The Development And Appliance Of High Performance Linear Solver Of PETSC

High performance toolkit for scientific computating is the essential part of large scale scientific and engineering computing.It promotes both the programming efficiency and the performance of numerical programme.The contents of this paper are including:First,this paper studies the disigning key of computing toolkit and the methods of implementing high performance.And then,from many toolkits for scientific computing,we choose Portable,Extensible Toolkit for Scientific Computation(PETSC)as the prototype for development.Second,by changing the computation sequence in the GMRES algorithm,we propose a modified Generalized Minimum Residual Method(MGMRES)algorithm.The numerical stability of MGMRES algorithm is the same as GMRES algorithm,but the synchronization overhead that represents the bottleneck of the parallel performance is effectively reduced by a factor of two.And all inner products of a single iteration step are independent and communication time required for inner product can be overlapped efficiently with computation time of vector updates.From the theoretical analysis it is found that MGMRES algorithm is faster than GMRES algorithm as the number of processors increases.Then,in order to enhance the parallel performance of PETSC,we integrate the proposed Modified Generalized Conjugate Residual and Modified Conjugated Gradient Squared(MCGS)by Kevin J.Webb and Howard Jay Siegel with PETSC as its solvers.Finally,experimental analyses is performed on PETSC to investigate the impact of this modification on the overall execution time by solving a Laplacian Equation.The result indicates that MGMRES and MCGS are approximately 30%faster than GCR and CGS on an 8-processor cluster.