Parallel geometric multigrid schemes for hermite collocation finite element MethodParallel geometric multigrid schemes for hermite collocation finite element Method Πλήρης Δημοσίευση σε Συνέδριο Conference Full Paper 2015-10-292009enNumerical algorithms with multigrid techniques are among the fastest iterative schemes for solving large and sparse linear systems. In this work, we deal with the problem of efficiently organizing the computation involved in the iterative solution of this type of li- near systems combined with a multigrid technique, in order to compute on a Grid/Cluster computing environment. These linear systems arise from the discretization of elliptic BVPs by the Collo- cation method based on Hermite bi-cubic finite elements. Taking advantage of the Collocation matrix’s red-black ordered structure we organize efficiently the whole computation for the Gauss- Seidel and the preconditioned Bi-CGSTAB iterative methods as multigrid smoothers and map it on a pipeline architecture with master-slave communication. Implementations, through the Mes- sage Passing Interface (MPI) standard, are realized first on a 64-core of a 16-node SUN X2200M2 Grid computer, interconnected through a 1Gbps ethernet network, and then on a Hewlett-Packard Blade ProLiant BL465c Cluster computer. The performance of two parallel algorithms is pre- sented by speedup and time measurements.http://creativecommons.org/licenses/by/4.0/9nd Hellenic-Europeαn Research on Computer Mαthemαtics and its Applications Mathioudakis Emmanouil Μαθιουδακης Εμμανουηλ Mandikas Vasileios Μανδικας Βασιλειος Greek mathematics mathematics greek greek mathematics