Corey Wetterer-Nelson

arXiv2023

Stabilized Isogeometric Collocation Methods For Scalar Transport and Incompressible Fluid Flow

In this work we adapt classical residual-based stabilization techniques to the spline collocation setting. Inspired by the Streamline-Upwind-Petrov-Galerkin and Pressure-Stabilizing-Petrov-Galerkin methods, our stabilized collocation schemes address spurious oscillations that can arise from advection and pressure instabilities. Numerical examples for the advection-diffusion equation, Stokes equations, and incompressible Navier-Stokes equations show the effectiveness of the proposed stabilized schemes while maintaining the high-order convergence rates and accuracy of standard isogeometric collocation on smooth problems.

math.NA↗

arXiv2021

Interactive Geometry Modification of High Performance Finite Element Simulations

In the context of high performance finite element analysis, the cost of iteratively modifying a computational domain via re-meshing and restarting the analysis becomes time prohibitive as the size of simulations increases. In this paper, we demonstrate a new interactive simulation pipeline targeting high performance finite element simulations where the computational domain is modifiable in situ, that is, while the simulation is ongoing. This pipeline is designed to be modular so that it may interface with any existing finite element simulation framework. A server-client architecture is employed to manage simulation mesh data existing on a high performance computing resource while user-prescribed freeform geometric modifications take place on a separate workstation. We employ existing in situ visualization techniques to rapidly inform the user of simulation progression, enabling computational steering. By expressing the simulation domain in a reduced fashion on the client application, this pipeline manages highly refined finite element simulation domains on the server while maintaining good performance on the client application.

cs.CE↗