PARALELIZAÇÃO DA RESOLUÇÃO DE EDPs PELO MÉTODO ...

Abstract
In this work efficient parallel numerical solution of finite-difference discretizations of
partial differential equations (PDEs) with the Hopscotch method is studied. A new technique
for adaptive mesh refinement and dynamic load balance is proposed, and tests are presented
on a distributed computing environment. Despite the many implementations already presented
for the method, some of which employ parallel processing, none of them has used adaptive
mesh refinement with load balance. Thus, in this work a package is built to solve PDEs
discretized by finite differences, with adaptive mesh refinement and load balance. The domain
is divided in subdomains, that are refined and coarsened during the execution. The process of
subdomain refinement change can be chosen by the user, which provides the trigger values. A
partition method that does not seek to minimize the communications is proposed. This method
achieves the balance quickly, resulting in an easy-to-use technique for parallel computers and
problems that frequently change the refinement. Tests are performed using three PDE types,
elliptic, parabolic and hyperbolic. The tests start with a sequential version, proceed with the
parallel version and end-up with the load balanced parallel version. Metrics are defined to
evaluate the package performance.
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