# Tag Info

11

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 ...

7

The idea of "ordering the nodes" in a finite element mesh to improve the computational time of the sparse solver originated in the large structural analysis FE codes of the 70's. Those codes typically used banded or variable-band storage schemes for the sparse matrices so reducing the bandwidth was the main criterion. That is the origin of the old Cuthill-...

6

Thermal stresses are self stresses that arises in two main cases. If one imposes displacement continuity at the interface between two materials with different thermal expansion subjected to a uniform temperature change; if an homogeneous material is subjected to a non uniform temperature change. (Here with uniform I mean constant with respect to space, i.e....

6

You're trying to have your cake and it it too. This does not work. As a general rule, for problems with features on different length scales, you need meshes that are fine in at least some parts of the mesh. This results in many cells, and this results in long computations, small time steps, and many linear iterations. All of these implications are rather ...

5

With conforming triangular meshes, it will be difficult to make an isotropic mesh which adapts to multiple dramatically different length scales in such a short space without introducing extraneous triangles, some of which may have very large/small angles. I'm not very familiar with them so take this with a grain of salt, but you may have better luck using ...

4

The biggest problem in answering to this question is that it's not as straightforward as you might think to see the physics in the equations until you see them fully developed, and even then you're doing your best to assign a meaning. As a graduate student in mechanical engineering, this was hard for me because I was used to using my physical intuition to ...

4

You might have to reassemble if your problem is non-linear and your method at a future step incorporates the solution in the formation of the matrix. If you are doing Picard iteration rather than Netwon-Raphson, then you should only have to reform the right-hand-side vector. I don't know enough about FEciCS and COMSOL to say what they do, but I suspect, for ...

4

You seem to be confused about which equation to solve. You have two: (i) the flow equations, (ii) the equations for your particle property $D$. The finite element method is suitable for part 1 of this. Or, if you really just have a pipe with laminar flow, then you actually know what the flow field is (namely, Poisseuille flow) and you don't need to solve ...

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 ...

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

Given a PDE choosing the correct numerical solving strategy requires some knowledge/expertise. (Computational Science is indeed a "Science" and one has to learn it.) In application specific software (e.g commercial FEM solvers for engineering problems like crash problems or metal forming) this knowledge is somehow "crystalized" and embedded, so that most ...

3

FEM is for solving boundary value problems. What you have here is an initial value problem (assuming $\alpha$ and $U_z$ are constant or functions of $z$), the same as solving a time-dependent ODE, except here $z$ is your time-like coordinate. The appropriate way to solve this kind of problem is with time-integration methods, e.g. Runge-Kutta schemes. In FEM ...

3

It is quite straightforward to demonstrate this for implicit Euler (aka backward Euler) on a scalar example. Consider the initial value problem $\dot{y}(t) = i \alpha y(t), \ y(0) = 1$ with solution $y(t) = \exp(i \alpha t) = \cos(\alpha t) + i \sin(\alpha t)$. The solution is a harmonic oscillation with amplitude 1 and this amplitude does not change ...

3

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

I don't see anything unusual here. You have a material property that is defined in terms of other material properties. In your particular case, the real and imaginary parts of the refractive index are functions defined from n_interp and k_interp, which usually denote the interpolated values (either supplied by COMSOL or user-supplied). In many simulations, ...

3

Your equation is not well posed: For general functions $f_1,f_2$, there is no function $\Phi$ so that the equation can be satisfied. For example, if you had $f_1=f_2=x$, then you are looking for a $\Phi(x,y)$ so that $$\Phi_x = x$$ and $$\Phi_y = y.$$ But the first of these equations imply that $$\Phi = x^2+by+c$$ whereas the second implies that $... 2 The correct boundary condition is in fact $$(D\nabla C - vC) \cdot n = g.$$ That is, it is not the vector-valued quantity in parentheses that you can describe, but only the normal component, where$n$is the normal vector to the boundary. The term in the parentheses is called the flux. It describes the amount of material (solute) that moves around, and ... 2 They are saying the same thing, at a fundamental level - it's just that the implementation is a bit different. The first equation you noted is valid throughout the system because it solves for the intrinsic values throughout the system, such as the local current density and local electric potential. The second equation you mentioned is a lumped-value ... 2 You question is unclear. However, rotations in the context of linear mechanics are often confusing. Therefore a response is probably needed. 1) I will assume you have a deformable body and a rigid body in your simulation, i.e., there are two objects that may interact. 2) I will assume the deformable body is subject to a torque while the rigid body has a ... 2 Finite Element Analysis is a mathematical tool very extended among engineers. However, after more than a year researching on the topic of computer simulation, where FEA plays such an important role, I couldn't yet find a satisfactory explanation on how they really really work... The main background of FEM is that of structural engineering in the 60s. ... 2 Mass is conserved always. That's the known fact. To show this holds true in convection-diffusion equation, I need to introduce material derivative to you. The material derivative of a scalar quantity as$C(\mathbf{r},t)$is defined as: $$\frac{D C(\mathbf{r},t)}{D t} = \frac{\partial C}{\partial t} + \mathbf{v} \cdot \nabla C$$ Where$\mathbf{v}$is the ... 1 Based on the comment by @TylerOlsen, I've applied the boost implementation of the reverse Cuthill-McKee ordering on the same matrix from the original question and here is the result: The structure looks very similar, but the bandwidth is significantly smaller compared to the original matrix with COMSOL ordering. Also changing the starting vertex in the ... 1 Due to the Euler's rotation theorem a rigid body in 3D space has 3 rotational degrees of freedom, (plus 3 displacement degrees of freedom for a total of 6 degrees of freedom.). This typically means that the rotation matrix (which has 9 components) is not the primary unknown but, when needed, is computed from the rigid body's rotational DOFs. Several ... 1 If you are familiar with the standard FEM analysis works, the idea of modal analysis is straightforward. In standard FEM analysis, you transfer the time-dependent elastic wave equation (ignoring damping for now) $$\ddot{r}(t) + A r(t) = f(t) \tag{1}\label{1},$$ which is a mathematical model describing the behavior of the displacement$r(t)\$ using the ...

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Under results node, there are Export and Reports options. Right click on Export will give you some options for exporting your data.

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The finite element methods, i.e., what COMSOL uses internally, does not solve the problem exactly. It only (i) provides an approximation to the solution, and (ii) does so in a way for which we can show that the approximation converges to the exact solution of the problem as mesh becomes finer and finer. This typically implies that on meshes that are too ...

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Actually that is possible to solve that set of equations in COMSOL. You can simply select a 1D domain problem, add physics and in particular use the general ODE/DAE interface. You can add multiple ODE/DAE equations and, for each of them, define all the conditions stated in your picture.

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Resolving small features in FEM will always be costly, there is no getting away from that fact. Your problem seems to be framed in terms of computational burden. In my own case, I was looking at electric field problems in anatomical structures, so had a similar set of problems to your own. The question is usually how detailed a mesh is "good enough" for the ...

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As far as I remember it is common to use splitting methods like Chorin's Method to ensure divergence free fields in fluid dynamics. Have a look into Demo 6 of Fenics on Incompressible Navier Stokes. Alternatively it is possible to implement certain Element Types like the H(curl)-Nédélec-Element that is often able to compute divergence-free fields. Although ...

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