The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement
Steven L. Liebling
TL;DR
This paper implements a distributed adaptive mesh refinement scheme using MPI for solving the nonlinear sigma model, extending previous work on critical phenomena and validating the approach through tests.
Contribution
It introduces a distributed AMR scheme for the nonlinear sigma model and demonstrates its correctness through comprehensive testing.
Findings
Successful implementation of distributed AMR with MPI
Validation tests confirm the correctness of the model
Extension of previous work on critical phenomena
Abstract
An adaptive mesh refinement (AMR) scheme is implemented in a distributed environment using Message Passing Interface (MPI) to find solutions to the nonlinear sigma model. Previous work studied behavior similar to black hole critical phenomena at the threshold for singularity formation in this flat space model. This work is a follow-up describing extensions to distribute the grid hierarchy and presenting tests showing the correctness of the model.
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