SPIKE: A parallel environment for solving banded linear systems. The hybrid banded linear solver SPIKE is proposed as a parallel environment for solving banded systems that are either dense or sparse within the band. The SPIKE algorithm is a domain decomposition technique that allows performing independent calculations on each subdomain or partition of the original linear system. The interface problem leads to a reduced linear system of much smaller size than that of the original system. Three different members of the SPIKE family are described. Each handles the reduced system in a different way depending on the characteristics of the system and the architecture of the high-end parallel computing platform. Numerical experiments are presented that demonstrate the effectiveness of our parallel scheme. Comparison with the corresponding algorithms of ScaLAPACK are also provided for those banded systems that are dense within the band. A SPIKE scheme with multi-level parallelism is also introduced for solving large banded systems that are sparse within the band.

References in zbMATH (referenced in 20 articles , 1 standard article )

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  1. Zuo, Xian-yu; Mo, Ze-yao; Gu, Tong-xiang; Xu, Xiao-wen; Zhang, Ai-qing: Multi-core parallel robust structured multifrontal factorization method for large discretized PDEs (2016)
  2. Esmaily-Moghadam, M.; Bazilevs, Y.; Marsden, A.L.: Impact of data distribution on the parallel performance of iterative linear solvers with emphasis on CFD of incompressible flows (2015)
  3. Ghosh, Debojyoti; Constantinescu, Emil M.; Brown, Jed: Efficient implementation of nonlinear compact schemes on massively parallel platforms (2015)
  4. Kim, Jae Wook: Quasi-disjoint pentadiagonal matrix systems for the parallelization of compact finite-difference schemes and filters (2013)
  5. Jönsthövel, T.B.; van Gijzen, M.B.; MacLachlan, S.; Vuik, C.; Scarpas, A.: Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials (2012)
  6. Manguoglu, Murat: A domain-decomposing parallel sparse linear system solver (2011)
  7. Manguoglu, Murat; Takizawa, Kenji; Sameh, Ahmed H.; Tezduyar, Tayfun E.: Nested and parallel sparse algorithms for arterial fluid mechanics computations with boundary layer mesh refinement (2011)
  8. Manguoglu, Murat; Takizawa, Kenji; Sameh, Ahmed H.; Tezduyar, Tayfun E.: A parallel sparse algorithm targeting arterial fluid mechanics computations (2011)
  9. Mata, Matthew R.; Bertozzi, Andrea L.: A numerical scheme for particle-laden thin film flow in two dimensions (2011)
  10. Maurer, Daniel; Wieners, Christian: A parallel block \itLU decomposition method for distributed finite element matrices (2011)
  11. Mendiratta, Karan; Polizzi, Eric: A threaded SPIKE algorithm for solving general banded systems (2011)
  12. Dimakopoulos, Yannis: An efficient parallel and fully implicit algorithm for the simulation of transient free-surface flows of multimode viscoelastic liquids (2010)
  13. Manguoglu, Murat; Koyutürk, Mehmet; Sameh, Ahmed H.; Grama, Ananth: Weighted matrix ordering and parallel banded preconditioners for iterative linear system solvers (2010)
  14. Naumov, Maxim; Manguoglu, Murat; Sameh, Ahmed H.: A tearing-based hybrid parallel sparse linear system solver (2010)
  15. Naumov, Maxim; Sameh, Ahmed H.: A tearing-based hybrid parallel banded linear system solver (2009)
  16. Schenk, Olaf; Manguoglu, Murat; Sameh, Ahmed; Christen, Matthias; Sathe, Madan: Parallel scalable PDE-constrained optimization: antenna identification in hyperthermia cancer treatment planning (2009)
  17. Manguoglu, Murat; Sameh, Ahmed H.; Tezduyar, Tayfun E.; Sathe, Sunil: A nested iterative scheme for computation of incompressible flows in long domains (2008)
  18. Mikkelsen, Carl Christian Kjelgaard; Manguoglu, Murat: Analysis of the truncated SPIKE algorithm (2008)
  19. Polizzi, Eric; Sameh, Ahmed: SPIKE: A parallel environment for solving banded linear systems (2007)
  20. Zlatev, Zahari: Parallel solution of very large sparse systems of linear algebraic equations (2004)