *) bs = 3.757;(* previously was same *) ht = 2.1; (* previously was same *) len = 30;(* previously was 30 *) vel = 27.778;(* previously was 21.9558 *) emod = 2.87*10^9;(* previously was 2.11E11 *) moi = (bs ht^3)/12;(* previously was 1/12 *) load = 100000;(* previously was 100000 *) ag = 9.81; Tfact = len/vel; \[Omega][j_] := (j^2 \[Pi]^2)/len^2 Sqrt[(emod moi)/mperl]; \[CapitalOmega][k_] := (k \[Pi])/Tfact; \[Kappa] = load/(ag mperl len); \[Alpha] = \[CapitalOmega][1]/\[Omega][1]; deflmid = (load len^3)/(48 emod moi); m = 7; n = 24; nn = 10; num = 10; \[Xi]i = Array[xi, m]; \[Tau]j = Array[ti, n]; intrfact = Table[0, {i, 1, num}, {j, 1, n}]; wdeflmass = Table[0, {i, 1, m}, {j, 1, n}]; \[Xi]i = Table[(i - 1)/(m - 1), {i, 1, m}]; \[Tau]j = Table[(1 - Cos[(j - 1)/(n - 1) \[Pi]])/2, {j, 1, n}]; sigfactor[\[Tau]_] := (\!\( \*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(nn\)] \*FractionBox[\(1\), \( \*SuperscriptBox[\(\[Omega][k]\), \(2\)] - \*SuperscriptBox[\(\[CapitalOmega][k]\), \(2\)]\)]\ \((\(- \*SuperscriptBox[\(\[CapitalOmega][ k]\), \(2\)]\)\ Sin[\[CapitalOmega][ k]\ \[Tau]] + \[CapitalOmega][k]\ \[Omega][ k]\ Sin[\[Omega][k]\ \[Tau]])\)\ Sin[\[Omega][ k]\ \[Tau]]\)); Timing[sigfactor[0.5]] intfact[nmode_, time_] := Re[\!\( \*SubsuperscriptBox[\(\[Integral]\), \(0\), \(time\)]\((\((Sin[\ \[CapitalOmega][ nmode]\ \[Tau]] - \[Kappa]\ Sin[\[CapitalOmega][ nmode]\ \[Tau]]\ sigfactor[\[Tau]])\)\ Sin[\[Omega][ nmode]\ \((time - \[Tau])\)])\) \[DifferentialD]\[Tau]\)]; Print["Passed"]; Timing[Table[ intrfact[[nmode, t]] = ( 2 \[Kappa] ag)/\[Omega][nmode] intfact[nmode, Tfact \[Tau]j[[t]]], {nmode, 1, num}, {t, 1, n}]] Print["Over"]; wdeflmass = Table[\!\( \*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(num\)]\((Sin[ k\ \[Pi]\ \[Xi]i[\([\)\(s\)\(]\)]]\ intrfact[\([\)\(k, t\)\(]\)])\)\), {s, 1, m}, {t, 1, n}]; ym = Table[{\[Tau]j[[j]], -wdeflmass[[(m + 1)/2, j]]/deflmid}, {j, 1, n}]; pm = ListPlot[ym, Joined -> True, PlotStyle -> Hue[0.7], InterpolationOrder -> 3] (* Code ends here *)