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Tuesday, April 23
An Introduction to Isogeometric Analysis with
Nathan Collier, King Abdullah University of Science and Technology, Saudi Arabia
Application to Richard's Equation and Gravity Fingering
Computer Science and Mathematics Division Seminar
11:00 AM — 12:00 PM, Research Office Building (5700), Room L-202
Contact: Richard Mills (firstname.lastname@example.org), 865.241.3198
AbstractIsogeometric analysis is a Galerkin finite element method which uses the B-spline, or more generally the NURBS, basis. The NURBS basis has been used in the computer-aided design (CAD) community for decades due to several of its properties. The original motivation of isogeometric analysis was to use CAD geometry descriptions directly in analysis to circumvent the need to mesh in the traditional sense.
This basis spans traditional finite element spaces as well as those which possess higher inter-element continuity. This higher order continuity enables the use of the finite element method on higher-order partial differential equations without the need of mixed forms. In this talk, I will not focus on the geometry benefits of isogeometric analysis so much as novel approaches to partial differential equations which the basis enables.
I will introduce a high-performance software framework for isogeometric analysis, PetIGA. PetIGA can be viewed as a thin layer that sits on top of PETSc and handles the assembly of matrices and vectors which come from weak form, discretized using the B-spline basis. The framework is open source and aims to provide researchers with a simplified interface into high-performance resources.
In the final portion of the talk, I will discuss recent work in extending Richard's equation to capture gravity fingering (Ruben Juanes' group of MIT). Their approach results in a 4th order partial differential equation which can be solved using the salient features of isogeometric analysis.
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.