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Although some existing Remote Procedure Call (RPC) systems provide support for remote invocation of parallel applications, these RPC systems lack powerful scheduling methodologies for the dynamic selection of resources for the execution of parallel applications. Some RPC systems support parallel execution of software routines with simple modes of parallelism. Some RPC systems statically choose the configuration of resources for parallel execution even before the parallel routines are invoked remotely by the end user. These policies of the existing systems prevent them from being used for remotely solving computationally intensive parallel applications over dynamic computational Grid environments. In this paper, we discuss a RPC system called GrADSolve that supports execution of parallel applications over Grid resources. In GrADSolve, the resources used for the execution of parallel application are chosen dynamically based on the load characteristics of the resources and the characteristics of the application. Application-level scheduling is employed for taking into account both the application and resource properties. GrADSolve also stages the user's data to the end resources based on the data distribution used by the end application. Finally, GrADSolve allows the users to store execution traces for problem solving and use the traces for subsequent solutions. Experiments are presented to prove that GrADSolve's data staging mechanisms can significantly reduce the overhead associated with data movement in current RPC systems. Results are also presented to demonstrate the usefulness of utilizing the execution traces maintained by GrADSolve for problem solving.