From avikbose1145 at gmail.com  Fri Jun  7 00:39:56 2013
From: avikbose1145 at gmail.com (Avik Bose)
Date: Fri, 7 Jun 2013 10:09:56 +0530
Subject: [Hotspot] Inclusion of thermal vias in hotspot simulation
Message-ID: <CAOwLHZ5B=Suk9GDSHjxh-qcQj1qUr8fm2S_osHpSqnDvbectMw@mail.gmail.com>

Respected friends,
                            In the HowTo file of HoSpot5.02 release it is
written that to model 3D chip's thermal vias we have to change manually in
the source code the thermal conductivity of the grid cells at which the
thermal vias are located, to the desired values. My question is in order to
do that which source code file I need to update and where, and also what
are the desired values that I need to put. If anybody knows please help me
out
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From waqasch86 at gmail.com  Fri Jun  7 08:09:03 2013
From: waqasch86 at gmail.com (waqas ch)
Date: Fri, 7 Jun 2013 14:09:03 +0200
Subject: [Hotspot] Inclusion of thermal vias in hotspot simulation
In-Reply-To: <CAOwLHZ5B=Suk9GDSHjxh-qcQj1qUr8fm2S_osHpSqnDvbectMw@mail.gmail.com>
References: <CAOwLHZ5B=Suk9GDSHjxh-qcQj1qUr8fm2S_osHpSqnDvbectMw@mail.gmail.com>
Message-ID: <CAAr8icLRyeyB6iOfdy1=kXedSZ8+0k-pmBQt2d=5JueZ6NP5ow@mail.gmail.com>

Hi

You can change the thermal conductivity of the individual grid cells in
temperature_grid.c file. The function where it is located is the
single_iteration_steady_grid and you can put 400W/mk if thermal via is of
copper as the thermal conductivity. I hope it helps.

Best regards

Waqas


On Fri, Jun 7, 2013 at 6:39 AM, Avik Bose <avikbose1145 at gmail.com> wrote:

> Respected friends,
>                             In the HowTo file of HoSpot5.02 release it is
> written that to model 3D chip's thermal vias we have to change manually in
> the source code the thermal conductivity of the grid cells at which the
> thermal vias are located, to the desired values. My question is in order to
> do that which source code file I need to update and where, and also what
> are the desired values that I need to put. If anybody knows please help me
> out
>
> _______________________________________________
> HotSpot mailing list
> HotSpot at mail.cs.virginia.edu
> http://www.cs.virginia.edu/mailman/listinfo/hotspot
>
>
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From avikbose1145 at gmail.com  Sun Jun  9 01:12:06 2013
From: avikbose1145 at gmail.com (Avik Bose)
Date: Sun, 9 Jun 2013 10:42:06 +0530
Subject: [Hotspot] Inclusion of thermal vias in hotspot 3D stacking
	simulation
Message-ID: <CAOwLHZ6uXX0h5T_OzryPadGiWXHkJYi_5FCGj0T-cNcV9T9tUw@mail.gmail.com>

Respected friends,
                            I have come to know that to include thermal
vias in hotspot 3D stacking capability, I have to change the thermal
conductivity of each grid cells that constitute the pillar node in the
single_iteration_steady_grid function of temperature_grid.c file of HotSpot
release. Now I have some question regarding this.

1) In that fuction, there are two variables csum and wsum which indicates
sum of the conductance and weighted sum of temperatures for a particular
cell. Depending upon the layer and row and column of a cell, these two
vaules are calculated using several macros like, NC,SC,EC,WC,BC,AC for
csum, and NT,ST,ET,WT,BT,AT for wsum.

    For example the NC macro look like this :
                 # define NC(l,n,i,j,nl,nr,nc) ((i > 0) ? (1.0/l[n].ry) :
0.0)
    I study some data structures and come to know that the l[n].ry field is
the resistor of Y direction of the cell located at ith row. My question is
what the value 1.0 signifies? Is it the thermal conductivity? or something
else.

2) I came to know that 400W/mK is the conductivity value for copper via.
Now suppose, if the pillar node constitutes (x1,y1),...,(xi,yi) cells then
to change the conductivity of those cells to 400, do I have to put directly
400 to the csum field by just checking the row and column of the cells or I
have to update the macros, that I am talking about above? If yes then how?

3) I am showing just a snippet of the first "if" construct of the function.
Can anybody tell how to change the conductivity of the csum field If csum
effects wsum then how to to that too?

          for(n=0; n < nl; n++) {
for(i=0; i < nr; i++) {
for(j=0; j < nc; j++) {
if((n==LAYER_SI) && model_secondary) {//top silicon layer: above is metal,
beneath is TIM
csum = NC(l,n,i,j,nl,nr,nc) + SC(l,n,i,j,nl,nr,nc) +
   EC(l,n,i,j,nl,nr,nc) + WC(l,n,i,j,nl,nr,nc) +
   1.0/l[metalidx].rz + BC(l,n,i,j,nl,nr,nc);
wsum = NT(l,v,n,i,j,nl,nr,nc) + ST(l,v,n,i,j,nl,nr,nc) +
   ET(l,v,n,i,j,nl,nr,nc) + WT(l,v,n,i,j,nl,nr,nc) +
   v[metalidx][i][j]/l[metalidx].rz + BT(l,v,n,i,j,nl,nr,nc);



          If anybody have made use of thermal vias in HotSpot or knows how
to do that then please help me out.
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From acoskun at bu.edu  Sun Jun  9 15:33:12 2013
From: acoskun at bu.edu (Ayse K. Coskun)
Date: Sun, 9 Jun 2013 15:33:12 -0400
Subject: [Hotspot] HotSpot Digest, Vol 87, Issue 2
In-Reply-To: <mailman.7.1370804417.29285.hotspot@mail.cs.virginia.edu>
References: <mailman.7.1370804417.29285.hotspot@mail.cs.virginia.edu>
Message-ID: <683F6F62-CADA-475A-9026-8EEB2FE91921@bu.edu>

BU's extended version on the HotSpot site (under "links") enables modeling thermal vias. I can provide an updated version of the extended version, too (a bit cleaner, some minor bugs fixed, no major differences).

Ayse


> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Sun, 9 Jun 2013 10:42:06 +0530
> From: Avik Bose <avikbose1145 at gmail.com>
> Subject: [Hotspot] Inclusion of thermal vias in hotspot 3D stacking
>    simulation
> To: HotSpot at mail.cs.virginia.edu
> Message-ID:
>    <CAOwLHZ6uXX0h5T_OzryPadGiWXHkJYi_5FCGj0T-cNcV9T9tUw at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
> 
> Respected friends,
>                            I have come to know that to include thermal
> vias in hotspot 3D stacking capability, I have to change the thermal
> conductivity of each grid cells that constitute the pillar node in the
> single_iteration_steady_grid function of temperature_grid.c file of HotSpot
> release. Now I have some question regarding this.
> 
> 1) In that fuction, there are two variables csum and wsum which indicates
> sum of the conductance and weighted sum of temperatures for a particular
> cell. Depending upon the layer and row and column of a cell, these two
> vaules are calculated using several macros like, NC,SC,EC,WC,BC,AC for
> csum, and NT,ST,ET,WT,BT,AT for wsum.
> 
>    For example the NC macro look like this :
>                 # define NC(l,n,i,j,nl,nr,nc) ((i > 0) ? (1.0/l[n].ry) :
> 0.0)
>    I study some data structures and come to know that the l[n].ry field is
> the resistor of Y direction of the cell located at ith row. My question is
> what the value 1.0 signifies? Is it the thermal conductivity? or something
> else.
> 
> 2) I came to know that 400W/mK is the conductivity value for copper via.
> Now suppose, if the pillar node constitutes (x1,y1),...,(xi,yi) cells then
> to change the conductivity of those cells to 400, do I have to put directly
> 400 to the csum field by just checking the row and column of the cells or I
> have to update the macros, that I am talking about above? If yes then how?
> 
> 3) I am showing just a snippet of the first "if" construct of the function.
> Can anybody tell how to change the conductivity of the csum field If csum
> effects wsum then how to to that too?
> 
>          for(n=0; n < nl; n++) {
> for(i=0; i < nr; i++) {
> for(j=0; j < nc; j++) {
> if((n==LAYER_SI) && model_secondary) {//top silicon layer: above is metal,
> beneath is TIM
> csum = NC(l,n,i,j,nl,nr,nc) + SC(l,n,i,j,nl,nr,nc) +
>   EC(l,n,i,j,nl,nr,nc) + WC(l,n,i,j,nl,nr,nc) +
>   1.0/l[metalidx].rz + BC(l,n,i,j,nl,nr,nc);
> wsum = NT(l,v,n,i,j,nl,nr,nc) + ST(l,v,n,i,j,nl,nr,nc) +
>   ET(l,v,n,i,j,nl,nr,nc) + WT(l,v,n,i,j,nl,nr,nc) +
>   v[metalidx][i][j]/l[metalidx].rz + BT(l,v,n,i,j,nl,nr,nc);
> 
> 
> 
>          If anybody have made use of thermal vias in HotSpot or knows how
> to do that then please help me out.
> -------------- next part --------------
> An HTML attachment was scrubbed...
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> 
> ------------------------------
> 
> _______________________________________________
> HotSpot mailing list
> HotSpot at mail.cs.virginia.edu
> http://www.cs.virginia.edu/mailman/listinfo/hotspot
> 
> 
> End of HotSpot Digest, Vol 87, Issue 2
> **************************************


