What I Talk About When I Talk About Event Simulation in Autodesk Fusion 360

JAESUNG EOM: Thank you for coming to this lecture. Hopefully, this is the less than an hour-long monologue about that event simulation in Fusion360. So before we start, this fine print statement talk about the Autodesk-- the plan of the future, and that what they want to do for the future product and service, and whatever they're talking on this talk is not really related directly.

And also this is a contents of proprietary, so be mindful about that. Then, let's get started. Hello again. I'm Jaesung Eom, and I'm a Principal Research Engineer at Autodesk. And I'm making this tool-- that Event Simulation solver and also generative design solver as well. And even though I posted the picture from the Florida, I'm writing the Fortran code for living, not for fishing, for sure.

So going back to the title when I talk about Event simulation is mostly about do not use in certain circumstances. And then mostly about today's talk is when you can avoid use event simulation because there's tons of other good alternatives inside of the Fusion360. And you can get what you really want from there. But if your problem is really necessary to use event simulation then I'll guide you to the how can achieve that goal.

So as I'm a big fan of late Professor Winston of MIT, and he had a really great lecture about how to speak, talk, and you can also find it on the YouTube. So the best way to start this kind of hour-long lecture is start with the promise-- so what you can expect after this lecture and you can become a better Fusion user.

So what I talk about is mostly about our tool has a certain assumption and the working condition, and when is the best time you can utilize those feature and when you shouldn't use that. So today is mostly about the event simulation. And the second thing is the second pillar is that if you want to use that, I'll guide you to the how to use it correctly, and how to interpret its outcome.

So, in this talk, I'll keep using the Professor Winston's-- the pedagogic skill. So I'll keep repeating after repeating to the main theme over and over, so you can get this main theme of lecture. Hopefully after this hour-long lecture, lecture is done. So please bear with me.

So one way to do this kind of technical lecture is to go start from the basics. So we made the simulation, and some theoretical background and history, and the formulation, and the other things. But today, I'd like to start a little bit different way. And hopefully it works. I think that maybe later this AU, the satisfaction the boat or Bali will tell whether this method is working or not.

But I think that there's another way to Learn something is not only right way, but there's some wrong way. And how the wrong way to learn is for someone is it really give us some better insight of what their common mistake and how can you avoid it. So today I'll try to cover most of the common mistake of you are the new user of a simulation tool. And, hopefully, this not only the content of this talk but how the way to learn is inspire you in the long way. So let's begin.

So do some role playing. So even though I'm showing the couple of pictures about the baseball that really low playing on-- you become a baseball player, but you have become baseball helmet designer and need to design the futuristic new helmet but you ensure that helmet is really protect the isolated the head and brain from the any brain injury.

So let's start with ChatGPT. And today everybody do that-- why not we start doing that way. So we can find it out the working condition of a helmet. And now you see that baseball is a hit the bat at the speed of 90 to 110 miles per hour. So, of course, there's some monstrous pitcher is destroying faster than this-- maybe? But you can range in that, for example, like 100 mile per hour. Then now you know the speed.

OK, then let's model. So I think that most of the user in the Fusion is really good at designing this geometric object and the Fusion provided design workspace with many different tools. So now you can make the helmet and the ball. OK, let's say hit the button to run the simulation. What happened?

He said, the total wall clock time for this simulation is estimated to exceed the allowable time limit of 12 hours. So whether you realize it or not, the simulation requires huge computing power. And many time our tool, our first handed device-- the laptop-- is not powerful enough to handle those kind of heavy number crunching job. So we using the cloud.

But another connotation is we cannot really use the cloud for independent amount of time. So that's why we have a 12-hour limit. So, yeah, that's a bummer. Then how can we fix this? So let's go back to our primary source of information-- ChatGPT, again. So I ask, so what should I do? How can I make it run faster?

So the suggestion is I think this quite badly suggestion for the explicit finite element and that any type of finite element. So you can use the less divided mesh and then simulation learn faster. So this is especially the good implication for the explicit analysis. Because of the explicit analysis-- I'll tell you more about explicit later-- is the whole runtime is dictated by the smallest size element.

Let me tell you again. So if you divided the whole geometry is more smaller pieces than long time is, of course, is running much longer not because of you make another degree of freedom inside of your model, but this whole time integration-- I'll try to minimize any jargon about the mathematical formulation or any serious theory. But you can think it very simple if your mesh which is small and it took longer.

