poor convergence in MEMS electromechanical switch

April 23, 2015, 11:57 am

≫ Next: how to realize convergence in highly doped semiconductor in COMSOL 4.4

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Greetings:

This is a grossly simplified form of a 3D model I'm doing of an electromechanical switch using the MEMS module.

There's a cantilever which is at zero bias, a "gate" electrode which is biased to a non-zero voltage, and a contact (which for purposed here is at a zero charge state). With a nonzero bias the cantilever is attracted to the gate electrode, bending, but then it makes physical contact with the contact electrode and the gap remains finite, preventing full collapse. If the bias were ramped further, eventually the gap at the gate electrode would also collapse, but this would take very high force.

In any case, I don't get anywhere close to this. I can ramp the bias up to on order 0.1 volts, and then it fails to converge.

I have two approaches. One is a standard "stationary" study in which the gate voltage is specified directly. The other is where the voltage is ramped up proportional to the square of the ramping parameter.

There is a 20 nm gap between the cantilever and the contact electrode but the total deflection at the tip maxes out at 3.6 pm (or milli-nm, if you prefer). So any geometric complexities are still minimal at this point.

I've tried to get this working for days and I'm afraid I'm missing something silly.

Anyone else have experience with these structures?

Link: www.dropbox.com/s/uvkue4m2xqv5...msolGeometry_2d_clean.mph?dl=0

The electrostatics, which converge only at low bias, are shown here:
i.imgur.com/IKKxXG6.png

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how to realize convergence in highly doped semiconductor in COMSOL 4.4

May 4, 2015, 5:44 pm

≫ Next: Evaluating the L2 and H1 norm of the difference of two solutions on different grids

≪ Previous: poor convergence in MEMS electromechanical switch

I meet the convergence problem when modeling highly doped semiconductor in COMSOL.
What I model is a P-n heterojuction, the concentration of the acceptor is 1e18/cm3, the concentration of
the donor is 3e15/cm3. The result is difficult to converge, even I refined the grids up to 60000!
Does anyone encounter the similar problem?

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Evaluating the L2 and H1 norm of the difference of two solutions on different grids

July 5, 2010, 11:26 am

≫ Next: convergence speed

≪ Previous: how to realize convergence in highly doped semiconductor in COMSOL 4.4

I did not find any help on this topic on the web, so I thought I should publish my simple results:

When working with FEM-models it is necessary to check grid-convergence of the solution. The L2-norm (and the H1 too) is a good measure for this, and it is not difficult to make a matalb-script to find the norm(s). Thanks to Bertil Nistad @ Comsol support for invaluable help making my scripts/functions.

First define a function for calculating the norm:

function norm=femL2H1norm(femA,femB,l2expr,h1expr)
% femA and femB are the fem structures we want to compare, femB has the finest mesh (most elements), so we will compare the results om femB's mesh.
% l2expr and h1expr are the expressions evaluated; typically 'u^2' and 'ux^2+uy^2', respectively. Note the string-notation. Replace u with your solution-variable in this string.

% initializing:
norm = [0 0] % if the returned value of the function is zero then something is wrong...
femA.xmesh=meshextend(femA, ...
'mcase',[1]); % This might not be necessary, but it makes the method more general.
femB.xmesh=meshextend(femB, ...
'mcase',[1]);
% Start mapping fem to current mesh:
% New mesh:
femA.mesh = femB.mesh;
% Mapping solution A to extended mesh
initA = asseminit(femB,'init',femA.sol,'xmesh',femA.xmesh,'blocksize','auto');
% Update models
femA.sol = initA;
% Multiphysics
femA = multiphysics(femA);
% Update extended mesh
femA.xmesh=femB.xmesh;
% update femA.sol to contain the *difference*:
init = asseminit(femA, 'init', femA.sol.u - femB.sol.u);
femA.sol = init;

