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.

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  1. Luo, Wei-Hua; Gu, Xian-Ming; Carpentieri, Bruno: A hybrid triangulation method for banded linear systems (2022)
  2. Parker, J. T.; Hill, P. A.; Dickinson, D.; Dudson, B. D.: Parallel tridiagonal matrix inversion with a hybrid multigrid-Thomas algorithm method (2022)
  3. Buttari, Alfredo; Hauberg, Søren; Kodsi, Costy: Parallel \textitQRfactorization of block-tridiagonal matrices (2020)
  4. Çuğu, İlke; Manguoğlu, Murat: A parallel multithreaded sparse triangular linear system solver (2020)
  5. Manguoğlu, Murat; Polizzi, Eric; Sameh, Ahmed H.: Parallel hybrid sparse linear system solvers (2020)
  6. Dessole, M.; Marcuzzi, F.: Fully iterative ILU preconditioning of the unsteady Navier-Stokes equations for GPGPU (2019)
  7. Tselepidis, N. A.; Filelis-Papadopoulos, C. K.; Gravvanis, G. A.: Distributed algebraic tearing and interconnecting techniques (2019)
  8. Esmaily, M.; Jofre, L.; Mani, A.; Iaccarino, G.: A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows (2018)
  9. Zhang, Zhengyi; Sameh, Ahmed H.: Block row projection method based on M-matrix splitting (2018)
  10. Capuano, F.; Mastellone, A.; De Angelis, E. M.: A conservative overlap method for multi-block parallelization of compact finite-volume schemes (2017)
  11. Li, Ang; Serban, Radu; Negrut, Dan: Analysis of a splitting approach for the parallel solution of linear systems on GPU cards (2017)
  12. Melanz, Daniel; Fang, Luning; Jayakumar, Paramsothy; Negrut, Dan: A comparison of numerical methods for solving multibody dynamics problems with frictional contact modeled via differential variational inequalities (2017)
  13. Stratulat, Sorin: Mechanically certifying formula-based Noetherian induction reasoning (2017)
  14. Barnaś, Dawid; Bieniasz, Lesław K.: Accelerated Thomas solver for (quasi-)block-tridiagonal linear algebraic equation systems, using SSE/AVX instruction sets for vectorizing dense block operations (2016)
  15. Bolukbasi, Ercan Selcuk; Manguoglu, Murat: A multithreaded recursive and nonrecursive parallel sparse direct solver (2016)
  16. Maurer, Daniel; Wieners, Christian: A scalable parallel factorization of finite element matrices with distributed Schur complements. (2016)
  17. 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)
  18. Esmaily-Moghadam, Mahdi; Bazilevs, Yuri; Marsden, Alison L.: A bi-partitioned iterative algorithm for solving linear systems arising from incompressible flow problems (2015)
  19. 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)
  20. Ghosh, Debojyoti; Constantinescu, Emil M.; Brown, Jed: Efficient implementation of nonlinear compact schemes on massively parallel platforms (2015)

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