OK, then what else we can do. To get better insight, I ask another angle, so-- OK, my model has a collision with the initial velocity. So how can you speed up the simulation? So it advised it in the addition to the mesh simplification, another way to improve is using that optimize the time step size. So another way you can say that-- so the whole simulation, the duration is subdivided by this time step.

And first time to step to the next time step is integrated over and over and over and over. So in the long story short, it's a movie. You shoot the movie with this cute little baseball. You hit that blue helmet. So if you make a runtime longer that it'll require more time. So and if you make it shorter-- runtime and that, of course, that whole simulation run much faster manner. Of course, this is short amount of time.

So in a good way is that we started ball is really a part from that helmet. But how about we start the initial condition. So initial condition and both the position. So in that way, I think that if you think about that any drag of the ball while playing from the pitcher to the hitter, you can fairly guess that most of the initial velocity will be preserved.

But changing the position, of course, you lose this really fancy animation or movie of a ball flying all the way to the helmet part. But you can still capture the essence. So what was our goal? We are the helmet designer and we like to ensure that our helmet is sturdy enough to protect the athlete.

So to check the purpose, then we can just start that right before or even just at the moment of the ball is hitting the helmet. In that way, we can minimize optimize our simulation runtime. And one more thing is that the ChatGPT advised us. So we can start that the bigger-- a little bit coarser mesh density-- that will also work. So let's see our outcome array.

Now we can see that ball hit the helmet and that how much stress concentrate on the part of the helmet hitting portion. So I think that all this strategy and all this thinking process can be captured in very simple form of a slogan. Our radical is 3S. So this is also I learned from the Professor Winston.

So if you symbolize or even make a slogan of the main theme, then it's more likely the audience that captured the core essence of the talk. So 3S is it consists of statics and the simple and short. So I think that this previous example showed already about that what is the simple, and what is the short mean.

So short means the short are simulation duration. So another way is total event duration in the Fusion360 terminology. And the simple means that simpler mesh, that means the less number of element to subdivide the model. Statics is that I'll tell more. So a little bit more elaboration of statics is a static first. So statics is opposite word of dynamics.

So it's trying to say that we don't really use that dynamic even though in the real life the model is running and that model is making some motion. But you don't really run that dynamic model or dynamic simulation to capture the engineering goal or engineering inspection or the better design, and the other two S again as a simple and short-- the making simple geometry, or making simple for the material, and make it simple for the boundary condition. And also make it short amount of your whole simulation movie.

So keep thinking your problem as a movie and that you do like to make the eight-hour long documentary or one-minute reels in the Instagram or the Facebook is the difference. So I think that what they suggest is better make a reels on the Instagram. And let's start a little bit more decision making about when to go to the static or dynamic.

So this is a quick diagram of how to determine which analysis type you need to use or consider. So first question is, oh, you have a part under the loads. So that means this can be the mechanical problem. So mechanics is about any physical object on the force, right. So if it's in the equilibrium, and that it will be static.

And the static means that over the time that the shape or object is not moving or deforming over the time. So and that there's no context of time, it's static. The other way is it's moving so then it's the realm of a kingdom of dynamic. So let's first look into the static. So then if that is a deformation is a small or big is another question you should ask.

So lucky for us and that as a mechanical engineer and that most of the part-- most of the material we use for the engineering or designing is quite sturdy, and we don't really use that soft material on purpose except there are some engineering goal for doing that. So if you're working with any stainless steels or the alloy, the aluminum, or any sort of alloys, their most basic behavior is quite steep.

So unless you apply the huge amount of load is almost make it permanent deformation or another way to call plastic deformation or just breaking or rupture. I think that 90%-- the most of the mechanics problem-- can be handled with the linear static analysis. So I highly recommend using the linear static analysis because of its simplicity.

And in case of a many time, even though it's like a discipline-bending problem, this deflection looks huge. But in that more microscopic level as a stress level, it is still under the elastic deformation. So elastic means that once the force is applied and it deform, but forces it up from the material or object, it goes back to the original state without any permanent deformation. So that's what is called elastic.

So the good thing is that in the BIM bending, the physical response looks large but many times in the stress level is still elastic. So you can safely treat it with the small deformation assumption with the linear static analysis. And also some sort of a complex loading or the loading is low enough to take it as your elastic in that even though complex model, you can treat it as the linear static.