% Compute the norms:
norm(1) = sqrt(postint(femA, l2expr));
norm(2)= norm(1) + sqrt(postint(femA, h1expr));

end

This function can be expanded and modified a lot. Read more about postint in the Reference guide. You could also use Matlabs nargin- and nargout-functions to create default values.
However, we also might want to know the number of elements in our mesh, to make it possible to plot the norm versus number of elements in mesh. This is easily done in the script where we call femL2H2norm(). The script should be based on the model .m-file. After the mesh-initializing or refinement add the lines:

% Initialize mesh
fem.mesh=meshinit(fem, ...
'hauto',4);
% initialize counter:
numMeshElem = 0;
% Number of elements in mesh:
el = get(fem.mesh,'el');
M = el{3}.elem;
numMeshElem(end) = size(M,2);
clear M el

This satisfied my need for generating some convergence plots for my models.

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convergence speed

December 9, 2011, 2:36 pm

≫ Next: Convergence: when should I stop the model?

≪ Previous: Evaluating the L2 and H1 norm of the difference of two solutions on different grids

Hello,

In some previous FEA software I looked at, there was an option to limit the degrees of freedom to speed up solution times. In a 3D model for example, one could only look at movement along the y axis, ignoring the x and z. I am wondering if there is a way to do this in COMSOL, and if so, would it be useful to increase convergence speed?

On a related note, are there any ideas on what convergence speed should I expect from a 3D model of laminar flow interacting with a solid, very simple geometry, on 8GIG 64 bit Windows 7? I realize it's hard to say, but some of my models have been running for days, so I'm wondering if I should expect convergence in days or in hours?

Thanks,
Anton

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Convergence: when should I stop the model?

March 15, 2012, 3:55 pm

≫ Next: What is convergence?

≪ Previous: convergence speed

Hi everyone

I have been working on models that take several days to solve. One of them is running at the moment, and I just have a general question.

When I look at the Convergence Plot 2, which is "Reciprocal of step size" vs "Time step", I can see the reciprocal of step size is between 10^5 and 10^6. It has been like this for several hours, and the progress value is at 2% without increasing.

I need results for this simulation by the beginning of next week. When do you know if you should stop the simulation or let it run and solve this convergence difficulty eventually? If I stop it, and the model could have advanced and solved, then I'll lose several hours of solving. But if I don't stop it, it might be at 2% for more than a day.

What should I do? What are the general guidelines on convergence?

Thank you so much!
Sylvana

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What is convergence?

March 10, 2013, 12:37 pm

≫ Next: Error in inductor modelling with Magnetic fields interface

≪ Previous: Convergence: when should I stop the model?

I'd just like to know what convergence is - in the context of COMSOL.

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Error in inductor modelling with Magnetic fields interface

May 6, 2013, 6:44 am

≫ Next: peristaltic pump model convergence

≪ Previous: What is convergence?

Dear all,

I'm using the Magnetic fields interface on an inductor model I'm currently working on. The idea is to do a multiphysics coupling with Heat transfer in solids so that I can compare it with results I've achieved using the Induction heating interface. My model is very similar to a tutorial model called "single_coil_boundary_feed" (www.comsol.com/showroom/documentation/model/14067/), and the physics are setup in exactly the same way. The difference is that my model has 17 turns instead of only one that we have in the tutorial model.

When I run a simulation only consisting of the coil and an air domain around it, I have no issues at all. But since this is supposed to be a more detailed model of an inductor I would like to incorporate a core (a very simple, rectangular box in the middle of the windings) and a circular shell surrounding the inductor.

However, when I try incorporating the shell the simulation won't converge. The error I'm getting is "Failed to find a solution. Divergence of the linear iterations. Returned solution is not converged". I've tried with a more detailed mesh and that doesn't solve the problem. I've also tried using a non-zero conductivity of the air and that doesn't do the trick either. I haven't tried incorporating the core yet since I suspect that it will also give the same error. I have no idea what the problem could be, so I really need your help.

