A processing system with multiple field programmable gate array (FPGA) cards is described. Each FPGA card can interconnect using six I/O (up, down, left, right, front, and back) terminals. The communication network among FPGAs is scalable according to user design. When the system operates multi-dimensional applications, transmission efficiency among FPGA improved through user-adjusted dimensionality and network topologies for different applications. We provide a fast and flexible circuit configuration method for FPGAs of a multi-dimensional FPGA array. To demonstrate the effectiveness of the proposed method, we assess performance and power consumption of a circuit that calculated 3D Poisson equations using the finite difference method.