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Wednesday, April 24

The Cost of Continuity

Nathan Collier, the King Abdullah University of Science and Technology, Saudi Arabia
Computer Science and Mathematics Division Seminar
11:00 AM — 12:00 PM, Research Office Building (5700), Room L-202
Contact: Richard Mills (rmills@ornl.gov), 865.241.3198

Abstract

Isogeometric analysis is a finite element method which uses the B-spline basis to discretize a Galerkin weak form. Apart from the benefits described in my previous talk (link to geometry and enabling solution to higher-order problems), the B-spline basis has been observed to possess superior approximability per degree of freedom when used to solve partial differential equations with smooth solutions. This has led to the belief that these so called C^k spaces (B-splines) are more efficient than their C0 counterparts (traditional FEM spaces). However, this assertion ignores the fact that linear systems resulting from C^k spaces become more expensive to solve when using both direct and iterative solvers. In this talk, I will introduce both multi-frontal direct and iterative solvers and highlight the features of higher continuous B-splines which cause solvers to become more expensive.

About the Speaker
Dr. Nathan Collier, Research Scientist in the Center for Numerical Porous Media at the King Abdullah University of Science and Technology, Saudi Arabia, will be visiting ORNL next week and presenting two seminars (11:00 a.m. on Tuesday and Wednesday) on his recent work in isogeometric analysis and the development of the open-source package PetIGA, which provides a "thin" layer on top of PETSc that handles parallel assembly of matrices/vectors resulting from discretized weak forms using B-splines.