Best regards
Bilal

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peristaltic pump model convergence

August 14, 2013, 7:34 pm

≫ Next: Convergence plots

≪ Previous: Error in inductor modelling with Magnetic fields interface

Hello,

I am working on a model that is similar to the peristaltic pump model available in the “model gallery”. I would like to use this example to present my problem.
The peristaltic pump model does not converge when a greater load is applied to the nylon tube to make it almost completely compressed (inside diameter to become very small). For instance, when I change the maximum load setting of Lmax to 1.6e8 instead of 1e8 N/m^2, it does not allow the model to converge. Setting Lmax to 1.5e8 N/m^2 still allows it to work but the force is not even near to allow the nylon to be completely compressed.
I have tried changing the Gaussian distribution which represents the force applied, Young’s Modulus to allow more compression, increasing the length of the tube, increasing and decreasing the diameter of the tube as well as changing the position of where the force is applied and it would still not allow the model to converge when trying to completely compress the tube.
I also tried out the adaptive mesh refinement and automatic re-meshing features but it didn't really help. There maybe some parameters that may work but I had no success so far. There may be another way to approach this problem with convergence when higher force is applied but I am stuck at this point.
I would appreciate some help!

Thank you.

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Convergence plots

December 13, 2013, 11:28 am

≫ Next: "Conjugate Heat transfer" failed to converge if a fluid is included.

≪ Previous: peristaltic pump model convergence

Does anyone know if it is possible to show a convergence plot during a livelink with Matlab? I'm using version 4.4 and matlab R2013a.

Thanks

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"Conjugate Heat transfer" failed to converge if a fluid is included.

February 7, 2014, 10:55 am

≫ Next: How can I manage individual cell values of a mesh in a convergence process?

≪ Previous: Convergence plots

A cylinder with a cavity filled with water is the geometry.
At the beginning, the outer wall hast a temperature different from the contents.
"Conjugate Heat transfer" is used to model the thermal equilibration with a time dependend solver.
The modelling does not converge:
"Failed to find consistent initial values./Last time step is not converged./ - Feature: Time-Dependent Solver 1 (sol1/t1)"
What is missing, to make it converge?

Note: "If I apply the "Heat transfer in solid" node with an included sub-node "Heat transfer in fluids" instead to the same model, convergence is reached."

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How can I manage individual cell values of a mesh in a convergence process?

May 3, 2014, 9:50 am

≫ Next: Silicon waveguide convergence value?

≪ Previous: "Conjugate Heat transfer" failed to converge if a fluid is included.

Using module Semiconductors for computing Electric Potential for a certain geometry, sometimes during convergence process one can observe how few cells close to both exterior limits of a domain and contacts (ohmic or Schottky), assume values clearly far from the expected. These sets of cells constitute a sort of splodges which prevent convergence uselessly. How to eliminate them? Can I manage the individual cell values in those cases when I am completely sure of a more appropriate ones?

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Silicon waveguide convergence value?

May 12, 2014, 3:10 am

≫ Next: Deformed geometry model converges until I try to use the lagrange multiplier

≪ Previous: How can I manage individual cell values of a mesh in a convergence process?

Hello.

I am studying silicon waveguide using RF module in COMSOL 4.2a version.

My questions are

what is the convergence in COMSOL multiphysics?

is it fine that I got the convergence value which is exact 1.0

and

how can I improve the convergence?

Thank you.

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Deformed geometry model converges until I try to use the lagrange multiplier

June 18, 2014, 6:59 pm

≫ Next: Model convergence dependent on mesh quality, confused!

≪ Previous: Silicon waveguide convergence value?

Hi all,

I'm trying to model the growth of a cavity in a block of ice in response to a flow of hot air. I have a model that works fairly well, with conjugate heat transfer and a deformed geometry to track the air / ice interface as melting progresses. At least, it works fine as long as I prescribe the melting rate at a fixed value of 0.001 m/s. In order to simulate melting I followed the approach of the Tin Melting Front example "Stefan problem" model: set the boundary temperature as a weak constraint, and use the lagrange multiplier as input to a prescribed normal deformation on that boundary.

The problem is that whenever I switch from the fixed value to the "Stefan problem" expression for the Prescribed Normal Mesh Velocity, my model no longer converges -- it says:

Nonlinear solver did not converge.
Time: 0
Attempt to evaluate real square root of negative number.