From acoskun at bu.edu  Sun Jun  9 15:33:12 2013
From: acoskun at bu.edu (Ayse K. Coskun)
Date: Sun, 9 Jun 2013 15:33:12 -0400
Subject: [Hotspot] HotSpot Digest, Vol 87, Issue 2
In-Reply-To: <mailman.7.1370804417.29285.hotspot@mail.cs.virginia.edu>
References: <mailman.7.1370804417.29285.hotspot@mail.cs.virginia.edu>
Message-ID: <683F6F62-CADA-475A-9026-8EEB2FE91921@bu.edu>

BU's extended version on the HotSpot site (under "links") enables modeling thermal vias. I can provide an updated version of the extended version, too (a bit cleaner, some minor bugs fixed, no major differences).

Ayse


> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Sun, 9 Jun 2013 10:42:06 +0530
> From: Avik Bose <avikbose1145 at gmail.com>
> Subject: [Hotspot] Inclusion of thermal vias in hotspot 3D stacking
>    simulation
> To: HotSpot at mail.cs.virginia.edu
> Message-ID:
>    <CAOwLHZ6uXX0h5T_OzryPadGiWXHkJYi_5FCGj0T-cNcV9T9tUw at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
> 
> Respected friends,
>                            I have come to know that to include thermal
> vias in hotspot 3D stacking capability, I have to change the thermal
> conductivity of each grid cells that constitute the pillar node in the
> single_iteration_steady_grid function of temperature_grid.c file of HotSpot
> release. Now I have some question regarding this.
> 
> 1) In that fuction, there are two variables csum and wsum which indicates
> sum of the conductance and weighted sum of temperatures for a particular
> cell. Depending upon the layer and row and column of a cell, these two
> vaules are calculated using several macros like, NC,SC,EC,WC,BC,AC for
> csum, and NT,ST,ET,WT,BT,AT for wsum.
> 
>    For example the NC macro look like this :
>                 # define NC(l,n,i,j,nl,nr,nc) ((i > 0) ? (1.0/l[n].ry) :
> 0.0)
>    I study some data structures and come to know that the l[n].ry field is
> the resistor of Y direction of the cell located at ith row. My question is
> what the value 1.0 signifies? Is it the thermal conductivity? or something
> else.
> 
> 2) I came to know that 400W/mK is the conductivity value for copper via.
> Now suppose, if the pillar node constitutes (x1,y1),...,(xi,yi) cells then
> to change the conductivity of those cells to 400, do I have to put directly
> 400 to the csum field by just checking the row and column of the cells or I
> have to update the macros, that I am talking about above? If yes then how?
> 
> 3) I am showing just a snippet of the first "if" construct of the function.
> Can anybody tell how to change the conductivity of the csum field If csum
> effects wsum then how to to that too?
> 
>          for(n=0; n < nl; n++) {
> for(i=0; i < nr; i++) {
> for(j=0; j < nc; j++) {
> if((n==LAYER_SI) && model_secondary) {//top silicon layer: above is metal,
> beneath is TIM
> csum = NC(l,n,i,j,nl,nr,nc) + SC(l,n,i,j,nl,nr,nc) +
>   EC(l,n,i,j,nl,nr,nc) + WC(l,n,i,j,nl,nr,nc) +
>   1.0/l[metalidx].rz + BC(l,n,i,j,nl,nr,nc);
> wsum = NT(l,v,n,i,j,nl,nr,nc) + ST(l,v,n,i,j,nl,nr,nc) +
>   ET(l,v,n,i,j,nl,nr,nc) + WT(l,v,n,i,j,nl,nr,nc) +
>   v[metalidx][i][j]/l[metalidx].rz + BT(l,v,n,i,j,nl,nr,nc);
> 
> 
> 
>          If anybody have made use of thermal vias in HotSpot or knows how
> to do that then please help me out.
> -------------- next part --------------
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> URL: http://www.cs.virginia.edu/pipermail/hotspot/attachments/20130609/f85421ed/attachment-0001.html 
> 
> ------------------------------
> 
> _______________________________________________
> HotSpot mailing list
> HotSpot at mail.cs.virginia.edu
> http://www.cs.virginia.edu/mailman/listinfo/hotspot
> 
> 
> End of HotSpot Digest, Vol 87, Issue 2
> **************************************


