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Un problema clásico que explota el procesamiento paralelo escalable, es la simulación de un flujo calórico. La física tras este fenómeno descansa en una ecuación diferencial en derivadas parciales.

Comenzaremos con una placa de metal unidimensional (también conocida como una barra), y avanzaremos hacia una placa bidimensional en los ejemplos posteriores. Al arranque, la barra se encuentra a cero grados Celsius. Luego metemos uno de sus extremos en vapor a 100 grados, y el otro extremo en hielo a cero grados. Queremos simular cómo es el flujo calórico de un extremo al otro, y observar las temperaturas resultantes a lo largo de los distintos puntos de la barra de metal, hasta que dichas temperaturas se estabilicen.

Para lograrlo, dividiremos la barra en 10 segmentos, y seguiremos la pista a la temperatura de cada segmento a lo largo del tiempo. Podemos ver intuitivamente que, en cada ciclo de la simulación, la temperatura que adquirirá cada porción de la barra será el promedio de las temperaturas a su alrededor. Dado que hay temperaturas fijas en ciertos puntos de la barra, el resto eventualmente convergerán a un estado estable tras un número suficiente de ciclos. La [link] muestra el estado al inicio de la simulación.

Flujo calórico en una barra

Esta figura es un diagrama de flujo que muestra cajas iniciando en la 100 y seguidas por una cadena de cajas etiquetadas 0. Las cajas también están numeradas del 1 al 10. Hay una flecha apuntando a la derecha, etiquetada flujo del calor, y bajo la cuarta, quinta y sexta cajas está la etiqueta promedio.

Una implementación simplista de tal simulación es como sigue:


PROGRAM HEATROD PARAMETER(MAXTIME=200)INTEGER TICKS,I,MAXTIME REAL*4 ROD(10)ROD(1) = 100.0 DO I=2,9ROD(I) = 0.0 ENDDOROD(10) = 0.0 DO TICKS=1,MAXTIMEIF ( MOD(TICKS,20) .EQ. 1 ) PRINT 100,TICKS,(ROD(I),I=1,10) DO I=2,9ROD(I) = (ROD(I-1) + ROD(I+1) ) / 2 ENDDOENDDO 100 FORMAT(I4,10F7.2)END

La salida de este programa será la siguiente:


% f77 heatrod.f heatrod.f:MAIN heatrod: % a.out1 100.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 21 100.00 87.04 74.52 62.54 51.15 40.30 29.91 19.83 9.92 0.0041 100.00 88.74 77.51 66.32 55.19 44.10 33.05 22.02 11.01 0.00 61 100.00 88.88 77.76 66.64 55.53 44.42 33.31 22.21 11.10 0.0081 100.00 88.89 77.78 66.66 55.55 44.44 33.33 22.22 11.11 0.00 101 100.00 88.89 77.78 66.67 55.56 44.44 33.33 22.22 11.11 0.00121 100.00 88.89 77.78 66.67 55.56 44.44 33.33 22.22 11.11 0.00 141 100.00 88.89 77.78 66.67 55.56 44.44 33.33 22.22 11.11 0.00161 100.00 88.89 77.78 66.67 55.56 44.44 33.33 22.22 11.11 0.00 181 100.00 88.89 77.78 66.67 55.56 44.44 33.33 22.22 11.11 0.00%

Claramente, para el ciclo de ejecución 101, la simulación converge con una precisión de dos decimales, conforme los números han dejado de cambiar. Debe tratarse de una aproximación a un estado de temperaturas estables al centro de cada segmento de la barra.

Ahora bien, para este momento los lectores más astutos estarán diciéndose: "Ey, por si no te has dado cuenta, este ciclo tiene una dependencia de flujo." Puede usted alegar que ello impedirá paralelizarlo siquiera un poquito. ¡Es tan grave que ni siquiera puede usted deshacer el bucle para lograr algo de paralelismo a nivel de instrucciones!

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Cómputo de alto rendimiento. OpenStax CNX. Sep 02, 2011 Download for free at http://cnx.org/content/col11356/1.2
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