To conduct a patient-specific computational modeling of the aortic valve, 3D aortic valve anatomic geometries of an individual patient need to be reconstructed from clinical 3D cardiac images. Currently, most of computational studies involve manual heart valve geometry reconstruction and manual FE model generation, which is both time-consuming and prone to human errors. A seamless computational modeling framework, which can automate this process based on machine learning algorithms, is desirable, as it can not only eliminate human errors and ensure the consistency of the modeling results, but also allows fast feedback to clinicians and permits a future population-based probabilistic analysis of large patient cohorts. In this study, we developed a novel computational modeling method to automatically reconstruct the 3D geometries of the aortic valve from CT images. The reconstructed valve geometries have built-in mesh correspondence, which bridges harmonically for the consequent FE modeling. The proposed method was evaluated by comparing the reconstructed geometries from ten patients to those manually created by human experts, and a mean discrepancy of 0.69 mm was obtained. Based on these reconstructed geometries, FE models of valve leaflets were developed, and aortic valve closure from end systole to mid-diastole was simulated for seven patients and validated by comparing the deformed geometries to those manually created by human experts, and a mean discrepancy of 1.57 mm was obtained. The proposed method offers great potential to streamline the computational modeling process and enables the development of a pre-operative planning system for aortic valve disease diagnosis and treatment.