So going back again, static first, right, because it's simple and that it runs short, right. So this 3S is applied in the many aspects of simulation. And another way to call it is even though the problem looks like the complex or dynamic, it could be much simpler in essence. So what you can check is the working condition or simulation condition is the range of the linearly assumable-- the loading zone or non-linear zone.

So one quick check you can do is the stress level. So the promises stress or the other type of equivalent stress can tell whether certain portion of your model is under the plastic or the elastic. So, of course, you apply the huge amount of load to make a permanent deformation then you better use the nonlinear static analysis. But still, otherwise, you better stay in the linear static.

So even just to tell whether you need to use the nonlinear static or even simulation, the first step is starting with the linear setting. That's why statics first. And another layer chance of complex contact condition happens in your simulation, then, of course, you better use the Event Simulation.

So but again in 90%-- so, for example, this is a control bar and the brake system of the motor vehicle. And even though this control arms working condition is dynamic, but we don't really need to simulate with the dynamic because of what we like to see is the certain snapshot of the moment of this model or this assembly is working, right.

So to capture that moment of where the stress is concentrated under this-- just like this right figure. So you don't really have to use the Event Simulation. So if it's going beyond the plastic-- the yielded stress-- then you better use a nonlinear static analysis. But first step again, the static first, right. So you can first run the static test-- oh, so stress level is beyond the safety factor or the plastic yield stress.

Then you can clone the study into the nonlinear static model and you can run with a nonlinear. So you can go step by step. So that way you can minimize any complication or any unnecessary agony to fixing the complex problem later.

So going back to this flow chart-- OK, going back to this motion or no motion. Oh, now think about that whether your model is in motion. And this is a way to tell that even though it's in motion but it won't really generate any deformation of the object. So, for example, you flip it, you just swinging some pen or-- let me show you this way-- so pen over and over.

Is this pen-- is it really deforming? No, this pen is just to keep moving without any pen's deformation. So we call this as really body motion, and we can take this object as a rigid. And so this doesn't require that fancy simulation. So you can go back to the [INAUDIBLE] workspace.

And you can find the tab called the assembly and the inside of assembly, you can make very fairly complicated mechanism inside of a motion study. So this motion study is a part of the assembling different component. So once you assemble the multiple body into that one assembly with a good definition, you can run the motion study without big difficulty.

So this model is showing the Geneva mechanism. And you can see that we don't postulate any deformation of each body of this mechanism component. But one thing you need to do is you apply each one as a rigid group, and you define the revolution joint and which part will be contact one another. Then you situate each component into the right axis and the right contact constraint. Then you can make this mechanism working without the fancy simulation.

The good thing is to hold this motion study is run on the real time in the inside of local fusion. And my advice for using this motion study is to do incrementally-- so moving one component after another instead of just don't throw everything at once. So, for example, you put the huge gear at first and then just try to rotate it and whether the revolution joint to constrain the well postulate or not by that way and going by other.

And another way is that do it one, one, one at a time. So in that way you can make fairly complex motion study or Cam or the linkage design with this motion study easily. So, OK, here we go with the flow chart again. So even though you try that linear static or nonlinear static analysis or motion study, but it's not math well, then the rest result is the Event Simulation finally.

So there's a two version of event simulation, but it's underlying the same. It's based on explicit finite element. Let's jump into the event simulation a little bit deeper. So finally is another half is when to use and when to finally really use the event simulation with the [INAUDIBLE].

The one good advice is check the world's energy goals. And not only this something is in motion or not-- something is some object is rigid or not-- so check that energy. Where will this energy go-- the 0.8 while doing this event? Give us some insight. So there's a couple of energy you probably run from that high school physics-- the potential energy and the kinetic energy.

And the potential energy in this case is a potential strain, internal energy-- the Reaper. And because, in many time, this explicit solver is heavily leveraging that a lot of small time step to simulate this whole event duration. So that's why it gives a really good answer. But when it goes wrong, it's really hard to fix it. So this is the last-- one more time-- but don't sweat on the not moving thing to run the event simulation.

So going back to when is the event simulation is really shining is things get ugly like a nonlinear. So what is linear and nonlinear? There is many definition could be possible. But the one-- in finite element context-- the one linear-nonlinear distinction can be happened material wise. So if the stiffness or compliance is constant, regardless of strain, then we take it linear, but otherwise it's nonlinear.

