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Interactive High‐Quality Visualization of Higher‐Order Finite Elements
Author(s) -
Üffinger Markus,
Frey Steffen,
Ertl Thomas
Publication year - 2010
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2009.01603.x
Subject(s) - computer science , visualization , resampling , rendering (computer graphics) , discretization , computational science , interactive visualization , discontinuous galerkin method , degree of a polynomial , polynomial , theoretical computer science , computer graphics (images) , algorithm , finite element method , mathematics , data mining , mathematical analysis , physics , thermodynamics
Higher‐order finite element methods have emerged as an important discretization scheme for simulation. They are increasingly used in contemporary numerical solvers, generating a new class of data that must be analyzed by scientists and engineers. Currently available visualization tools for this type of data are either batch oriented or limited to certain cell types and polynomial degrees. Other approaches approximate higher‐order data by resampling resulting in trade‐offs in interactivity and quality. To overcome these limitations, we have developed a distributed visualization system which allows for interactive exploration of non‐conforming unstructured grids, resulting from space‐time discontinuous Galerkin simulations, in which each cell has its own higher‐order polynomial solution. Our system employs GPU‐based raycasting for direct volume rendering of complex grids which feature non‐convex, curvilinear cells with varying polynomial degree. Frequency‐based adaptive sampling accounts for the high variations along rays. For distribution across a GPU cluster, the initial object‐space partitioning is determined by cell characteristics like the polynomial degree and is adapted at runtime by a load balancing mechanism. The performance and utility of our system is evaluated for different aeroacoustic simulations involving the propagation of shock fronts.