Jihuan TianSep 12, 2025

πŸš€ I’ve been working on HierBEM, a 3D Galerkin boundary element method (BEM) library. It uses hierarchical matrices (\(\mathcal{H}\)-matrices) for near log-linear complexity.

πŸ”§ Built on deal.II, written in C++ with CUDA acceleration. Still early in development, but it could already be useful β€” and might serve as a nice supplement to deal.II.

πŸ’‘ Feedback and thoughts are very welcome!

https://github.com/jihuan-tian/hierbem

#HierBEM #bem #dealii #fem #NumericalSimulation #NumericalComputation

GitHub - jihuan-tian/hierbem: Hierarchical matrix based 3D Galerkin boundary element method library

Hierarchical matrix based 3D Galerkin boundary element method library - jihuan-tian/hierbem

GitHub
doctorambientNov 13, 2022

By way of another #introduction, I noticed that this shelf of somewhat random #books that we've finally managed to get unpacked does a pretty good job of showing at least one span across my interests.

#science #scicomm #math #statistics #stochasticprocesses #stochastic #simulation #numericalcomputation #computing #programming #occult #photography #hieroglyphic #psychology #hypnosis #middleegyptian #gnosis #gnosticism #eeg #history #1950s #nlp (both kinds) #psychedelics #psychedelia #pinup

claudeMay 7, 2020

> RenΓ© Lozi. "Can we trust in numerical computations of chaotic solutions of dynamical systems?". World Scientific Series on Nonlinear Science, World Scientific, 2013, Topology and Dynamics of Chaos
In Celebration of Robert Gilmore’s 70th Birthday, 84, pp.63-98. 10.1142/9789814434867_0004 . hal-
00682818 HAL Id: hal-00682818 https://hal.archives-ouvertes.fr/hal-00682818

#AmReading slowly as it's quite long (42 pages)

#Chaos #DynamicalSystems #NumericalComputation #Math #Maths

Can we trust in numerical computations of chaotic solutions of dynamical systems ?

Since the famous paper of E. Lorenz in 1963 numerical computations using computers play a central role in order to display and analyze solutions of nonlinear dynamical systems. By these means new structures have been emphasized like hyperbolic and/or strange attractors. However theoretical proofs of their existence are very diΒ’ cult and limited to very special linear cases. Computer aided proofs are also complex and require special interval arithmetic analysis. Nevertheless, numerous researchers in several fields linked to chaotic dynamical systems are confident in the numerical solutions they found using popular software and publish without checking carefully the reliability of their results. In the simple case of discrete dynamical systems (e.g. HΓ©non map) there are concerns about the nature of what a computer find out : long unstable pseudo-orbits or strange attractors? The shadowing property and its generalizations which ensure that pseudo-orbits of a homeomorphism can be traceable by actual orbits even if rounding errors are not inevitable are not of great help in order to validate the numerical results. Continuous dynamical systems (e.g. Chua, Lorenz, RΓΆssler) are even more difficult to handle in this scope and researchers have to be very cautious to back up theory with numerical computations. We present a survey of the topic based on these, only few, but well studied models.