Field Programmable Gate Arrays (FPGAs) have proven their potential in accelerating High Performance Computing (HPC) Applications. Conventionally such accelerators predominantly use, FPGAs that contain fine-grained elements such as LookUp Tables (LUTs), Switch Blocks (SB) and Connection Blocks (CB) as basic programmable logic blocks. However, the conventional implementation suffers from high reconfiguration and development costs. In order to solve this problem, programmable logic components are defined at a virtual higher abstraction level. These components are called Processing Elements (PEs) and the group of PEs along with the inter-connection network form an architecture called a Virtual Coarse-Grained Reconfigurable Array (VCGRA). The abstraction helps to reconfigure the PEs faster at the intermediate level than at the lower-level of an FPGA. Conventional VCGRA implementations (built on top of the lower levels of the FPGA) use functional resources such as LUTs to establish required connections (intra-connect) within a PE. In this paper, we propose to use the parameterized reconfiguration technique to implement the intra-connections of each PE with the aim to reduce the FPGA resource utilization (LUTs). The technique is used to parameterize the intra-connections with parameters that only change their value infrequently (whenever a new VCGRA function has to be reconfigured) and that are implemented as constants. Since the design is optimized for these constants at every moment in time, this reduces the resource utilization. Further, interconnections (network between the multiple PEs) of the VCGRA grid can also be parameterized so that both the inter- and intraconnect network of the VCGRA grid can be mapped onto the physical switch blocks of the FPGA. For every change in parameter values a specialized bitstream is generated on the fly and the FPGA is reconfigured using the parameterized run-time reconfiguration technique. Our results show a drastic reduction in FPGA LUT resource utilization in the PE by at least 30% and in the intra-network of the PE by 31% when implementing an HPC application.