Parallel Solution to the Radiative Transport Szirmay-Kalos László

Parallel Solution to the Radiative Transport

• Szirmay-Kalos László

• Liktor Gábor

• Tamás Umenhoffer

• Tóth Balázs

• Glenn Lupton

• Kumar Shree

Overview

• Radiative transport

• Challenges of parallel iteration

• Our approach

• Initial estimation
• Modified iteration
• FCC GRID
• CUDA

• Results

Radiative transport

Solution methods

• Monte-Carlo simulation

• O(m -0.5)
• Parallelization is trivial

• Iteration

• O(m)
• Parallelization is a challenge

Iteration

• Finite-element approaches (grid)

• Iteratively refines the estimation

• Error depends on the initial guess

Parallel Iteration

• Costly data exchanges

• Less frequent data exchanges

• Few iteration steps: Good initial guess

• Unscattered component
• Homogeneous solution
• Approximate inhomogeneous

Initial approximation

• Direct term

• Direct + Indirect

• Solve diff. equation for each ray assuming spherical symmetry

Reduced data exchanges

Iteration solution: CUDA

Iteration solution: CUDA

Iteration solution: CUDA

Iteration solution: CUDA

Iteration solution: CUDA

Scalability

Results

Conclusions

• Interactive solution of the radiation transport

• Scalable iteration scheme

• Current limitations

• No specular reflections
• Point sources