Iterative solution of elliptic collocation systems on a cognitive parallel computerIterative solution of elliptic collocation systems on a cognitive parallel computer Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-292004enThe performance of parallel algorithms implementing the block SOR iterative method, used for the solution of linear systems arising from the discretization of elliptic BVPs by the finite element collocation method, is investigated in this paper. By making use of a recently introduced block tridiagonal partitioning of the collocation matrix, which yields faster rates of convergence, and its associated modified red-black ordering of unknowns and equations, we succeeded to increase the scalability of the problem. The study of the communicational and computational needs of the problem on a virtual parallel machine made possible the mapping of the resulted SOR-algorithm on a fixed size distributed memory parallel system, utilizing a simple pipeline architecture among its processors, in an optimum way. The proposed parallel schemes are being realized on a Parsytec cognitive computer via an SPMD programming model. Speedup measurements are used to reveal the efficiency of our implementation.http://creativecommons.org/licenses/by/4.0/Computers and Mathematics with Applications5-648951-970 Mathioudakis Emmanouil Μαθιουδακης Εμμανουηλ Papadopoulou Eleni Παπαδοπουλου Ελενη Saridakis Ioannis Σαριδακης Ιωαννης Elsevier Automatic computers Automatic data processors Computer hardware Computing machines (Computers) Electronic brains Electronic calculating-machines Electronic computers Hardware, Computer computers automatic computers automatic data processors computer hardware computing machines computers electronic brains electronic calculating machines electronic computers hardware computer