On well-separated sets and fast multipole methods

• Autores: Stefan Engblom
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 61, Nº. 10, 2011, págs. 1096-1102
• Idioma: inglés
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• Resumen

  • The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more liberal than in conventional codes. Such variants offer a particularly elegant implementation with a balanced multipole tree, a feature which might be very favorable on modern computer architectures.