Like a plastic deformation, initially, most of steel is the parallel linear in elastic region. And once it start to deforming, permanent deformation or plastic deformation, it go flat. So this graph-- the slope-- is changing over the different strain that we can call it material nonlinearity.

And other nonlinearity we can think of is geometry. So if you deform the really slender beam or shell and you bend it, then you can see that there's a linear strain the assumption is violated by the huge rigid body motion of the modal, so then we can call it geometric nonlinearity.

And one last is the nonlinearity is contact. So contact is really the [INAUDIBLE] for the event simulation. So again even simulation is explicit time integration finite solver and that it do really well on the time-dependent and the dynamic event-- so like this small bead is hitting the sunglasses. This kind of impact is really well simulated and this whole various contact can be captured well with event simulation.

But this run in very, very small step size-- time step size. So the more step size means that this require more the solving time on the other end. So why do we use the event simulations? And the larger picture is based-- it could really simulate that nearly impossible simulation with nonlinear static. And, furthermost, it can be really robust. It always can get visual because there is no matrix inversion process inside of simulation.

Hopefully, in the future, we can show more advanced simulation capability like fluid structure interaction. And even though I keep talking about explicit, if there's the explicit, that means there's the implicit as well, right. And this is the two different way to treat the time integration instead of this simulation. And the battery locked away without any formula to explain the explicit is explicitly required small time step but implicit can run the much larger time step.

But implicit require that matrix inversion process, and also it requires some iteration instead of a single time step. So it has a both pro and con, but even the simulation is explicit solver we use. And in the time wise-- I mean the duration wise-- which is simulation is more appropriate for each region is roughly making this chart. So like this glacier is moving kind of event happened over the day or month or year-- that called creep.

And those kind of event is running the explicit is not really a nice thing. So most of them explicit is for that millisecond or microsecond level even very, very generous assumption you can run that second. But in my rule of thumb, if any simulation duration in the fusion event simulation running more than 10 to the negative power of 3, then you should double think about what's going on with it, but, yeah.

And one really nice thing about the explicit, on the other hand, is this run fairly robust without less number of parameters that-- of course. So if you put the wrong parameter setting in the beginning, it will run indefinitely in the first example of helmet designing problem. But this gives a really robust answer regardless of a different deformation or the mechanical problem.

So this showed the buckle simulation and that this kind of a multi-staged and the simulation over the time is a really nice thing for the explicit solver. But you can still see that this model is not fully made and that we using the symmetry to make a simplify and minimize the number of degree of freedom you need to solve.

So it goes one of the 3S I mentioned before. And explicit solver is-- since it doesn't require the iteration inside reiteration or inversion process. So that gave a huge freedom to simulate the contact model or the nonlinear behavior or the material failure. So I'll show one example of impact simulation on the router.

So router is a model with the 3D parent component, and this metal ball is hit from the top. And we are using that maximum principal strain to decide which element can be the go test. So it's called the element deletion over, so that's the austerity of explicit solver. So once that certain element has reached more the maximum certain criteria of a maximum principal strain, that element is deleted.

So as you see the ball is hitting that, you can see that is a part is broken away due to the deleted element or the desktop element. So getting closer and you can see the more clear picture. So that's a brief outline of the event simulation. Let's go for the wrong way simulation, and hopefully-- I hope this following simulation is not a real but pictures.

But this is really-- many of this is coming from the customer support case or the internal letter. So let's go one by one how can we learn from the wrong way. So first one is time duration. So in the model, of course, I remake the model because I cannot expose that the actual customer case. So all this model is the fictitious.

And you can see that huge subdivision is really dense. The mesh subdivision happened on the left hand side. And the worst thing is that even the total event duration is set up as a 10 second that I told you is this bigger than in a 10 to the negative? One second is eternity in terms of the event simulation. So this then means 10 times of eternity.

So this simulation cannot make it within 12 hours for sure. But if you make that more sensible, the mesh density, mesh size, and the shorter amount of duration, and put the ball right before it collide, it is sure to run. So think again. And if total duration-- your setting is have a total duration is bigger than .001 second and that you need to do something on your model.

Second case was either the object fly the 1 kilometer in the 1 millisecond and/or under that load of the 172 million neuron. The 172 neuron is almost the weight of 2000 [INAUDIBLE] is on the model or on your part. So I think that most of the mistake happened that they didn't look closer of what unit they are using or that either below the velocity or ranks or the first unit so--

And that will prevent the misuse of simulation and that you can get the right outcome out of it. So, so far we've been going through that some beginning of failure of the helmet design and some core principles to tell which kind of simulation you need to use and another common mistakes on the event simulation. And following section is more about then how can we make it correct.

