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A finite element method based three-dimensional heat transfer model with adaptive remeshing is presented to simulate the building of multiple tracks and layers in laser powder bed fusion of metallic powders with enhanced computational competence. A dimensional analysis is undertaken to define the heat source dimensions as function of laser parameters and properties of alloy powder. The computational model is used to calculate the melt pool cross sections for multiple combinations of laser power and scanning velocities considering multi-track-multi-layer builds of SS316L powder. The computed results are verified extensively with the corresponding experimentally measured ones. The model is utilized further to examine its ability to predict defects such as melt track discontinuity and incomplete fusion between neighboring tracks and layers. Overall, the adaptive remeshing and the proposed heat source expression could significantly enhance the model competence by reducing the computational time and memory while maintaining the accuracy of results in simulating laser powder bed fusion of multiple tracks and layers.