From shuaiwanghit at gmail.com  Mon Jun 10 10:37:14 2013
From: shuaiwanghit at gmail.com (Shuai Wang)
Date: Mon, 10 Jun 2013 22:37:14 +0800
Subject: [Hotspot] 'Block not found' problem in 3D IC simulation
Message-ID: <CAP0TYTDeUi90AA=2xJe2ncS2QnPsJXXDB4y-gnGFQCa6Rabv1Q@mail.gmail.com>

Dear Sir?



I am using Hotspot 5.02 in grid mode for 3D IC simulation. But it tells me
that ?block Unit2 not found?. I am wondering the reason.

In detail, the lcf file *example0609.lcf *goes:

# Layer 0: Silicon

0

Y

Y

1.75e6

0.01

0.00015

floorplan0609EXCEL1.flp



# Layer 1: thermal interface material (TIM)

1

Y

N

4e6

0.25

2.0e-05

floorplan0609EXCEL1.flp



# Layer 2: Silicon

2

Y

Y

1.75e6

0.01

0.00015

floorplan0609EXCEL2.flp



# Layer 3: thermal interface material (TIM)

3

Y

N

4e6

0.25

2.0e-05

floorplan0609EXCEL2.flp



The *floorplan0609EXCEL1.flp* file goes:

Unit1    .0001    .000118    0    0

Unit3    .0001    .000102    0    .000118

Unit5A    .0001    .000127    0    .00022



The *floorplan0609EXCEL2.flp* file goes:

Unit2    .0001    .000118    0    0

Unit4    .0001    .000102    0    .000118

Unit5B    .0001    .000127    0    .00022



The *gcc0609EXCEL1.flp* file goes:

Unit1    Unit2    Unit3    Unit4    Unit5A    Unit5B

.01647        .01647       .01425       .01425        .01781       .01781




Then, I type the following code in the Linux operation system:

[root at localhost HotSpot-5.02]# ./hotspot -c hotspot.config -f
floorplan0609EXCEL2.flp -p gcc0609EXCEL1.ptrace -o example060922.ttrace
-model_type grid -grid_layer_file example0609.lcf



But the sytem tell me the following information:

warning: layer configuration file specified. overriding default floorplan
with those in lcf file...

*error: block Unit2 not found*



I have also tried similar code for 3D IC simulation in the past days, and
everything goes well. Could you tell me what is wrong this time? I am
really appreaciated if you could help me solve this problem. Thank you in
advance.



Best wishes.

Shuai Wang

Harbin Institute of Technology, China
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From wh6p at virginia.edu  Tue Jun 11 11:44:26 2013
From: wh6p at virginia.edu (Wei Huang)
Date: Tue, 11 Jun 2013 10:44:26 -0500
Subject: [Hotspot] 'Block not found' problem in 3D IC simulation
In-Reply-To: <CAP0TYTDeUi90AA=2xJe2ncS2QnPsJXXDB4y-gnGFQCa6Rabv1Q@mail.gmail.com>
References: <CAP0TYTDeUi90AA=2xJe2ncS2QnPsJXXDB4y-gnGFQCa6Rabv1Q@mail.gmail.com>
Message-ID: <CANYeXBqxUTD+yWOhSb51M1jsb1FbAmj9D=4eBJiHXbXrQa_PLQ@mail.gmail.com>

Hi, in the power trace file, you need to use the same sequence as the
blocks appear in the flp files, from layer 0 to layer N. So in your case,
the entries in the *.ptrace file should be:

"Unit1 Unit3 Unit5A Unit2 Unit4 Unit5B"

