arXiv:2610.33273v1 Announce Type: new Abstract: Hybrid analytical--finite-element methods support scan-resolved, part-scale thermal simulation of laser powder bed fusion, but their analytical evaluation cost grows as scan-line contributions accumulate. This work develops a space--time localized hybrid formulation that restricts where and how long each contribution is evaluated analytically. Residual terms and boundary conditions derived from the heat equation allow the finite-element correction to account for the thermal effect of contributions removed from the analytical field. The formulation is assessed using a single-line benchmark against an independent full finite-element solution and multiline comparisons with the conventional hybrid formulation. Localization limits the number of analytical contributions retained while maintaining close agreement with the conventional solution. A comparison with uncompensated temporal truncation demonstrates the importance of the residual correction in retaining the thermal effect of removed contributions. In the 500-line case, analytical and total simulation times are reduced by factors of approximately 25.5 and 3.92, respectively, with a relative nodal 2-norm difference of 0.139%.
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