13

Not sure if you find the COMSOL Model Wizard somewhere else, maybe other commercial Multi-physics software but not in the open-source community. I had the same question a couple of years ago and I listed all Finite-element, Multi-physics framework. As you may know there are many of them. The one that I found really useful and close, at least in the way that ...


10

We should keep in mind that models are just representations of a portion of reality (a narrow portion), therefore a divide by zero error or other mathematical error (negative concentration, for instance) is not necessarily a flaw in the conceptual model, only that the model is used beyond its proper range of application. For example, let's consider a model ...


8

I would say that you have, mainly, two methods: Being consistent in all your code, as already suggested in another answer. For that purpose, I always keep a table like this one with me, since it might prove really useful. Use nondimensional equations. That way, all my parameters and variables are consistent already. For that purpose, I suggest reference 1. ...


8

Just simply by being consistent in all of my code? Yes this is the only way. Matlab or any other programming language does not know about units. They only know about numbers. As an example consider incompressible flow. If you set your velocity in m/sec, length in meters (how you generate the grid), pressure in Newton/m^2, kinematic viscosity in m^2/sec, ...


8

Many of us in scientific computing simply have well-equipped laptops for regular software development tasks, some multicore workstations for smaller-scale testing, and access to clusters for larger runs. To give you an idea: My laptop is a Dell M3800 (4-core Intel i7, hyperthreading, 16GB of RAM). This is good enough to regularly compile my software and do ...


7

To solve this problem as you have described it, you need to set up a simple system of ordinary differential equations. For each segment in your "fishing rod" you just need to use conservation of linear and angular momentum ($F=ma$ and $\tau = \frac{dL}{dt}$). Each segment will experience forces and torques from its neighbors. There are many ways to formulate ...


5

So bottom line is I don't see any comprehensive work on the use of AI in M&S as a whole, let's say having models that can learn how to produce new improved models using the existing models. There's definitely some work out there on this. This is the field of scientific machine learning. Currently there's three major paths that I'd break it into: Neural ...


5

Numerical judgement of model choice: You model 36 observations with a model consisting of 12 or 13 predictor variables. This is most likely not a good model. Even if you reach a high $R^2_{adj}$, you most likely model a random pattern. Try to compare a computed $AIC$ (Akaike information criterion) or $BIC$ (Bayesian information criterion) of this model to ...


4

The obvious answer is "it depends". However, it's not helpful. I would certainly separate the work in mathematical modeling and actual numerical simulation. Sometimes it might be a bit tough to draw the line in between, but I think it's usually possible. Thus, by using work in mathematical modeling and numerical simulation does not seem to be redundant and ...


4

Welcome to the site. You are actually virtually finished, but may not have realised it yet. A tridiagonal linear system is another name for a matrix problem which only has non zero entries on the leading diagonal and the one above and below it, so lets try writing your problem like that. We want a form $$ \mathbf{A} (\mathbf{\Delta W}^m) = \mathbf{b},$$ ...


4

You need to know which equations you need to solve inc initial conditions. IMO, a disadvantage of click&result software is that it's not transparent to what you are actually solving. Why don't you try solving the equations using a ODE solver in Python (using SciPy) and visualize using Matplotlib? At least you will have exact control over what you are ...


4

You might also want to have a look at: Elmer https://www.csc.fi/web/elmer Kratos http://www.cimne.com/kratos/ OpenFoam http://www.openfoam.com/ CaeLinux http://caelinux.com/CMS/


3

For me, there is a clear hierarchy going from reality to a simulation. The first step is to understand reality as much as you can and propose a model for this reality, typically without formally writing down equations. You define what physical/chemical/biological/... processes are involved. Already in this step, you introduce an error: you can never model ...


3

This "model" is the incompressible (constant density) Navier Stokes problem, the second equation being the mass balance: $$ \frac{\partial\rho }{\partial t}+\nabla\cdot(\rho v)=0 $$ I have worked in the past with Comsol, and I believe that the Navier Stokes weak forms are readily implemented in the CFD module as states the Comsol modeling manual in this LINK....


