An Optimized Covering Spheroids by Spheres
2020
Alexander Pankratov | Tatiana Romanova | Igor Litvinchev | Jose Antonio Marmolejo-Saucedo
Covering spheroids (ellipsoids of revolution) by different spheres is studied. The research is motivated by packing non-spherical particles arising in natural sciences, e.g., in powder technologies. The concept of an <inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">ε</mi> </semantics> </math> </inline-formula>-cover is introduced as an outer multi-spherical approximation of the spheroid with the proximity <inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">ε</mi> </semantics> </math> </inline-formula>. A fast heuristic algorithm is proposed to construct an optimized <inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">ε</mi> </semantics> </math> </inline-formula>-cover giving a reasonable balance between the value of the proximity parameter <inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">ε</mi> </semantics> </math> </inline-formula> and the number of spheres used. Computational results are provided to demonstrate the efficiency of the approach.
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