Interactive visualisation of spins and clusters in regular and small-world Ising models with CUDA on GPUs

Abstract Three-dimensional simulation models are hard to visualise for dense lattice systems, even with cutaways and flythrough techniques. We use multiple Graphics Processing Units (GPUs), CUDA and OpenGL to increase our understanding of computational simulation models such as the 2-D and 3-D Ising systems with small-world link rewiring by accelerating both the simulation and visualisation into interactive time. We show how interactive model parameter updates, visual overlaying of measurements and graticules, cluster labelling and other visual highlighting cues enhance user intuition of the model’s meaning and exploit the enhanced simulation speed to handle model systems large enough to explore multi-scale phenomena.

[1]  Thomas Ertl,et al.  Computer Graphics - Principles and Practice, 3rd Edition , 2014 .

[2]  Daniel Gooch,et al.  Communications of the ACM , 2011, XRDS.

[3]  M. Carter.  Computer graphics: Principles and practice , 1997 .

[4]  Martin Rumpf,et al.  Nonlinear Diffusion in Graphics Hardware , 2001, VisSym.

[5]  E. Ising.  Beitrag zur Theorie des Ferromagnetismus , 1925 .

[6]  Pat Hanrahan,et al.  Volume Rendering , 2020, Definitions.

[7]  L. Smarr,et al.  Metacomputing : Siggraph'92 Showcase , 1992 .

[8]  Ivan Poupyrev,et al.  A framework and testbed for studying manipulation techniques for immersive VR , 1997, VRST '97.

[9]  Haim Levkowitz,et al.  Proceedings of the 1992 workshop on Volume visualization , 1992, VVS.

[10]  Kenneth A. Hawick,et al.  Visualising Vector Field Model Simulations , 2009, MSV.

[11]  Greg Humphreys,et al.  A multigrid solver for boundary value problems using programmable graphics hardware , 2003, HWWS '03.

[12]  Jason Lee,et al.  Using High-Speed WANs and Network Data Caches to Enable Remote and Distributed Visualization , 2000, ACM/IEEE SC 2000 Conference (SC'00).

[13]  Mathias Schott,et al.  A Directional Occlusion Shading Model for Interactive Direct Volume Rendering , 2009, Comput. Graph. Forum.

[14]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[15]  Alvy Ray Smith,et al.  3-D transformations of images in scanline order , 1980, SIGGRAPH '80.

[16]  Philip K. Robertson,et al.  Interactive shading for surface and volume visualization on graphics workstations , 1993, Proceedings Visualization '93.

[17]  Wolff,et al.  Collective Monte Carlo updating for spin systems. , 1989, Physical review letters.

[18]  Ren Ng,et al.  Real-Time Programmable Volume Rendering , 2002 .

[19]  鈴木 増雄.  Time-Dependent Statistics of the Ising Model , 1965 .

[20]  Louis Turcotte,et al.  Proceedings of the 2000 ACM/IEEE conference on Supercomputing , 2000 .

[21]  Tobias Ritschel.  Fast GPU-based Visibility Computation for Natural Illumination of Volume Data Sets , 2007, Eurographics.

[22]  Kenneth A. Hawick,et al.  Regular Lattice and Small-World Spin Model Simulations Using CUDA and GPUs , 2010, International Journal of Parallel Programming.

[23]  U. Wolff.  Comparison Between Cluster Monte Carlo Algorithms in the Ising Model , 1989 .

[24]  Ross T. Whitaker,et al.  Feasibility of GPU-assisted iterative image reconstruction for mobile C-arm CT , 2009, Medical Imaging.

[25]  Johanna Beyer,et al.  GPU-based Multi-Volume Rendering of Complex Data in Neuroscience and Neurosurgery , 2011 .

[26]  Michael John Flynn.  Medical Imaging 2005: Physics of Medical Imaging , 2001 .

[27]  Stefan Bruckner,et al.  Enhancing Depth-Perception with Flexible Volumetric Halos , 2007, IEEE Transactions on Visualization and Computer Graphics.

[28]  Philip K. Robertson,et al.  Volume rendering on the MasPar MP-1 , 1992, VVS.

[29]  Christopher R. Johnson,et al.  A framework for exploring numerical solutions of advection–reaction–diffusion equations using a GPU-based approach , 2009 .

[30]  Robert Michael Kirby,et al.  Display of vector fields using a reaction-diffusion model , 2004, IEEE Visualization 2004.

[31]  Ross T. Whitaker,et al.  Topology, Accuracy, and Quality of Isosurface Meshes Using Dynamic Particles , 2007, IEEE Transactions on Visualization and Computer Graphics.

[32]  Stefan Friedrich,et al.  Topology , 2019, Arch. Formal Proofs.