So again 3S-- statics first, simple, and short. So I run into this really interesting illustration book by the Katsushika Hokusai as he is a huge many popular by the huge wave-- the printing, right. And he start any sort of illustration with a simple form and then make it more detailed, more interesting picture out of the simple.

So I think that this is a really good example of the 3S. So start simple and start very short quick drawing, and then make a successful drawing after all so he can draw this amazing picture of under the wave of the Kanagawa. So with that 3S in mind, let me start the quick tips.

The first thing is be mindful on the step size and the simulation duration. Again and again, this is the one key component to affect the whole simulation runtime. And another thing is you can think of another option of quasi-static event simulation. So I think that one suggestion is that I'll show you more typical example about the quasi-static analysis.

But if your model is nonlinear or possibly not same as the nonlinear static, but it has a little bit component of contact and also it doesn't do many motion in your model, then you can think of quasi-static. And another rule of thumb for the contact is it turned on the auto contact setting. And so, OK, then again the static first.

Run linear static ahead to catch the mistake on your mesh or boundary condition or other thing even before you worry about that-- all these events simulation parameter. The living motifs is-- loading is not only the number. It has a direction. So mindful on how the direction is working. And again, the unit-- what unit you are working on and the unified single unit system is really minimize the problem.

And this chart is a really simple rule of thumb atypical loading case you can think of. But another way you can find is-- that I use the ChatGPT in the beginning of this talk-- you can simply go to the ChatGPT and, oh, I have this kind of a model and this object under this and what is the estimated Newton. And surprisingly, the ChatGPT gave a good range most of the time so far.

And small time step is required many times. But bear in mind the Fusion360 simulation runtime is limited by 12 hours. So there is many suggestions. But first thing is be mindful about the total event duration. Second thing is think about the mesh. So if you mesh is too dense, you can relax or you can try it a little bit coarse mesh at the same time and use the linear static.

But instead of running the whole duration, you just start with just a little bit tiny duration you think of. Then with that simple testing, you can check whether any modeling mistake or the parameter setting is wrong. And even though the event simulation can handle very well on the nonlinear material model, but please start with the elastic model in the beginning.

And applying the load-- I'll tell you more on the multiplier of the loading. But if you're using the-- if you're simulating that quasi-static case, think about a little bit smooth transition even though you can use your ramp-loading model with a straight line. But using this kind of a sinusoidal curve in the beginning make much more smoother transition and you get more chance without any hiccup on your simulation.

And, again, the one of the 3S-- short. So your total event duration should be just as much as you need. So if your object is really far away and get together and just to simulate that most of the climactic moment of your problem that the whole duration of this each body is flying in the empty space. And double check the mesh size.

So if you are lucky enough to the working with a few similar-sized body in the problem, then my suggestion is using that absolute size. So using that measuring tape-- not the measuring tape, but the measuring tool inside of Fusion-- you can measure the length of each add and between edge to face, face to face, the point to point. So whatever you can look up, then you can find the actual dimension.

And you can set up this all my-- the average element size should be this big. And in that way, you can minimize any iteration of finding out the right mesh size in the long run. So damping-- so if you're aware of the damping well, you can set it up, but my advice is unless you really run into it. So you have to be a little bit mindful about the change the value of the damping.

And again, so this simulation cannot run if you missed any the stress-- if you missed any result output from this checkbox, then you need to run the whole simulation again. So, for example, if you run the simulation over the seven hours, and, oh, I forgot the reaction force, then you need to run another seven hours. So before you hit the run button, please check double check this result output and, oh, if I need this and you make sure to check ahead.

So I briefly talk about that smooth transition on the smooth loading curve. So many time this smooth loading curve is really beneficial. So I think that one way you can generate is the selection of linear ramp is the default, but try some other option-- the rigorously testing it. And then even though in the long run, it won't give a huge disruption on the simulation, but it's sure to give the visual at the end.

And finally, you are lucky enough to get a visual, then how can you interpret it. So that's the big issue. And, again, the thing is not believing. So in many times, people have a issue to tell didn't think carefully about what is the scale deformation on your simulation is applied. So this color printed plot or contour plot is a really fancy, but it's not always give a good insight.

