다중 색상 알고리즘과 행렬 연산자를 적용한 LU-SGS 기법의 성능 분석

초록

In this study, the performance of lower-upper symmetric Gauss-Seidel(LU-SGS) methods with multi-coloring algorithm and block operator were compared on shared memory parallelism. The LU-SGS scheme is one of the most popular time integration methods in CFD due to its remarkable robustness and convergence performance; however, data dependency has obstructed the application of the shared memory parallelism. To handle this problem, Colored LU-SGS method is introduced, removing data dependency by applying multi-coloring algorithm to unstructured grid. Albeit the multi-coloring algorithm has high concurrency in parallel execution, it may degrade the implicit property of the numerical method and affect convergence efficiency. Colored Block LU-SGS method uses a block operator, which maintains matrix property of the flux Jacobian so that it can improve convergence stability. Numerical experiments were conducted to validate its efficiency and performance compared with the Colored LU-SGS method. The analysis confirmed that the Colored Block LU-SGS method has a greater maximum CFL number and faster convertgence rate with reference to the total iteration number, and computation time.