       Re: How can I acceralate calcution by improving coding?

• To: mathgroup at smc.vnet.net
• Subject: [mg30345] Re: [mg30314] How can I acceralate calcution by improving coding?
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Sat, 11 Aug 2001 03:40:05 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```One thing that will make some improvement is wrapping  Evaluate around
your  your function inside Plot3D. Here is what I get running the
preview version of  Mathematica 4.1 for Mac OS X on a 400 mghz PowerBook
G4:

Timing[Plot3D[u[r, t], {t, 0, 2}, {r, a, b}, PlotRange -> {-1, 1},
AxesLabel -> {" t sec", "  r m", "u K  "},
FaceGrids -> {{0, -1, 0}, {1, 0, 0}, {0, 1, 0}, {-1, 0, 0}},
PlotPoints -> 50]]
{Graphic}

{338.16 Second,SurfaceGraphics}

and

Timing[Plot3D[Evaluate[u[r, t]], {t, 0, 2}, {r, a, b}, PlotRange -> {-1,
1},
AxesLabel -> {" t sec", "  r m", "u K  "},
FaceGrids -> {{0, -1, 0}, {1, 0, 0}, {0, 1, 0}, {-1, 0, 0}},
PlotPoints -> 50]]

{Graphic}

{252.77 Second Second, SurfaceGraphics}

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/

> Hello,
>
> I want to accelerate calculation speed of a function u1[r, t], which
> is a
> transient temperature distribution of a hollow cylinder with inner/outer
> radii of a and b, respectively.
>
> (* u is in an asymptotic form using 0 th order Bessel function of 1st
> and
> 2nd kind.
> The eigenvalue rho is a root of the f[\Rho]==0. *)
>
> f[\[Rho]_] = (\[Rho]*BesselJ[1, \[Rho]*a] + \[Alpha]0*BesselJ[0,
> \[Rho]*a])*
>      BesselY[1, \[Rho]*b] - (\[Rho]*BesselY[1, \[Rho]*a] +
> \[Alpha]0*BesselY[0, \[Rho]*a])*
>      BesselJ[1, \[Rho]*b];
>
> (* The concrete values used for numerical evaluation are as follows. *)
>
> a = 0.005; b = 0.015;\[Kappa]=
> 0.0130/3600;\[Alpha]0=10000000/10.9;\[Omega]=
>   2\[Pi];
>
> (* n th root \[Rho]n and constant \[Beta]n are obtained as follows *)
>
> nmax=96;
>
> ddn = Table[FindRoot[ f[d] == 0, {d, 100+(j-1) 314.2},
>                         MaxIterations->100],{j,1,nmax}];
>
> Subscript[\[Rho], n_] := ddn[[n,1,2]];
>
> Subscript[\[Beta], n_] :=
>    BesselJ[1, Subscript[\[Rho], n]*b]/BesselY[1, Subscript[\[Rho],
> n]*b];
>
> (* Now, let's defined u[r,t] *)
>
>
> Subscript[R, n_][r_] := BesselJ[0, Subscript[\[Rho], n]*r] -
>     Subscript[\[Beta], n]*BesselY[0, Subscript[\[Rho], n]*r];
>
>   u[r_, t_] = Sin[\[Omega]*t] +
>     Sum[((\[Omega]*(\[Kappa]*Subscript[\[Rho], n]^2*
>           (E^((-\[Kappa])*Subscript[\[Rho], n]^2*t) -
>            Cos[\[Omega]*t]) - \[Omega]*Sin[\[Omega]*t]))/
>        ((\[Kappa]*Subscript[\[Rho], n]^2)^2 + \[Omega]^2))*
>       ((2*\[Alpha]0*a)/Subscript[\[Rho], n]^2)*
>       ((Subscript[R, n][a]*Subscript[R, n][r])/
>        ((b*Subscript[R, n][b])^2 -
>         (1 + (\[Alpha]0/Subscript[\[Rho], n])^2)*
>          (a*Subscript[R, n][a])^2)), {n, 1, nmax}];
>
> (* Can anyone help to accelarate calculation ?
> The following Plot3D takes 180 sec on a Pentium III 800 MHz machine.
> I tried to ues Module, but it did not contribute in speed up*)
>
> Timing[Plot3D[u[r, t], {t, 0, 2}, {r, a, b}, PlotRange -> {-1, 1},
>    AxesLabel -> {" t sec", "  r m", "u K  "},
>    FaceGrids -> {{0, -1, 0}, {1, 0, 0}, {0, 1, 0}, {-1, 0, 0}},
>    PlotPoints -> 50]]
>
> -Toshi
>
>
>

```

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