RUDN mathematician boosted domain decomposition method for asynchronous parallel computing

RUDN mathematician boosted domain decomposition method for asynchronous parallel computing

RUDN University mathematician and his colleagues from France and Hungary developed an algorithm for parallel computing, which allows solving applied problems, such as electrodynamics or hydrodynamics. The gain in time is up to 50%. The results are published in the Journal of Computational and Applied Mathematics.

Parallel computing methods are often used to process practical problems in physics, engineering, biology, and other fields. It involves several processors joined in a net to simultaneously solve a single problem -- each has its own small part. The way to distribute the work between the processors and make them "communicate" with each other is a choice based on the specifics of a particular problem. One possible method is domain decomposition. The study domain is divided into separate parts -- subdomains -- according to the number of processors. When that number is very high, especially in heterogeneous high-performance computing (HPC) environments, asynchronous processes constitute a valuable ingredient. Usually, Schwarz methods are used, in which the subdomains overlap each other. This provides accurate results but does not suit when overlap is not straightforward. RUDN University Mathematician and his colleagues from France and Hungary proposed a new algorithm that makes the asynchronous decomposition easier in many structural cases -- the subdomains do not overlap; the result remains accurate with less time needed for computation.

"Until now, almost all investigations of asynchronous iterations within domain decomposition frameworks targeted methods of the parallel Schwarz type. A first, and sole, attempt to deal with primal nonoverlapping decomposition resulted in simultaneously iterating on the subdomains and on the interface between them. That means that computation scheme is defined on the whole global domain", Guillaume Gbikpi-Benissan, Engineering Academy of RUDN University.

Mathematicians proposed an algorithm based on the Gauss-Seidel method. The essence of the innovation is that the calculation algorithm is not run simultaneously on the entire domain, but alternately on the subdomains and the boundaries between them. As a result, the values obtained during each iteration within the subdomain can be immediately used for calculations on the boundary at no additional cost.

Mathematicians tested the new algorithm on the Poisson equation and the linear elasticity problem. The first one is used, for example, to describe the electrostatic field, the second one is used in hydrodynamics, to describe the motion of liquids. The new method was faster than the original one for both equations. A gain of up to 50% was indeed achieved -- with 720 subdomains, the computation of the Poisson equation took 84 seconds while the original algorithm spent 170 seconds. Moreover, the number of synchronous alternating iterations decreases with an increase in the number of subdomains.

"It is a quite interesting behavior which can be explained by the fact that the ratio of alternation increases as the subdomains sizes are reduced and more of interface appears. This work therefore encourages for further possibilities and new promising investigations of the asynchronous computing paradigm", Guillaume Gbikpi-Benissan, Engineering Academy of RUDN University.

All news
30 Jan
RUDN University Chemists Create Substances for Supramolecules Self-assembly

RUDN University chemists derived molecules that can assemble into complex structures using chlorine and bromine halogen atoms. They bind to each other as “velcro” — chlorine “sticks” to bromine, and vice versa. As a result supramolecules are assembled from individual molecules. The obtained substances will help to create supramolecules with catalytic, luminescent, conducting properties.

20 Jan
RUDN University chemist creates nanocatalysts for vanillin synthesis

RUDN University chemist proposed a new method to create catalysts on a porous silicon matrix with metal nanoparticles. Efficient catalysts for organic reactions are obtained, for example, for the synthesis of vanillin, which is in demand in the food and perfume industry.

16 Jan
RUDN University Linguist: Intimidation and Military Rhetoric in the Media during the Pandemic Make People Pessimistic

When talking about COVID-19, television, newspapers, magazines, and social media turn to battle metaphors that make the fight against the pandemic feel like a war. Also, the coronavirus is often discussed in an excessively alarming and threatening tone. This problem is so acute that there is even the term for that — infodemia. It describes the panic in the media and social networks. A linguist of RUDN University studied how such a language affects the notions of people regarding COVID-19.