Recent progress in switch-based high-speed Local Area Networks (LANs) makes distributed network computing promising. Three evolving switch-based high-speed networks are the High Performance Parallel Interface (HIPPI), Fiber Channel (FC), and Asynchronous Transfer Mode (ATM) standards. In this paper, we study how high-performance computing can be carried out over such networks. High-performance computing can be characterized as follows: (1) It includes multiple modules and each module is executed in a processor, (2) Its communication data flow forms a special application topology and usually such application topologies are regular, and (3) It requires frequent communication between adjacent modules in the application topology. Two traditional network protocols which allow processors to communicate in switch-based networks are circuit switching and packet switching. In order to reduce the amount of time required for a processor to set up a connection during the execution of an application, we propose a new communication protocol called the Virtual Permanent Connection (VPC). For a given application topology, a set of connections are set up and permanently maintained during the execution of the application. Communication between processors are via this group of connections. In this paper, we study how a set of VPCs are chosen based on a given application topology (this process is called an Application Topology Embedding). We also study and compare the performance of circuit switching, packet switching and the proposed VPC approach.