# ON THE DEVELOPMENT OF A REDUCED APPROACH TO THE RE- CURSIVE COORDINATE BISECTION IN THE CONTEXT OF PARAL- LEL SIMULATIONS OF THE MATERIAL POINT METHOD

## Palavras-chave:

Parallel Computing, Message Passing Interface, Material Point Method, Recursive Coordinate Bisection, Computational Statistics## Resumo

This paper aims to develop a reduced approach to the Recursive Coordinate Bisection (RCB) in the

context of parallel simulations of the Material Point Method (MPM). The simulation environment considers the

usage of parallel computing, a powerful tool that allows us to increase computational performance and to reduce

the simulation time. In this environment, a set of computers provides processors, allocates processes and commu-

nicates data among them. MPM can be used to simulate various engineering problems, including those involving

submarine landslides, installation of torpedo anchors and dynamical analysis of structures. Numerical simulations

of MPM can be computationally intensive, especially for those containing a large number of particles. In this work,

the geometrical information of particles inside each solution sub-domain is reduced into statistical information of

centroid and standard deviation in order to avoid excessive data communication during simulations. The root pro-

cess simulates the entire domain geometry from the collected data for each sub-domain. The partitioning algorithm

and statistical strategy were developed using the C++ language and the Message Passing Interface (MPI) library.

The MPI library allows the exchange of data among the several processors in a distributed memory system. The

partitioning quality obtained in this method depending on input parameters such as the number of processes, the

mesh discretization for each sub-domain and the number of points generated in the statistical domain. Numerical

experiments were conducted in order to measure a load balance metric and the processing time (speed up). The

obtained values for the parametric study were compared to an analytical reference of balance. The results show that

the partitioning method generates better load balance values depending on the combination of the input parameters.