This paper presents an adaptive non-rigid registration method for aligning pre-operative MRI with intra-operative MRI (iMRI) to compensate for brain deformation during brain tumor resection. This method extends a successful existing Physics-Based Non-Rigid Registration (PBNRR) technique implemented in ITKv4.5. The new method relies on a parallel adaptive heterogeneous biomechanical Finite Element (FE) model for tissue/tumor removal depicted in the iMRI. In contrast the existing PBNRR in ITK relies on homogeneous static FE model designed for brain shift only (i.e., it is not designed to handle brain tumor resection). As a result, the new method (1) accurately captures the intra-operative deformations associated with the tissue removal due to tumor resection and (2) reduces the end-to-end execution time to within the time constraints imposed by the neurosurgical procedure. The evaluation of the new method is based on 14 clinical cases with: (i) brain shift only (seven cases), (ii) partial tumor resection (two cases), and (iii) complete tumor resection (five cases). The new adaptive method can reduce the alignment error up to seven and five times compared to a rigid and ITK's PBNRR registration methods, respectively. On average, the alignment error of the new method is reduced by 9.23 and 5.63 mm compared to the alignment error from the rigid and PBNRR method implemented in ITK. Moreover, the total execution time for all the case studies is about 1 min or less in a Linux Dell workstation with 12 Intel Xeon 3.47 GHz CPU cores and 96 GB of RAM.