User-Directed Hybrid Deterministic and Monte Carlo Parallel Light Transport Algorithms

这个项目将研究可扩展的并行算法，用于求解复杂表面几何组成的环境中的光传输平衡方程。虽然蒙特卡罗方法可以在输入几何形状复杂(例如，1亿个曲面)时求解此类平衡方程，但其收敛速度很慢。为了克服这一局限性，将使用有限元算法来粗略地描述环境中的光流，并将这些大尺度信息用于指导蒙特卡罗算法的采样策略。由于光学系统的设计者通常知道系统中发生大能量流的位置，因此将使用3D计算机图形控制前端来帮助指导有限元阶段的细分和蒙特卡罗阶段的采样策略。尽管正在进行的研究试图改进光传输问题的解决方案，但确定性方法、蒙特卡罗方法和人工辅助方法的优势的系统组合可以应用于通常使用蒙特卡罗方法的许多高维问题。

This project will investigate scalable parallel algorithms for the solution of light transport balance equations for environments composed of complex surface geometry. Although Monte Carlo methods can solve such balance equations when the input geometry is complex (e.g., 100 million surfaces), their convergence is slow. To overcome this limitation, finite element algorithms will be used to roughly characterize the light flow in the environment, and this large-scale information will be used to guide the sampling strategies of the Monte Carlo algorithms. Because designers of optical systems typically know where the large energy flow occurs in their systems, a 3D computer graphics steering front-end will be used to help guide both the subdivision in the finite element phase, and the sampling strategies of the Monte Carlo phase. Although the research being conducted attempts to improve solutions to the light transport problem, the systematic combination of the strengths of deterministic, Monte Carlo, and human-assisted methods could have applications in many high-dimensional problems where Monte Carlo methods are typically used.