JANUARY2020|COMPUTER SHOPPER|ISSUE383 103
ASIMPLE EXAMPLE
First, awordofwarning: this is quitemathematical. Having said
that, what we present here isn’t at all difficult, and if you’re
prepared to put up with the odd differential equation here and
there,itwill give you amuchbetter feel forhow simulation
works. We’re going to look at amodel of the spread of an
infectious disease,which is aclassic textbook example of
simulation. The model comprises the following three equations:dS/dt=–aSI
dI/dt=aSI–bR
dR/dt=bRIn these equations,Srepresents the number of healthy people
who are susceptible,thatistheyhavenot succumbed to the
disease;Iis the number of people whoare infected, and hence
also infectious; andRis the number of people whohave
recovered and are therefore immune.aandbare two constants
that represent the rateatwhich susceptible people are infected,
and the rateatwhich infected people recover.
The equations should now make sense because they
correspond to acommon-sense view of how an epidemic
progresses. So,for example,the first equation shows that the
rateatwhich the number of susceptible people changes is a
decrease (because of the negative sign) and is equal to the
product of the number of susceptible and the number of
infectious people,multiplied by the infection rate. Theother
equations should make perfect sense,too.
We’re not going to look at exactly how these equations
are solved in software,but it’s not difficult, so if you want to
know more,search forEuler Method, which is one of the
simplest algorithms. What we will do,however,isshow the
results if we start with 99 healthy people,one infected
person and no recovered people.Agraph of these three
populations against time appears below.And if you want to
try this out yourself,without getting bogged down in the
maths of solving differential equations, take alookatthe
‘DIY simulation’box on page 106.Not only that, but we can’t solve the equations foreachpoint in
the atmosphere individually because the weather at one point
depends on what’s happening in neighbouring points. When we
bear in mind that some of the Met Office’s modelssolve all those
equations foragrid of 2,560by1,920 points at 70 vertical levels –a
total of almost half abillion points –weeventually get to see the
enormity of the computing challenge.Nosurprise, then,thatthe
MetOffice’scomputer system is the world’s 27th fastest
supercomputer,and itsquarter of amillion cores can executeseven
quadrillion (thousand trillion) floating point operations per second.
RACINGAHEAD
Despitethe massive computing resources needed, simulation is a
technology that reaps major benefits, as an example reveals.
The Formula Student racing series brings together about 100
teams from all over the world to design and build asingle-seat racing
car.Competing teamsspend one year designing, building and testing
their cars. Then, at the Silverstone circuit, theypresent their projects
to the judges, as well as demonstrating their technical solutions on
the racetrack by competing in various static and dynamic events.
As with most engineering challenges, simulation is crucial.
While computer simulation is sometimes thought of as ameans of
seeing intothe future –asort of high-tech crystal ball, if you like,asit
is in weather forecasting, forexample –hereit’sused for‘what if?’
exercises. In other words, instead of building acar and trying it out,
the much more efficient approach of trying out several options by
simulation before starting manufacturing is adopted.
MathWorks is aFormula Student sponsor,and many of the teams
usethe company’s software products. Included here is MATLAB,
which is aprogramming environment fortechnical computing
including simulation, and the Simulink add-on, which allows models
to be created by connecting blocks together onscreen. Dr Veer
Alakshendra, MathWorks’ Student Competition technical evangelist,
explains that modelling and simulation is away to createavirtual
representation of avehicle that includes software and hardware.
“Iterating between modelling and simulation can improve the
quality of the vehicle design early,thereby reducing the number of
errors found later in the design process,”heexplains.
“In aFormula Student car,one can model and simulate
components like suspension, steering, tyres and powertrain,ABOVE:With manufacturing plants costing billions, semiconductor firms need
to prove achip design by simulation before spending all that cash
ABOVE:Simulink is widely used forsimulation in engineering, with design
applications ranging from wind turbines to racing cars
ABOVE:Solving three differential equations allows the spread of an
infectious disease to be simulated. Green represents susceptible people,
blue is those who are infected, and red is those who have recovered