Extreme Ultraviolet Lithography (EUVL) is one of the most promising Next Generation Lithography (NGL) technologies. Due to the surface roughness of the optical system used in EUVL, the rather high level of flare (i.e., scattered light) becomes one of the most critical issues in EUVL. In addition, the layout density nonuniformity and the flare periphery effect (the flare distribution at the periphery is much different from that in the center of a chip) also induce a large flare variation within a layout. Both of the high flare level and the large flare variation could worsen the control of critical dimension (CD) uniformity. Dummification (i.e., tiling or dummy fill) is one of the flare compensation strategies to reduce the flare level and the flare variation for the process with a clear-field mask in EUVL. However, existing dummy fill algorithms for Chemical-Mechanical Polishing (CMP) are not adequate for the flare mitigation problem in EUVL due to the flare periphery effect. This paper presents the first work that solves the flare mitigation problem in EUVL with a specific dummification algorithm flow considering global flare distribution. The dummification process is guided by dummy demand maps, which are generated by using a quasi-inverse lithography technique. In addition, an error-controlled fast flare map computation technique is proposed and integrated into our algorithm to further improve the efficiency without loss of computation accuracy. Experimental results show that our flow can effectively and efficiently reduce the flare level and the flare variation, which may contribute to the better control of CD uniformity.