Reinhard Piltner

Research Interests: Computational Mechanics, Finite Element Methods, Boundary Element Methods, Medical Imaging, Radial Basis Functions, Complex Valued Functions

[Reinhard Piltner @rpiltner]

The classical Boussinesq solution written in terms of Piltner's complex 3D representation.
Can this be conveniently written in terms of quaternions? #CliffordAlgebra @Clifford_ICCA #quaternions #mathvisualization #SolidMechanics #ElasticityTheory #ComputationalMechanics #Meshing

[Reinhard Piltner @rpiltner]

The 3D displacement functions given in 1987 satisfy the Navier equations (equilibrium equations) for any choice of complex functions. Muskhelishvili solution is included. (3D complex elasticity solutions https://t.co/RWmubOYxTe https://t.co/m8ZcU28M6x ) @ruhrunibochum @UCBerkeley

[Reinhard Piltner @rpiltner]

@DrGrimmTweets @Harvard @Columbia @DukeU @GeorgiaTech @VanderbiltU @EmoryUniversity Vielen Dank!

[Reinhard Piltner @rpiltner]

My daughter Helen is interested in studying Biomedical Engineering. Here is Helen's "College Decision Reactions 2021" video. ( @Harvard, @Columbia, @DukeU, @GeorgiaTech, @VanderbiltU, @EmoryUniversity )

https://t.co/DtUwGBqo3K

[Reinhard Piltner @rpiltner]

@Hornegger @Harvard Thank you very much, Achim!

[Reinhard Piltner @rpiltner]

Congratulations, Helen! Some interesting years at Harvard ( @Harvard ) lie ahead.

[Reinhard Piltner @rpiltner]

@justin17171 @Harvard @Columbia @DukeU @GeorgiaTech @VanderbiltU @EmoryUniversity Thanks!

[Reinhard Piltner @rpiltner]

The 3D displacement functions of M.G. Slobodyanskii satisfy the Navier equations (equilibrium equations) if harmonic functions are used. Thank you Dr. Dmitrii Legatiuk for the link to the photo!

[Reinhard Piltner @rpiltner]

The Papkovich-Neuber solution is probably the most popular 3D function representation for elastic deformations. The displacements satisfy the Navier equations (equilibrium equations) if harmonic functions are used.

[Reinhard Piltner @rpiltner]

Here are the 3D displacement functions of Galerkin. The elastic displacements satisfy the Navier equations (equilibrium equations) if biharmonic functions are used.

[Reinhard Piltner @rpiltner]

For 3D elastic deformations we can utilize complex variables involving the spatial coordinates x, y, and z.
https://t.co/RWmubOY03G

[Reinhard Piltner @rpiltner]

3D elastic deformations can be written in terms of complex valued functions. The Kolosov-Muskhelishvili representation is included as a special case. https://t.co/RWmubOY03G
https://t.co/9H0xvJJebV

[Reinhard Piltner @rpiltner]

@Hornegger Achim, I agree with you that a complex function representation of elastic deformations could be of interest for image registration. Some useful complex functions are listed in: https://t.co/ig4Go3wvTv

[Reinhard Piltner @rpiltner]

For 2D elastic deformations, the use of complex valued functions can be a very convenient option because we do not have to worry about the satisfaction of differential equations.
https://t.co/9H0xvJJebV

[Reinhard Piltner @rpiltner]

Here is Amanda Gorman’s inspirational inauguration poem https://t.co/0rTmB1Cy9j via @TheGeorgeAnne

[Reinhard Piltner @rpiltner]

Music, dance, mathematics, engineering and computer science combined: Former MIT Professor Marc Raibert https://t.co/i3n6mmHwD2
made this video possible through research in his company Boston Dynamics ( https://t.co/1uuU3b7LFc ).
Very impressive research! https://t.co/VEXayxMfi0

[Reinhard Piltner @rpiltner]

The Python program pyFormex ( https://t.co/NpUwemDW2A ) is used for the meshing of blood vessels into finite elements in the following videos:
https://t.co/3F1AreFCn6
https://t.co/1ILKDo8xrq
https://t.co/wKQvs73lbl
PhD thesis of Gianluca De Santis: https://t.co/szzXFydDmn

[Reinhard Piltner @rpiltner]

Professor Benedict Verhegghe from Ghent University
released version 2.1 of pyFormex ( https://t.co/NpUwemDW2A ).
pyFormex is a Python based program for generating
hexahedral finite element meshes, triangulated surfaces or CFD grids. Helps to get 3D models from medical images.

[Keenan Crane @keenanisalive]

Poles of a complex function can be nicely visualized as vector field singularities—but are rarely drawn that way (try Google images!). In computer graphics, vector field singularities can be thought of as poles and zeros of complex functions—but are rarely understood that way!

[Reinhard Piltner @rpiltner]

@UniFAU @Hornegger Congratulations!! Herzlichen Glueckwunsch.