On the Computational Power of Particle Methods
Abstract
We investigate the computational power of particle methods, a wellestablished class of algorithms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of problems it can solve. Automata theory allows describing the computational power of abstract machines (automata) and the problems they can solve. At the top of the Chomsky hierarchy of formal languages and grammars are Turing machines, which resemble the concept on which most modern computers are built. Although particle methods can be interpreted as automata based on their formal definition, their computational power has so far not been studied. We address this by analyzing Turing completeness of particle methods. In particular, we prove two sets of restrictions under which a particle method is still Turing powerful, and we show when it loses Turing powerfulness. This contributes to understanding the theoretical foundations of particle methods and provides insight into the powerfulness of computer simulations.
 Publication:

arXiv eprints
 Pub Date:
 April 2023
 DOI:
 10.48550/arXiv.2304.10286
 arXiv:
 arXiv:2304.10286
 Bibcode:
 2023arXiv230410286P
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 Mathematics  Numerical Analysis
 EPrint:
 16 pages, 24 appendix pages