The model is attached. Thanks in advance for any advice!

Aaron

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Model convergence dependent on mesh quality, confused!

July 7, 2014, 5:57 pm

≫ Next: Different convergence requirement (relative tolerance) for different components of coupled model

≪ Previous: Deformed geometry model converges until I try to use the lagrange multiplier

Hi all,

My COMSOL model only solves when the mesh size is "above" the predefined Normal size. When I increase the mesh resolution to "Fine" or higher, the step BiCGStab in the progress tab stalls at around 96%, and continues iterations forever until infinity trying to converge.

I'll describe the model briefly in this paragraph, and include an attachment of it. I'm simulating a very small, simple, conductive, flattened-conical tip (sliced in half vertically for symmetry) that radiates microwave (~6GHz) energy into the surrounding region via a coaxial lumped port. I'm using the Electromagnetic Waves, Frequency Domain physics module. The model behaves exactly as desired when the lower-limit of mesh quality is met, but endlessly iterates otherwise. I've tested varying the geometry and size of the tip to no avail. It seems that the minimum element size I can reach before causing non-convergence is about 3e-7 meters. (My model size is on the order of 1e-6 meters).

I'm so confused; there's obviously nothing wrong with the model setup/geometry/physics, because it solves for lower-quality meshes. Is this a computer memory problem? (I've got 8GB). Is there a lower-limit to element size / calculation in the [EMW, Frequency Domain] module that I've reached?

Thanks for the help.

Jon Michelson

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Different convergence requirement (relative tolerance) for different components of coupled model

July 16, 2014, 2:06 pm

≫ Next: Geometry Units and Convergecne

≪ Previous: Model convergence dependent on mesh quality, confused!

I am working on a time-dependent model that couples two different physics branches. If I disable the second branch in the time-dependent solver, I can get a solution to converge with a relative tolerance of 0.1. If I disable the first branch (and enable the second), I need to use a much larger relative tolerance (~1000) to get the solution to converge.

Furthermore, I do not get a convergent solution in the first branch if I use this larger relative tolerance.

Is there a way to impose different tolerances for the different variables that I am solving for?

Sorry for the lack of details. Hopefully my question is general enough that they are unnecessary.

Thank you.

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Geometry Units and Convergecne

July 24, 2014, 3:27 am

≫ Next: Periodic Stimulation of Electric Currents Interface

≪ Previous: Different convergence requirement (relative tolerance) for different components of coupled model

Hello,

Does anyone know why changing the "geometry unit" raises convergence issues? For instance, when I change mm to cm, while all other parameters are the same, simulation diverges!

Thank you in advance for your time and consideration!

AR

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Periodic Stimulation of Electric Currents Interface

July 25, 2014, 12:27 am

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Hello,

I am trying to simulate an electrode with a periodic biphasic square pulse through a periodic piecewise function to stimulate it. The piecewise goes between 1, -1 and 0 and I multiply it by my input current to simulate this stimulation. I am doing this in a time-dependent study using the electric currents interface. The convergence continues to oscillate up and down until eventually it says the solution wasn't converged. Is this oscillation in the convergence due to the oscillation of the stimulation? What does an oscillating convergence mean? Does the electric currents interface only converge if a DC signal is given for a current source?

Thanks,
Trevor Davis

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cfd simulation

October 20, 2014, 11:44 am

≫ Next: Solution is not converging for solar cell problem.

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Hello everybody!
I would like to know what is the residual and tolerance factors, in the tab solver/fully coupled.
How can we change them in order for the solution to converge?
Thanks in advance.

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Solution is not converging for solar cell problem.

January 9, 2015, 12:35 pm

≫ Next: poor convergence in MEMS electromechanical switch

≪ Previous: cfd simulation

Hello everyone,

I'm trying to simulate a solar cell with four layers, and I got success with the one dimensional problem. But when I tried the same in two dimensions, the solution is not converging. I'd done the things I can do with my little knowledge in Comsol, still I am not getting positive results.

Thanks in advance for your help.

Regards
Binoy

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