Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1992
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1992

[Date Index] [Thread Index] [Author Index]

Search the Archive

problems with mathematica

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: problems with mathematica
  • From: mdiglio%email at yoda.physics.unc.edu (Michael DIGLIO)
  • Date: Tue, 15 Dec 92 04:02:47 EST

		(* PROBLEMS WITH MATHEMATICA *)
			
	(* Computed Temperatures in Pulsed Weldings *)      

(* PROBLEM: The calculation of temp[x, y, z, t] gets slower and slower ! WHY??
	    Look at the example at the bottom. *)      

temp[x_, y_, z_, t_] := (
   
   Up = 32;
   Ip = 700;
   Ug = 24;
   Ig = 175;					(* Welding Parameters *)
   tc = 2;
   tp = 0.4;
   v = 3.33;
 
Block[{Ta = 25, etap = 0.95, etag = 0.7,  a = 6, ro = 7550, cp = 680,
       p1 = 0.3, p2 = 0.7},
				
    const = N[2/(cp*ro*(4*3.14159*a*10^-6)^1.5), 4];	(* Physical Constant *)
   
    q = (Up*Ip*tp + Ug*Ig*(tc - tp))/(v*10*tc);
    B = 14.4485 - 27.0392*10^-6*q + 5.5453*10^-9*q^2;
    ky = Log[20]/((B/2)^2);
    kx = ((p1/p2)^2)*ky;     (* Calculation of the Distribution Coefficients *)
    toy = N[1/(4*a*ky), 3];
    tox = N[1/(4*a*kx), 4];
	
    qp = Round[Up*Ip*etap];		(* Effective Power *)
    qg = Round[Ug*Ig*etag];
    n = Floor[t/tc];


(* Explanation of tempfunc:
	qp and qg depend on the integration variable d:
		if  n*tc <= d < (n*tc + tp)  >> qp;   for d = 0 to t.
		if  (n*tc + tp) <= d < n*tc  >> qg;   for d = 0 to t. *)
  
   tempfunc =
      Ta + const*(
	 qp*NIntegrate[
	    Exp[- z^2/(4*a*(t - d))
	    ]/Sqrt[t - d]
	    *(
	      p1*Exp[- ((x - v*d)^2 + y^2)/(4*a*(toy + t - d ))
	         ]/(toy + t - d)
	      +
	      p2*Exp[- ((x - v*d)^2/(4*a*(tox + t - d))
		     + y^2/(4*a*(toy + t - d)))
	         ]/(Sqrt[(tox + t - d)*(toy + t - d)])
	      ),
	  {d, 0.001, tp}, 
	  AccuracyGoal -> 0, PrecisionGoal -> 4
	  ] 
	  +
	  qg*Sum[
	     NIntegrate[
	       Exp[- z^2/(4*a*(t - d))
	       ]/Sqrt[t - d]
	       *(
		 p1*Exp[- ((x - v*d)^2 + y^2)/(4*a*(toy + t - d ))
		    ]/(toy + t - d)
		 +
		 p2*Exp[- ((x - v*d)^2/(4*a*(tox + t - d))
		        + y^2/(4*a*(toy + t - d)))
		    ]/(Sqrt[(tox + t - d)*(toy + t - d)])
		),
	     {d, d1*tc + tp, (d1 + 1)*tc},
	     AccuracyGoal -> 0, PrecisionGoal -> 4
	     ],
	  {d1, 0, n - 1}     
	  ]   
	  +
	  qp*Sum[
	     NIntegrate[
	       Exp[- z^2/(4*a*(t - d))
	       ]/Sqrt[t - d]
	       *(
	 	 p1*Exp[- ((x - v*d)^2 + y^2)/(4*a*(toy + t - d ))
		    ]/(toy + t - d)
		 +
		 p2*Exp[- ((x - v*d)^2/(4*a*(tox + t - d))
		        + y^2/(4*a*(toy + t - d)))
		    ]/(Sqrt[(tox + t - d)*(toy + t - d)])
	       ),
	     {d, d1*tc, d1*tc + tp},
	     AccuracyGoal -> 0, PrecisionGoal -> 4
	     ],
	  {d1, 1, n - 1}
	  ]
	  +
	  Which[
	    (t - n*tc) == 0, 0,
	    (t - n*tc) <= tp,
	       qp*NIntegrate[
		  Exp[- z^2/(4*a*(t - d))
		  ]/Sqrt[t - d]
		  *(
		    p1*Exp[- ((x - v*d)^2 + y^2)/(4*a*(toy + t - d ))
		       ]/(toy + t - d)
		    +
		    p2*Exp[- ((x - v*d)^2/(4*a*(tox + t - d))
			   + y^2/(4*a*(toy + t - d)))
		       ]/(Sqrt[(tox + t - d)*(toy + t - d)])
		  ),               
	       {d, n*tc, t - 0.001},
	       AccuracyGoal -> 0, PrecisionGoal -> 4
	       ],
	    (t - n*tc) > tp,
	       qp*NIntegrate[
	   	  Exp[- z^2/(4*a*(t - d))
		  ]/Sqrt[t - d]
		  *(
		    p1*Exp[- ((x - v*d)^2 + y^2)/(4*a*(toy + t - d ))
		       ]/(toy + t - d)
		    +
		    p2*Exp[- ((x - v*d)^2/(4*a*(tox + t - d))
			   + y^2/(4*a*(toy + t - d)))
		       ]/(Sqrt[(tox + t - d)*(toy + t - d)])
		  ),               
	       {d, n*tc, n*tc + tp},
	       AccuracyGoal -> 0, PrecisionGoal -> 4
	       ]              
	       +
	       qg*NIntegrate[
		  Exp[- z^2/(4*a*(t - d))
		  ]/Sqrt[t - d]
		  *(
		    p1*Exp[- ((x - v*d)^2 + y^2)/(4*a*(toy + t - d ))
		       ]/(toy + t - d)
		    +
		    p2*Exp[- ((x - v*d)^2/(4*a*(tox + t - d))
			   + y^2/(4*a*(toy + t - d)))
		       ]/(Sqrt[(tox + t - d)*(toy + t - d)])
		  ),               
	       {d, n*tc + tp, t - 0.001},
	       AccuracyGoal -> 0, PrecisionGoal -> 4
	       ]	               
	  ]
       )
    ];
Return[tempfunc]
)
temptable[x_, y_, z_, t1_, t2_, ti_] :=
        Table[temp[x, y, z, t], {t, t1, t2, ti}]

(*
EXAMPLE: 
Timing[temp[120, 0, 5, 36]]
{6.43 Second, 1076.07}

Timing[temp[120, 0, 5, 36]]
{9.39 Second, 1076.07}

Timing[temp[120, 0, 5, 36]]
{12.52 Second, 1076.07}
*)

(*
If you have any idea to solve the problem,
please send an email to:
mdiglio at email.tuwien.ac.at

Looking forward getting an answer, thanks 
			
			Frank Peter
*)





  • Prev by Date: Re: What should Mma be, part II
  • Next by Date: Re: What should Mma be, part II
  • Previous by thread: re: Plotting a polygon
  • Next by thread: Numerical Analysis text