So I prefer to using the line plot of a certain point or certain region you would really like to inspect. So it gave the trend of the physical state value like a stress, stress strain, and deformation and other measure on that any given time step. So in that way, this gives a more clear insight-- physical insight-- you can reflect back to your model or design.

And another-- really this is a huge hidden gem of any kind of simulation or events-- not only events simulation but also linear static or nonlinear static analysis. This feature provided the solver data. Solver data gave a more detailed solver errors and warnings, and that how the mesh is organized, the quality of mesh, and the other things.

And one of the most well-educated way to using the simulation is not just checking the color, but first click the solver data, and get the solver data and the solver output file from it. Let me go a little bit of detail. So once you get the solver run is done, and then go to the result tab and the inspect and that click this solver data button, you can choose either solver data and the solver output.

Solver data is on default, and the solver data is mostly showing that the quality of mesh. But in event simulation, we can go a little bit further. And we don't really expose directly to the user on certain key-- in my opinion, key engineering-- the quantity. That is the energy. And you can dig up that information from this output.

And so once you open this dialog box, and you can save the file in your local hard disk drive, and open it with whatever your favorite spreadsheet. I use the Excel but you can do the same thing with a Google spreadsheet or Numbers in the Mac. So you can get this fairly large. Most of the time, the solver log file or solver output data file could be the megabyte easily.

But you can find the whole this energy and then you just click that energy part in another sheet and using the text to column wizard converter. And use the fixed width because we are in those using mind. So each column is the fixed width. You can easily extract each column with the digital.

So this is a few example I'm using. So you can get that the yield stress of the material you are simulating. And also you can get the energy trend. So one is the kinetic energy and another one is internal energy. You can also check the viscosity energy level and the external work. So external work is all the energy is produced by applied load and viscous energy can be generated by the damping you added or some other numerical damping can be included.

And the internal energy is how much energy required to the deform the either elastic or plastic deformation of the model. And the kinetic energy is mainly the kinetic-- so the mass multiplied by the square of velocity divided by half. And that's the quick check. So in our softball team, try to make the better user experience for the event simulation. We keep on working.

Here's the feature or the enhancement of the solver is briefly introduced. So the quasi-static event simulation is the automation of the event simulation. So internally the solver run the event simulation multiple time to give a same outcome-- almost a good alternative to the nonlinear static analysis without much ease.

But this year we can present to the customer is that we increase the speed of quasi-static event simulation is almost 1.5 to the twice faster than previous year. So this is that one billet-- one example about the billet. So it's just squeezing and the compress dominant and release the problem. So this chart on the right showed that the kinetic energy and the internal energy-- by the way, this chart is exactly I use the solver data and that I the extracted from the Excel and that I can load it like this.

So what you can see is that before an updated, we have almost same energy trend. But this new algorithm can speed up the twice faster than previous one and on other nonlinear static, nonlinear material, nonlinear static analysis showed that 1.9 times faster than before. This is a clip snap model and it engaged some slide contact condition-- sliding and contact condition right at that snap it into this clip is fastened.

So in this way this new algorithm gave a 0.5 times faster than previous one. And this is the simulation run. So we see that same trend over and over. And, hopefully, the quasi-static simulation is become more popular to the simulation user and that they get a better result with the same accuracy as before with the small amount of time.

So it's almost the last section of this talk. So what you can take it. So I warn you that I'll do keep cycle this 3S-- statics first, and to make it simple and make it short. So this way, of course, if you need to run the static first or think static first might be a little bit more mental energy you need to prepare even before you start this event simulation.

But just trying the linear static at first or think about it will really minimize the many errors like loading condition or meshing issue. And you can also in many time you will satisfy the outcome from the linear static. And once that is not enough, then you can move on to the event simulation without any issue using the cloning the study for that and switch the simulation type in simulation or quasi-static event simulation.

And to make it simple is the use simple by the mesh, and the use simple by the boundary condition, and use simple by content condition. That also minimizes the less error and the faster the simulation outcome can be guaranteed through the event simulation.

Last but not least, short-- make it short. So that doesn't mean that make a short time step size, but whole duration you just focusing on the most climax of your simulation, then you really minimize the extra effort and the computing time to waiting for that outcome.

So, again, as late Professor Winston suggests, joke is a better way than thank you at the last of lecture. So here's joke from the ChatGPT. Why did the engineer bring a letter to the bars? Because they heard the drink were on the house. OK, let's go home.