BACKGROUND: Abdominal multi-organ segmentation remains a challenging task. Semi-supervised domain adaptation (SSDA) has emerged as an innovative solution. However, SSDA frameworks based on UNet struggle to capture multi-scale and global information. PURPOSE: Our work aimed to propose a novel SSDA method to achieve more accurate abdominal multi-organ segmentation with limited labeled target domain data, which has a superior ability to capture the multi-scale features and integrate local and global information effectively. METHODS: The proposed network is based on UNet. In the encoder part, a scale-aware with domain-specific batch normalization (SAD) module is integrated to adaptively extract multi-scale features and to get better generalization across source and target domains. In the bottleneck part, a global-local fusion (GLF) module is utilized for capturing and integrating both local and global information. They are integrated into the framework of self-ensembling mean-teacher (SE-MT) to enhance the model's capability to learn common features across source and target domains. RESULTS: To validate the performance of the proposed model, we evaluated it on the public CHAOS and BTCV datasets. For CHAOS, the proposed method obtains an average DSC of 88.97% and ASD of 1.12 mm with only 20% labeled target data. For BTCV, it achieves an average DSC of 88.95% and ASD of 1.13 mm with 20% labeled target data. Compared with the state-of-the-art methods, DSC and ASD increased by at least 0.72% and 0.33 mm on CHAOS, 1.29% and 0.06 mm on BTCV, respectively. Ablation studies were also conducted to verify the contribution of each component of the model. The proposed method achieves a DSC improvement of 3.17% over the baseline with 20% labeled target data. CONCLUSION: The proposed SSDA method for abdominal multi-organ segmentation has a powerful ability to extract multi-scale and more global features, significantly improving segmentation accuracy and robustness.