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A reconfigurable mesh consists of a mesh-connected topology augmented by a dynamically reconfigurable bus system. Efficient utilization of processing resources in a large, multiuser parallel system depends on the reliable processor management scheme. We present a dynamic and reliable processor allocation strategy to increase the performance of mesh-connected parallel systems with faulty processors. The idea is to reconfigure a faulty mesh system into a maximum convex system using the fault-free boundary nodes to compensate for the nonboundary faulty nodes. To utilize the nonrectangular shaped system parts, our strategy tries to allocate L-shaped submeshes instead of signaling the allocation failure. Extensive simulations show that the strategy performs more efficiently than other strategies in terms of the completion time, the job response time and the system utilization.