With the introduction of the Adaptive Intelligence Engine (AIE), the Versal Adaptive Compute Acceleration Platform (Versal ACAP) has garnered great attention. However, the current focus of Vitis Libraries and limited research has mainly been on how to invoke AIE modules, without delving into a thorough discussion on effectively utilizing AIE in its typical use cases. As a result, the widespread adoption of Versal ACAP has been restricted. The Communication Avoidance (CA) algorithm is considered a typical application within the AIE architecture. Nevertheless, the effective utilization of AIE in CA applications remains an area that requires further exploration. We propose a top-down customized design framework, EA4RCA (Efficient AIE accelerator design framework for regular Communication-Avoiding Algorithm), specifically tailored for CA algorithms with regular communication patterns, and equipped with AIE Graph Code Generator software to accelerate the AIE design process. The primary objective of this framework is to maximize the performance of AIE while incorporating high-speed data streaming services. Experiments show that for the RCA algorithm Filter2D and Matrix Multiple (MM) with lower communication requirements and the RCA algorithm FFT with higher communication requirements, the accelerators implemented by the RA4RCA framework achieve the highest throughput improvements of 22.19×, 1.05×, and 3.88× compared with the current highest performance acceleration scheme (SOTA), and the highest energy efficiency improvements of 6.11×, 1.30× and 7.00×.