Multi-frontal parallel direct solver for one dimensional isogeometric collocation method

by

Multi-frontal parallel direct solver for one dimensional isogeometric collocation method

Paweł Lipski, Maciej Paszyński

AGH University of Science and Technology, al. Mickiewicza 30, Krakow, Poland.

DOI:

https://doi.org/10.7494/cmms.2015.1.0522

Abstract:

In this paper we present a new multi-frontal solver for the isogeometric collocation method (ISO-C) on GPU. The ISO-C method constitutes an alternative for the isogeometric finite element method (ISO-FEM). The key advantage of ISO-C over ISO-FEM is that it does not include the computationally intensive operation of integrating the variational formulation. The ISO-C method requires using only a single collocation point per one basis function, whereas in ISOFEM, Gaussian quadrature is applied on many points at each finite element. The presented multi-frontal solver for collocation method results in logarithmic execution time assuming that large enough number of GPU processors is available. In this article, the method is employed for an exemplary 1D nanolithography problem of Step-and-Flash Imprint Lithography (SFIL). The algorithm, however, may be applied to a wide class of 2D and 3D problems.

Cite as:

Lipski, P., & Paszyński, M. (2015). Multi-frontal parallel direct solver for one dimensional isogeometric collocation method. Computer Methods in Materials Science, 15(1), 192-197. https://doi.org/10.7494/cmms.2015.1.0522

Article (PDF):

Keywords:

Step-and-flash imprint litography, Collocation method, Isogeometric analysis, GPU, CUDA

References: