Parallel multigrid solver of radiative transfer equation for photon transport via graphics processing unit

Area of Science:

• Computational physics
• Numerical analysis
• Scientific computing

Background:

• Radiative transfer equations (RTEs) are crucial for simulating light transport in various media.
• Solving RTEs, especially in heterogeneous media with complex geometries, presents significant computational challenges.
• Existing solvers often lack the efficiency required for large-scale or real-time applications.

Purpose of the Study:

• To develop and present a graphics processing unit (GPU)-based parallel multigrid solver for the radiative transfer equation.
• To handle heterogeneous media with complex geometries using 2D triangular or 3D tetrahedral meshes.
• To achieve significant computational speedups compared to previous methods.

Main Methods:

• Implementation of a parallel multigrid solver leveraging GPU architecture.
• Application of vacuum or reflection boundary conditions.
• Utilizing a full multigrid method to minimize iterative computations.
• Meshing strategies for 2D triangular and 3D tetrahedral discretizations.

Main Results:

• The parallel solver exhibits computational complexity linearly proportional to degrees of freedom in angular and spatial variables.
• Achieved speedup ranges from 30 to 300 times compared to prior multigrid solvers.
• Performance gains are dependent on the specific physical regime and parallelization efficiency.
• Numerical validations are provided via MATLAB codes.

Conclusions:

• The developed GPU-based parallel multigrid solver offers a highly efficient approach for solving radiative transfer equations.
• The method is effective for complex geometries and heterogeneous media, demonstrating substantial performance improvements.
• The availability of MATLAB codes facilitates further research and application of this solver.