Below you will find pages that utilize the taxonomy term “Linear System”
Elmer vs FEniCS - Part 3
In the Elmer vs FEniCS - Part 2 episode we studied the effect of mesh size on accuracy. We largely found the same results observed in the Mesh Order and Accuracy episode. We also confirmed that the agreement between
Elmer is very good. However, we noticed that
FEniCS was significantly slower than
Elmer. This because we used a
MUMPS direct method on
FEniCS and a
BiCGStabl iterative method on
Elmer. In this episode we will explore the iterative solver options for
FEniCS and attempt to optimize execution time for our simulation.
Elmer vs FEniCS - Part 2
In the Elmer vs FEniCS - Part 1 episode we solved the Pulsating Sphere problem over a fairly coarse mesh. We solved the problem both with
FEniCS based Helmholtz solver. We found that
FEniCS produce the same solution. This solution compares well to the exact solution, but has some appreciable magnitude error. In this episode we will study how this error changes with mesh size, and whether
FEniCS keep on providing the same solution.
Elmer vs FEniCS - Part 1
In the Writing Your Packages - Part 1 and Writing Your Packages - Part 2 episodes we introduced the most important concepts in writing your own simulation packages. We chosen
Python as a language and implemented two simple packages,
acoupy_helmholtz. In this episode we will use the Pulsating Sphere benchmark problem to compare
acoupy_helmholtz to our old trustworthy
Elmer. Since our software is little more than syntactic sugar around
FEniCS this will allow us to compare with
Tuning Fork - Part 4
In the Tuning Fork - Part 3 episode we seen how to setup a weak vibroacoustic coupling problem. We applied an harmonic body force to our tuning fork, and used its displacement field to wake the acoustic field within a coupled volume of air. In this episode we will review the results.
Tuning Fork - Part 3
In the Tuning Fork - Part 1 and Tuning Fork - Part 2 we set up and solved an Elmer study for the modes of vibration of a tuning fork. We learned that the principal mode of the fork, the one related to the nominal frequency of the fork, is very marginally affected by boundary conditions affecting the handle of the fork. In this episode we will attempt studying the acoustic field emitted by the fork in the surrounding air. In other words, we will start exploring the coupling of vibration and acoustics.
Tuning Fork - Part 2
In the Tuning Fork - Part 1 episode we setup a new study for the determination of the elastic modes of vibration of a tuning fork. Our study made use a few meshing and solver setting ideas we learned along the way, including the use of $p$-elements. In this episode we will examine the results from the Elmer simulation.