3

EDIT: No, that process will not be compatible with any adaptive time-stepper. It's not deterministic, and even for non-adaptive ODE solvers, your proposed process will degrade the accuracy of your solution. You'll have to describe what you want to do in more detail. In general, changing a parameter changes the equations you want to solve. If your parameter ...


2

In order to do this, you'll need to convert inequalities to equality constraints by introducing slack variables and then add these slack variables to your matrix variable as an additional LP block. Let $ X=\left[ \begin{array}{ccc} W_{1} & B & 0 \\ B^{T} & W_{2} & 0 \\ 0 & 0 & \mbox{diag}(v) \\ \end{array} \right] $ ...


2

What you describe is called Differential-Algebraic Equation (DAE) system. Depending on the index of the system, these can be easy to solve or very hard. Take a look at: http://www.mathworks.com/matlabcentral/fileexchange/7481-manuscript-of--solving-index-1-daes-in-matlab-and-simulink- Solvers ode15s and ode23t of Matlab can handle index-1 DAEs. If the ...


2

Just to point out to a great free Open Source software used exactly for the purpose of modeling of a multibody system, just like your fishing rod. It's called MBDyn, and I've used it to model the dynamics of multicomponent airfoils. There is ample documentation available, and also slides that describe the physics. See for instance slide 25 of this ...


2

There are a number of software packages out there that you can use -- most are curated by the Computational Infrastructure in Geodynamics initiative (see http://www.geodynamics.org). The fundamental question you will need to answer is what time scale and material description you want to investigate. For example, if you care about short term (at the ...


2

You can work with classes. There's a book called "What every engineer should know about MATLAB and Simulink" by Biran, and the problem you're describing is the example that is given in the OOP chapter. In short, he defines a class of "physicalProperty" whose objects have properties which are the power of the basic units for length, mass and time. Whenever a ...


2

This a followup to my comment about smoothing the expression for $k$ that is a function of $x$ and $\dot x$. I converted your expression for $k$ into the following function to make experimentation easier. The input variable xxdot is just $x\dot x$ function k=calcK(xxdot) k = 4; if(xxdot>0) k = k + 4; end end Then I wrote a second version of ...


2

You should take a look at the book (or, really, "tome") called "A new kind of science" by Steven Wolfram. It is about many questions like the one you state. But, more concretely, think of starting with, say, the Navier-Stokes equations and then discretizing it in space and time on a uniform mesh. So $U(i,j,k)$ represents, for example, the state of the fluid ...


1

I have been thinking that it might be easier if one changes first the variables in the differential equation. That way one can bypass the function $h(t)$ and deal with fewer functions. Since $$\hat{y}(t) = \hat{y}_{\theta}(t) = \hat{y}(t \,| \, \theta) = \theta \, \sqrt{2g} \, \sqrt{h(t)}$$ change the dependent variable $$\hat{y} = \theta \, \sqrt{2g} \, \...


1

I don't see how two equations give $z$ as output. Nevertheless, your sequence of computations looks reasonable, except I would combine steps one and two into: Simultaneously solve for $x$ and the sensitivities $z$. This is a extended ODE system that you could throw at a built-in MATLAB ODE solver: $$ \begin{bmatrix} x'(t,\hat{\theta}) \\ z'(t,\hat{\theta}...


1

"A New Kind of Science" (NKS) has been brought up, in this case for a very legitimate reason; this book provides a lot of information on the actual rules generation & analysis, universal computation, etc. However, I feel the need to add a link to the famous Review of "A New Kind of Science" by C. Shalizi. However, I bring it up not for the reason of ...


1

Enclose each one of your arcs by a box that connects the two end points on one diagonal and choose the other two points to make things into a box. Then replace the original polygon-with-arcs $P$ by the polygon $P'$ that contains all of the straight line segments plus, say, the inside two sides of all of the boxes. (Or the outsides, or choose randomly.) Then,...


1

No this is not possible. And actually, it is a good practice to not to rely on this type of inferences. Well before anything they tend to get in the way and certain operations are not structure preserving such as balancing and model reduction. Unit wise they are not that useful either. For example, a noise on the measurement signal shouldn't have any units ...


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