Hope this helps.
-Wei


On Mon, Jun 10, 2013 at 9:37 AM, Shuai Wang <shuaiwanghit at gmail.com> wrote:

> Dear Sir?
>
>
>
> I am using Hotspot 5.02 in grid mode for 3D IC simulation. But it tells me
> that ?block Unit2 not found?. I am wondering the reason.
>
> In detail, the lcf file *example0609.lcf *goes:
>
> # Layer 0: Silicon
>
> 0
>
> Y
>
> Y
>
> 1.75e6
>
> 0.01
>
> 0.00015
>
> floorplan0609EXCEL1.flp
>
>
>
> # Layer 1: thermal interface material (TIM)
>
> 1
>
> Y
>
> N
>
> 4e6
>
> 0.25
>
> 2.0e-05
>
> floorplan0609EXCEL1.flp
>
>
>
> # Layer 2: Silicon
>
> 2
>
> Y
>
> Y
>
> 1.75e6
>
> 0.01
>
> 0.00015
>
> floorplan0609EXCEL2.flp
>
>
>
> # Layer 3: thermal interface material (TIM)
>
> 3
>
> Y
>
> N
>
> 4e6
>
> 0.25
>
> 2.0e-05
>
> floorplan0609EXCEL2.flp
>
>
>
> The *floorplan0609EXCEL1.flp* file goes:
>
> Unit1    .0001    .000118    0    0
>
> Unit3    .0001    .000102    0    .000118
>
> Unit5A    .0001    .000127    0    .00022
>
>
>
> The *floorplan0609EXCEL2.flp* file goes:
>
> Unit2    .0001    .000118    0    0
>
> Unit4    .0001    .000102    0    .000118
>
> Unit5B    .0001    .000127    0    .00022
>
>
>
> The *gcc0609EXCEL1.flp* file goes:
>
> Unit1    Unit2    Unit3    Unit4    Unit5A    Unit5B
>
> .01647        .01647       .01425       .01425        .01781       .01781
>
>
>
>
> Then, I type the following code in the Linux operation system:
>
> [root at localhost HotSpot-5.02]# ./hotspot -c hotspot.config -f
> floorplan0609EXCEL2.flp -p gcc0609EXCEL1.ptrace -o example060922.ttrace
> -model_type grid -grid_layer_file example0609.lcf
>
>
>
> But the sytem tell me the following information:
>
> warning: layer configuration file specified. overriding default floorplan
> with those in lcf file...
>
> *error: block Unit2 not found*
>
>
>
> I have also tried similar code for 3D IC simulation in the past days, and
> everything goes well. Could you tell me what is wrong this time? I am
> really appreaciated if you could help me solve this problem. Thank you in
> advance.
>
>
>
> Best wishes.
>
> Shuai Wang
>
> Harbin Institute of Technology, China
>
> _______________________________________________
> HotSpot mailing list
> HotSpot at mail.cs.virginia.edu
> http://www.cs.virginia.edu/mailman/listinfo/hotspot
>
>
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From fkaplan3 at bu.edu  Fri Jun 21 11:50:26 2013
From: fkaplan3 at bu.edu (Fulya Kaplan)
Date: Fri, 21 Jun 2013 11:50:26 -0400
Subject: [Hotspot] rk4 solver with adjusted step size
Message-ID: <CAM8cC1pJR0zpu0oKd7LfJ10N4_ECYbVr-4tksP=Z4f8oi+rqQw@mail.gmail.com>

Hi,
I was examining the 4th order Runge Kutta solver with adaptive step size
for the grid model.

for (t = 0, new_h = MIN_STEP; t < time_elapsed && new_h >= MIN_STEP*DELTA;
t+=h) {
  h = new_h;
  /* pass the entire grid and the tail of package nodes
   * as a 1-d array
   */
  new_h = rk4(model, model->last_trans->cuboid[0][0],  p,
     /* array size = grid size + EXTRA */
     model->rows * model->cols * model->n_layers + extra_nodes, &h,
     model->last_trans->cuboid[0][0],
     /* the slope function callback is typecast accordingly */
     (slope_fn_ptr) slope_fn_grid);
  new_h = MIN(new_h, time_elapsed-t-h);
  #if VERBOSE > 1
   i++;
  #endif
 }

The loop starts with the step size *h= MIN_STEP*. For the current power and
temperatures, the function finds the new step size (new_h) that obeys the
temperature accuracy constraints. At the end of a single rk4 function call,
the grid temperatures that are computed based on the *new_h* are assigned
as the current temperature (*yout* or *model->last_trans->cuboid[0][0]*).
However, for the next iteration of the for loop, t is incremented by *h*,
which is the previous step size. Shouldn't it be the *new_h*, intuitively?
Basically, from time t=0 to t= new_h, you solve the differential equation
and update the temperature, but increment the t by the old value *h. *Why
is it so?

