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30 votes

Future enhancements for the finite element method

A useful feature that I regularly use in COMSOL and would like to be able to use in Mma is the "AdaptiveMeshRefinement" (as it is called in COMSOL). This means that COMSOL makes a mesh. With this ...
Alexei Boulbitch's user avatar
22 votes

Future enhancements for the finite element method

I think user21 needs to be congratulated for developing the finite element method and for asking this question. My thoughts are as follows: The purpose of finite elements is to solve differential ...
Hugh's user avatar
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20 votes
Accepted

How to make the boundary of a 3D region smooth?

Sometimes, it is easier to discretize before intersecting. ...
Henrik Schumacher's user avatar
20 votes

Future enhancements for the finite element method

In my opinion one thing that is still missing for really useful FEM framework is better quality of meshing (of Boolean representations of geometries) in 3D (...
Pinti's user avatar
  • 6,513
19 votes

Future enhancements for the finite element method

It is obligatory that I make a wish for finite elements on immersed curves and surfaces. This has a plethora of applications in geometry processing, but also in physics, chemistry and microbiology. ...
Henrik Schumacher's user avatar
19 votes

Future enhancements for the finite element method

I think that it might be beneficial to write down the tutorial describing the ways to choose and to fine-tune the solvers used. This proposal is close to that of @Rom38, but slightly differs from his ...
Alexei Boulbitch's user avatar
18 votes

How to make the boundary of a 3D region smooth?

Using OpenCascadeLink from version 12.1 makes this easier and better quality: ...
user21's user avatar
  • 40k
18 votes

Future enhancements for the finite element method

I guess, that one of the best improvements will be the detailed guide "how it works". I mean, for example the step-by-step solution of let's say transient 2D (or even 3D) heat transfer equation with ...
Rom38's user avatar
  • 5,149
18 votes

Future enhancements for the finite element method

Support for PDE Whose Spatial Derivative Order Exceeds 2 I've been stopped in v9 for a long time and don't consider myself as somebody actively using the FEM framework, but since nobody has mentioned ...
xzczd's user avatar
  • 67k
18 votes

How to graph a solid common to multiple functions

Related https://mathematica.stackexchange.com/a/269363/72111 ...
cvgmt's user avatar
  • 77k
16 votes

Future enhancements for the finite element method

Anisotropic Meshing The following is a feature request for anisotropic meshing. A proper mesh is as or more important than just having the proper equations to obtain accurate simulation results. The ...
Tim Laska's user avatar
  • 16.4k
15 votes

How to make the boundary of a 3D region smooth?

ri = RegionIntersection[Cylinder[{{0, 0, -2}, {0, 0, 2}}], Cylinder[{{0, -2, 0}, {0, 2, 0}}], Cylinder[{{-2, 0, 0}, {2, 0, 0}}]]; You can use ...
kglr's user avatar
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14 votes
Accepted

Define a region of revolution

You can use the new in V12.1 OpenCascaeLink to do something like this. It's not quite the way you want it but works well. Define a 3D polygon of the surface you want to compute ...
user21's user avatar
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14 votes
Accepted

Balanced flux in FEA using NeumanValue

Update (Steady-State Solution) I think the fundamental issue is that you are over constraining your system. Whether you are solving the "heat equation" or not, your operator has the same ...
Tim Laska's user avatar
  • 16.4k
14 votes

How can I generate a Swiss-Cheese type region and render it transparent?

...
cvgmt's user avatar
  • 77k
13 votes

How to make the boundary of a 3D region smooth?

In order to completeness,here we provide another ways to do this. Thanks @xzczd suggestion。 Related How to graph a solid common to multiple functions MeshFunctions ...
cvgmt's user avatar
  • 77k
13 votes

3D FEM Vector Potential

I am a chemical engineer, so this is not in my field, but I am able to match the results given in the reference. Background According to COMSOL's Multiphysics Cyclopedia, the magnetostatic equation ...
Tim Laska's user avatar
  • 16.4k
11 votes

How to make the boundary of a 3D region smooth?

Yet another way to discretize the Steinmetz solid is to directly derive the required inequalities using RegionMember[]: ...
J. M.'s missing motivation's user avatar
11 votes

Future enhancements for the finite element method

I see one more expansion of MMA tools in the FEM for nonlinear PDEs. This is a "Parametric Continuation." The point is that provided equation has a parameter, say, eps varying from 0 to 1 ...
Alexei Boulbitch's user avatar
11 votes

3D FEM Vector Potential

I can answer the first question. Have I implemented the pde in MM correctly? No, both gauged one and ungauged one are incorrect. The underlying issue is quite similar to that discussed in this post. ...
xzczd's user avatar
  • 67k
11 votes

3D FEM Vector Potential

I am physicist from the first education, so it is apparently my field. As it follows from my experience in 3D FEM testing with application to the magnetic field calculation there is a problem with ...
Alex Trounev's user avatar
  • 45.8k
11 votes

How to make a high resolution mesh from RegionIntersection in 3D

Use the OpenCascadeLink for this: ...
user21's user avatar
  • 40k
10 votes

Future enhancements for the finite element method

I would greatly appreciate some support for non-local operators. What I have in mind are the fractional powers of the Laplace operator that now appear quite frequently in modeling non-standard ...
Francois Vigneron's user avatar
10 votes
Accepted

Cylindrical coordinates in FEM

This appears to be a lid driven flow problem. I am in agreement with @user21's perspective that you should solve this in Cartesian Coordinates. It should simplify the boundary condition ...
Tim Laska's user avatar
  • 16.4k
10 votes
Accepted

How to union 3D region to calculate volume?

You can use OpenCascadeLink for that. Convert the pieces you have into a boundary element mesh, convert those to OpenCascade, make the union and convert back: ...
user21's user avatar
  • 40k
10 votes

How to graph a solid common to multiple functions

...
yode's user avatar
  • 26.8k
10 votes
Accepted

STL generation for Ball-in-a-maze puzzle

Using OpenCascadeLink, which comes with Mathematica, will give you excellent results. We start by loading the package and writing a little helper function to convert the annuli to polygons in 3D space ...
user21's user avatar
  • 40k
9 votes

How to make the boundary of a 3D region smooth?

...
chyanog's user avatar
  • 15.6k
9 votes
Accepted

Raytracing using Regions & NSolve

This is not a direct answer to your question, but an alternate approach. You could create a list of primitives and a build function that contains the Computational Solid Geometry (CSG). ...
Tim Laska's user avatar
  • 16.4k
9 votes

How to make a high resolution mesh from RegionIntersection in 3D

DiscretizeRegion before RegionIntersection. ...
cvgmt's user avatar
  • 77k

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