Figure 1

The desire to optimize the size and shape of the melt pool is reduced to a problem of tracking maximum temperatures on paths. (a) Temperature distribution due to a moving beam. (b) Maximum temperature obtained during melting, with the solidified volume highlighted. (c) Introduction of beam path \(\mathcal{C}^{\mathrm{s}}\) and secondary path \(\mathcal{C}^{\mathrm{wd}}\). The secondary path is drawn along the desired liquid-solid interface. (d) Maximum temperature after optimization, with the solidified volume highlighted. The shape of this volume is optimized due to the tracking of reference temperatures \(u_{\mathrm{surf}}\) and \(u_{\mathrm{melt}}\) on \(\mathcal{C}^{\mathrm{s}}\) and \(\mathcal{C}^{\mathrm{wd}}\), respectively.