Best.
Fulya
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From ks4kk at virginia.edu  Fri Jun 21 12:57:53 2013
From: ks4kk at virginia.edu (Karthik Sankaranarayanan)
Date: Fri, 21 Jun 2013 12:57:53 -0400
Subject: [Hotspot] rk4 solver with adjusted step size
In-Reply-To: <CAM8cC1pJR0zpu0oKd7LfJ10N4_ECYbVr-4tksP=Z4f8oi+rqQw@mail.gmail.com>
References: <CAM8cC1pJR0zpu0oKd7LfJ10N4_ECYbVr-4tksP=Z4f8oi+rqQw@mail.gmail.com>
Message-ID: <CAPE+kwBwxG2TQnyjTyRtDUhHO77QGa2dwq25d2tc2=3rT3XF0A@mail.gmail.com>

Hi Fulya,

The adaptive step-sizing that you have outlined happens inside the rk4
function in RCutil.c. It is the rk4 function that integrates from t=0 to
t=h. It returns the new step-size to be used for the *next* rk4 call. Here
is the snippet from that function. It is basically what you had outlined:

 /* try until accuracy is achieved   */
    do {
        h = new_h;

    ...

        /* accuracy OK. increase step size  */
        if (max <= RK4_PRECISION) {

        ...

        /* inaccuracy error. decrease step size and compute again */
        } else {

        ...

        }

    } while (new_h < h);

The code in temperature_grid.c that you have shown just uses that step size
returned by rk4 function for time stepping. In other words, the rk4
function is internally consistent - it advances the solution by "h" (its
argument) no matter what. The new_h calculated by it is for the *next* call.

Thanks,
-karthik


On Fri, Jun 21, 2013 at 11:50 AM, Fulya Kaplan <fkaplan3 at bu.edu> wrote:

> Hi,
> I was examining the 4th order Runge Kutta solver with adaptive step size
> for the grid model.
>
> for (t = 0, new_h = MIN_STEP; t < time_elapsed && new_h >= MIN_STEP*DELTA;
> t+=h) {
>   h = new_h;
>   /* pass the entire grid and the tail of package nodes
>    * as a 1-d array
>    */
>   new_h = rk4(model, model->last_trans->cuboid[0][0],  p,
>      /* array size = grid size + EXTRA */
>      model->rows * model->cols * model->n_layers + extra_nodes, &h,
>      model->last_trans->cuboid[0][0],
>      /* the slope function callback is typecast accordingly */
>      (slope_fn_ptr) slope_fn_grid);
>   new_h = MIN(new_h, time_elapsed-t-h);
>   #if VERBOSE > 1
>    i++;
>   #endif
>  }
>
> The loop starts with the step size *h= MIN_STEP*. For the current power
> and temperatures, the function finds the new step size (new_h) that obeys
> the temperature accuracy constraints. At the end of a single rk4 function
> call, the grid temperatures that are computed based on the *new_h* are
> assigned as the current temperature (*yout* or *
> model->last_trans->cuboid[0][0]*). However, for the next iteration of the
> for loop, t is incremented by *h*, which is the previous step size.
> Shouldn't it be the *new_h*, intuitively? Basically, from time t=0 to t=
> new_h, you solve the differential equation and update the temperature, but
> increment the t by the old value *h. *Why is it so?
>
> Best.
> Fulya
>
> _______________________________________________
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> HotSpot at mail.cs.virginia.edu
> http://www.cs.virginia.edu/mailman/listinfo/hotspot
>
>
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From shravanec2011 at gmail.com  Sun Jun 30 09:45:48 2013
From: shravanec2011 at gmail.com (Shravankumar S Malagihal)
Date: Sun, 30 Jun 2013 16:45:48 +0000 (UTC)
Subject: [Hotspot] Invitation to connect on LinkedIn
Message-ID: <2021979301.24619906.1372610748210.JavaMail.app@ela4-bed78.prod>

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