Scalable Parallel Fluid Simulation Based On The Schur Complement Method

Nowadays,fluid simulation is widely used in the game and film industry.Film industry's requirements for fluid simulation with high resolution are increasing.The projection step is the most expensive step in fluid simulation and the Poisson equation is the most expensive part to be solved in the projection step.If we can reduce the time consumption of the Poisson equation with the same accuracy,the fluid simulation will be accelerated a lot and the work expense in visual effects will be saved as well.We present an algorithmically efficient and parallelized domain decomposition based approach to solving Poisson equation on irregular domains.On the basis of the Schur complement idea,the preconditioned conjugate gradient method is leveraged to solve the Schur system.We create a novel pre-conditioner for Schur complement method which achieves faster convergence,and uses less memory and computation time.Our domain decomposition approach permits a high degree of parallel efficiency on multi-core systems.What's more,our solver allows the employment of different linear solvers for each subdomain and we use the FFT-based fast Poisson solver on regular subdomains,which will also save the consumption of memory and computation time.Our solver is designed for parallel execution both on shared-memory platform and distributed system.With the system,the Poisson equation can be solved with high parallel efficiency and much less computation time.Our solver solves the test Poisson system with 512~3 voxels and the system with 1024~3 voxels accurately.We draw the graphs of the test result,including the runtime of different solvers,including the speedup compared with the original incomplete Cholesky factorization preconditioned conjugate gradient method,the speedup over different cores and the parallel efficiency of each solver.Our solver is also used for the pressure projection step of grid based fluid simulations.With the test for different fluid simulation scenes,we show the efficiency of our solver for the fluid simulation without importing any visual effects.Our results demonstrate considerable speedup over preconditioned conjugate gradient methods commonly employed to solve such problems,including multi-grid preconditioned conjugate gradient method.