PETSc-NURBS: Parallel, High Performance Isogeometric Analysis Implemented Using PETSc

LISANDRO DALCIN; NATHAN COLLIER; MATTHEW KNEPLEY; ARON AHMADIA; DAN LECOCQ; VICTOR CALO

Minneapolis

Congreso; 11th US National Congress on Computational Mechanics; 2011

  This talk presents an implementation of single patchNURBS-based isogeometric analysis implemented using the Portable,Extensible Toolkit for Scientific Computation (PETSc). We dependheavily on PETSc’s data structures for communication,solvers (linear and nonlinear), as well as timesteppers (including the Generalized-α method).  We take advantageof the NURBS parameter space being a regular grid to definesimple com- munication using PETSc data structures. Thiscommunication does not require the geometric data to bepre-partitioned. The partitioning of data is handled internallyby PETSc, drastically reducing the barrier to writing new codesand solving new problems. The tensor product nature of the basisis also exploited by precomputation of one dimensional basisfunctions and derivatives. The multidimensional assembly occursat the element assembly level.  We have the ability to work in aparametric mode, that is, where the parameter space is also thegeometry as well as isoparametric mode, when the geometry ismapped. Furthermore, excessive computation is avoided by enablinga B-spline mode which should be used anytime the NURBS weights ina problem are equal over the entire mesh. Periodic domains can betrivially handled by the implementation of the periodic knotvector. In place of using open knot vectors and enforcingperiodic boundary conditions, the functions spaces are designedto be periodic.  We have implemented several different weak formsin 1, 2, and 3D inlcuding: Laplace, Helmholtz, Cahn-Hilliard,Linear Elasticity, Shallow Water Equations, Diffusive WaveApprox- imation to Shallow Water Equations. Extending the code tosolution of different weak forms from the provided examplesrequires only minimal changes to a single routine within ourframe- work.  We have also created a NURBS plugin for VisIt,which enables native reading of NURBS geometries and fields forfast visualization. This too is part of the effort to minimizethe amount of output required from the scientific code and takeadvantage of tools already created in the visualizationcommunity.  We present numerical results generated from thisseries of codes as well as performance on a variety of hardware,including laptops, workstations and super computers. Our code isfreely available and under active development. We hope tointroduce simplified boundary condition enforcement, support formultiple patches, and geometric multigrid.