The cost of continuity: a study of the performance of isogeometric finite elements using direct solvers

We study the performance of direct solvers on linear systems of equations resulting from isogeometric analysis. The problem of choice is the canonical Laplace equation in three dimensions. From this study we conclude that for a fixed number of unknowns and polynomial degree of approximation, a higher degree of continuity k drastically increases the CPU time and RAM needed to solve the problem when using a direct solver. This paper presents numerical results detailing the phenomenon as well as a theoretical analysis that explains the underlying cause.Fil: Collier, Nathan. King Abdullah University Of Science And Technology;Fil: Pardo, David. Universidad del Pais Vasco - Euskal Herriko Unibertsitatea, Campus Bizkaia;Fil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Paszynski, Maciej. Agh University Of Science And Technology;Fil: Calo, V.M.. King Abdullah University Of Science And Technology