Electronic Journal of Differential Equations, Conference 02 (1999), pp. 75-85. Title: Implementing parallel elliptic solver on a Beowulf cluster Authors: Marcin Paprzycki (Univ. of Southern Mississippi, Hattiesburg, MS, USA) Julian Sanchez (Univ. of Southern Mississippi, Hattiesburg, MS, USA) Svetozara Petrova (Bulgarian Academy of Sciences, Sofia, Bulgaria) Abstract: In a recent paper \cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared. Published December 9, 1999. Math Subject Classifications: 65F10, 65N20, 65N30. Key Words: Elliptic solvers; separation of variables; parallel computing; problems with sparse right-hand side.