Many problems in engineering and scientific domains require solving large sparse systems of linear equations, as a computationally intensive step towards the final solution. It has long been a challenge to develop efficient parallel formulations of sparse direct solvers due to several different complex steps involved in the process.\parIn this paper, we describe PSPASES, one of the first efficient, portable, and robust scalable parallel solvers for sparse symmetric positive definite linear sytems that we have developed. We discuss the algorithmic and implementation issues involved in its development; and present performance and scalability results on Cray T3E and SGI Origin 2000. PSPASES could solve the largest sparse system (1 million equations) ever solved by a direct method, with the highest performance (51 GFLOPS for Cholesky factorization) ever reported.

References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Amestoy, Patrick; Ashcraft, Cleve; Boiteau, Olivier; Buttari, Alfredo; L’Excellent, Jean-Yves; Weisbecker, Clément: Improving multifrontal methods by means of block low-rank representations (2015)
  2. da Silva, M. Vicente; Antão, A.N.: Upper bound limit analysis with a parallel mixed finite element formulation (2008)
  3. Grigori, Laura; Demmel, James W.; Li, Xiaoye S.: Parallel symbolic factorization for sparse LU with static pivoting (2007)
  4. Son, Seung Woo; Malkowski, Konrad; Chen, Guilin; Kandemir, Mahmut; Raghavan, Padma: Reducing energy consumption of parallel sparse matrix applications through integrated link/CPU voltage scaling (2007)
  5. Henz, Brian J.; Shires, Dale R.: Parallel finite element software development and performance analysis in an object-oriented programming framework (2005)
  6. Davis, Timothy A.: A column pre-ordering strategy for the unsymmetric-pattern multifrontal method (2004)
  7. Irony, D.; Shklarski, G.; Toledo, S.: Parallel and fully recursive multifrontal supernodal sparse Cholesky (2002)
  8. Li, Xiaoye S.; Martin, Michael C.; Thompson, Brandon J.; Tung, Teresa; Yoo, Daniel J.; Demmel, James W.; Bailey, David H.; Henry, Greg; Hida, Yozo; Iskandar, Jimmy; Kahan, William; Kang, Suh Y.; Kapur, Anil: Design, implementation and testing of extended and mixed precision BLAS (2002)
  9. Rischmüller, Volker; Kurz, Stefan; Rucker, Wolfgang M.: Parallel field computation based on coupling of differential and integral methods (2001)
  10. Acharya, A.; Beaudoin, A.J.: Grain-size effect in viscoplastic polycrystals at moderate strains (2000)
  11. Joshi, Mahesh V.; Karypis, George; Kumar, Vipin; Gupta, Anshul; Gustavson, Fred: PSPASES: Building a high performance scalable parallel direct solver for sparse linear systems (1999)