1887

Abstract

Summary

The purpose of the study is to show the effectiveness of recent algorithmic advances in Balancing Domain Decomposition by Constraints (BDDC) preconditioners for the solution of elliptic PDEs with highly heterogeneous coefficients, and discretized by means of the finite element method. Applications to large linear systems generated by div- and curl- conforming finite elements discretizations commonly arising in the contexts of modelling reservoirs and electromagnetics will be presented.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201414030
2015-11-16
2020-07-07
Loading full text...

Full text loading...

References

  1. AmestoyP. R., DuffI. S., KosterJ. and L’ExcellentJ. Y.
    [2001] A fully asynchronous multi-frontal solver using distributed dynamic scheduling, SIAM Journal of Matrix Analysis with Applications23, 15–41.
    [Google Scholar]
  2. BadiaS., MartinA. F. and PrincipeJ.
    [2014] A highly scalable parallel implementation of balancing domain decomposition by constraints, SIAM Journal of Scientific Computing36, C190–C218.
    [Google Scholar]
  3. BalayS., AbhyankarS., AdamsM. F., BrownJ., BruneP., BuschelmanK., EijkhoutV., GroppW. D., KaushikD., KnepleyM. G., CurfmannMcInnes L., RuppK., SmithB. F., ZhangH.
    [2014] PETSc Web page, http://www.mcs.anl.gov/petsc.
  4. BoffiD., BrezziF. and FortinM.
    [2013] Mixed finite element methods and applications, Springer Series in Computational Mathematics44.
    [Google Scholar]
  5. CarcioneJ. M.
    [2010] Simulation of electromagnetic diffusion in anisotropic media, Progress in Electromagnetics Research B. 26, 425–450.
    [Google Scholar]
  6. Dohrmann, C. R.
    [2003] A preconditioner for substructuring based on constrained energy minimization. SIAM Journal of Scientific Computing25, 246–258.
    [Google Scholar]
  7. DohrmannC. R. and WidlundO. B.
    [2015] A BDDC algorithm with deluxe scaling for three-dimensional H(curl) problems, appeared electronically in April 2015 inCommunications in Pure and Applied Mathematics.
    [Google Scholar]
  8. DongarraJ. et al.
    [2011] The international exascale software project roadmap, International Journal of High Performance Computing and Applications6, 1–58.
    [Google Scholar]
  9. HaberE.
    [2015] Computational methods in geophysical electromagnetics, SIAM.
    [Google Scholar]
  10. KimH. H. and ChungE. T.
    [2015] A BDDC algorithm with optimally enriched coarse spaces for two-dimensional elliptic problems with oscillatory and high contrast coefficients, Submitted.
    [Google Scholar]
  11. KlawonnA., RheinbachO. and WidlundO. B.
    [2008] An analysis of a FETI-DP algorithm on irregular subdomains in the plane, SIAM Journal of Numerical Analysis46, 2484–2504.
    [Google Scholar]
  12. Klawonn, A. and Rheinbach, O.
    [2010]. Highly scalable parallel domain decomposition methods with an application to biomechanics, ZAMM Journal of Applied Mathematics and Mechanics90, 5–32.
    [Google Scholar]
  13. KlawonnA., RadtkeP. and RheinbachO.
    [2015] FETI-DP methods with an adaptive coarse space. SIAM Journal of Numerical Analysis53, 297–320.
    [Google Scholar]
  14. KolevT. V., VassilevskyP. S.
    [2009] Parallel auxiliary space AMG solver for H(curl) problems, Journal of Computational Mathematics27, 604–632.
    [Google Scholar]
  15. [2012] Parallel auxiliary space AMG solver for H(div) problems, SIAM Journal of Scientific Computing34.
    [Google Scholar]
  16. LoggA. and WellsG. N.
    [2012] DOLFIN: automated finite element computing, ACM Transactions on Mathematical Software37.
    [Google Scholar]
  17. LiJ. and WidlundO. B
    [2006] FETI-DP, BDDC, and block Cholesky methods, International Journal of Numerical Methods in Engineering, 66, 250–271.
  18. MandelJ.
    [1993] Balancing domain decomposition, Communications in Applied Numerical Methods9, 233–241.
    [Google Scholar]
  19. MandelJ., DohrmannC. R. and TezaurR.
    [2005] An algebraic theory for primal and dual substructuring methods by constraints, Applied Numerical Mathematics54, 167–193.
    [Google Scholar]
  20. MandelJ., SousedikB. and DohrmannC. R.
    [2008] Multispace and multilevel BDDC, Computing3, 55–85
    [Google Scholar]
  21. MandelJ., SousedikB. and SistekJ.
    [2012] Adaptive BDDC in three dimensions, Mathematics and Computers in Simulation82, 1812–1831.
    [Google Scholar]
  22. OhD.-S., WidlundO. B. and DohrmannC. R.
    [2013] A BDDC algorithm for Raviart—Thomas vector fields, Courant Institute Technical Report TR2013-951.
    [Google Scholar]
  23. PechsteinC. and DohrmannC. R.
    [2013] Modern domain decomposition methods BDDC, deluxe scaling, and an algebraic approach. Seminar talk, Linz, http://people.ricam.oeaw.ac.at/c.pechstein/pechstein-bddc2013.pdf
    [Google Scholar]
  24. PechsteinC. and ScheichlR.
    [2008] Analysis of FETI methods for multiscale PDEs, Numerische Mathematik111, 293–333.
    [Google Scholar]
  25. SistekJ, BrezinaJ. and SousedikB.
    [2015] BDDC for mixed-hybrid formulation of flow in porous media with combined mesh dimensions, http://arxiv.org/abs/1504.07085.
    [Google Scholar]
  26. ToselliA.
    and WidlundO. B. [2005] Domain decomposition methods - Algorithms and theory, Springer Verlag.
    [Google Scholar]
  27. TuX.
    [2005] A BDDC algorithm for a mixed formulation of flow in porous media, Electronic Transactions on Numerical Analysis20, 164–179
    [Google Scholar]
  28. [2007] A BDDC algorithm for flow in porous media with a hybrid finite element discretization, Electronic Transactions on Numerical Analysis26, 146–160.
    [Google Scholar]
  29. WidlundO.B. and DohrmannC. R.
    [2014] BDDC deluxe Domain Decomposition, proceedings of the XXII International conference on Domain Decomposition Methods in Science and Engineering.
    [Google Scholar]
  30. ZampiniS.
    [2014] Dual-primal methods for the cardiac bidomain model. Mathematical Models and Methods in Applied Sciences24, 667–696.
    [Google Scholar]
  31. [2015] PCBDDC: a class of robust dual-primal methods in PETSc, Submitted.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201414030
Loading
/content/papers/10.3997/2214-4609.201414030
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error