On the Parallelization of Meshless Methods for the Solution of the Diffusion Equation

R. Trobec and M. Šterk (Slovenia)


Parallel implementation, computational complexity, meshless method, MLPG, MLM, diffusion equation


Meshless methods are becoming popular for the numerical solution of partial differential equations (PDE), particularly in more complicated domains with moving boundaries. The computational complexity of meshless methods in particular local Petrov-Galerkin method (MLPG) has been analyzed. Parallelization of the MLPG method was implemented with two different approaches to domain decomposition. The measurements of parallel complexity and speed-up indicate that parallel MLPG scales similar to finite elements method (FEM) and remains competitive on larger systems for applications with moving domains and in cases where human assistance is needed for meshing.

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