Cayley Transforms in Micromagnetics

dc.contributor.authorKrishnaprasad, Perinkulam S.en_US
dc.contributor.authorTan, Xiaoboen_US
dc.contributor.departmentISRen_US
dc.contributor.departmentCDCSSen_US
dc.date.accessioned2007-05-23T10:11:40Z
dc.date.available2007-05-23T10:11:40Z
dc.date.issued2001en_US
dc.description.abstractMethods of numerical integration of ordinary differential equations exploiting the Cayley transform arise in a variety of contexts, ranging from the classical mid-point rule to symplectic and (almost) Poisson integrators, to numerical methods on Lie Groups. In earlier work, the first author investigated the interplay between the Cayley transform and the Jacobi identity in establishing certain error formulas for the mid-point rule (with applications to coupled rigid bodies). In this paper, we use the Cayley transform to lift the Landau-Lifshitz-Gilbert equation of micromagnetics to the Lie algebra of the group of currents (on a compact magnetic body) with values in the 3-dimensional rotation group. This follows an idea of Arieh Iserles and, we use the lift to numerically integrate the Landau-Lifshitz-Gilbert equation conserving automatically the norm of the magnetization everywhere.en_US
dc.format.extent183999 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/6250
dc.language.isoen_USen_US
dc.relation.ispartofseriesISR; TR 2001-34en_US
dc.relation.ispartofseriesCDCSS; TR 2001-6en_US
dc.subjectSensor-Actuator Networksen_US
dc.titleCayley Transforms in Micromagneticsen_US
dc.typeTechnical Reporten_US

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