A parallel direct solver for the self-adaptive hp Finite Element Method

Journal of Parallel and Distributed Computing

Volumn 70, Issue 3, 2010, Pages 270-281

  Paszyński, Maciej ^a   Pardo, David ^b   Torres Verdín, Carlos ^c   Demkowicz, Leszek ^c   Calo, Victor ^d  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

^b BCAM BASQUE CENTER FOR APPLIED MATHEMATICS   (Spain)

^c UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^d KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

Author keywords

3D borehole resistivity; Finite Element Method; hp adaptivity; Parallel direct solvers

Indexed keywords

3D BOREHOLE RESISTIVITY; AUTOMATIC MODE; COMPUTATIONAL TIME; CPU TIME; DEGREES OF FREEDOM; DIRECT CURRENT; DIRECT SOLVERS; ELIMINATION TREE; EXECUTION TIME; EXPONENTIAL CONVERGENCE; FINITE ELEMENT; HP ADAPTIVITY; HP-FINITE ELEMENT METHODS; HP-REFINEMENT; LONGEST PATH; LU FACTORIZATION; MEMORY USAGE; NUMBER OF DEGREES OF FREEDOM; PARALLEL DIRECT SOLVERS; PARALLEL SOLVER; POLYNOMIAL ORDER; REGULAR MESHES; RESISTIVITY MEASUREMENT; SELF-ADAPTIVE;

FACTORIZATION; MECHANICS; POLYNOMIAL APPROXIMATION; THREE DIMENSIONAL;

FINITE ELEMENT METHOD;

EID: 74449087311     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpdc.2009.09.007     Document Type: Article

References (23)

1. Amestoy P.R., Duff I.S., and L'Excellent J.-Y. Multifrontal parallel distributed symmetric and unsymmetric solvers. Computer Methods in Applied Mechanics and Engineering 184 (2000) 501-520
2. Amestoy P.R., Duff I.S., Koster J., and L'Excellent J.-Y. A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM Journal on Matrix Analysis and Applications 23 1 (2001) 15-41
3. Amestoy P.R., Guermouche A., L'Excellent J.-Y., and Pralet S. Hybrid scheduling for the parallel solution of linear systems. Parallel Computing 32 2 (2006) 136-156
4. Demkowicz L. Computing with h p-adaptive finite elements. One and Two Dimensional Elliptic and Maxwell Problems, vol. I. Chapman & Hall/CRC Applied Mathematics and Nonlinear Science (2007)
5. L. Demkowicz, D. Pardo, W. Rachowicz, 3D h p-adaptive finite element package (3Dhp90) version 2.0, The ultimate data structure for three-dimensional, anisotropic h p refinements, TICAM Report 02-24, 2002
6. Duff I.S., and Reid J.K. The multifrontal solution of indefinite sparse symmetric linear systems. ACM Transactions on Mathematical Software 9 (1983) 302-325
7. Duff I.S., and Reid J.K. The multifrontal solution of unsymmetric sets of linear systems. SIAM Journal on Scientific and Statistical Computing 5 (1984) 633-641
8. Geng P., Oden T.J., and van de Geijn R.A. A parallel multifrontal algorithm and its implementation. Computer Methods in Applied Mechanics and Engineering 149 (2006) 289-301
9. Giraud L., Marocco A., and Rioual J.-C. Iterative versus direct parallel substructuring methods in semiconductor device modeling. Numerical Linear Algebra with Applications 12 1 (2005) 33-55
10. Irons B. A frontal solution program for finite-element analysis. International Journal for Numerical Methods in Engineering 2 (1970) 5-32
11. M.S. Khaira, G.L. Miller, T.J. Sheffler, Nested dissection: A survey and comparison of various nested dissection algorithms, CMU-CS-92-106R, Computer Science Department, Carnegie Mellon University, 1992
12. Karypis G., and Kumar V. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing 20 1 (1999) 359-392
13. Lonestar cluster users' manual. http://www.tacc.utexas.edu/services/userguides/lonestar, 2007
14. A multifrontal massively parallel sparse direct solver version 4.7.3. http://www.enseeiht.fr/lima/apo/MUMPS/, 2007
15. Pardo D., Calo V.M., Torres-Verdín C., and Nam M.J. Fourier series expansion in a non-orthogonal system of coordinates for simulation of 3D DC borehole resistivity measurements. Computer Methods in Applied Mechanics and Engineering 197 (2008) 1906-1925
16. Pardo D., Demkowicz L., Torres-Verdín C., and Paszyński M. Simulation of resistivity Logging-While-Drilling (LWD) measurements using a self-adaptive goal-oriented h p-finite element method. SIAM Journal on Applied Mathematics 66 (2006) 2085-2106
17. Paszyński M. Agent based hierarchical parallelization of complex algorithms on the example of h p finite element method. Lecture Notes in Computer Science 4488 (2008) 912-919
18. Paszyński M., and Demkowicz L. Parallel fully automatic h p-adaptive 3D finite element package. Engineering with Computers 22 3-4 (2006) 255-276
19. Paszyński M., Kurtz J., and Demkowicz L. Parallel fully automatic h p-adaptive 2D finite element package. Computer Methods in Applied Mechanics and Engineering 195 7-8 (2006) 711-741
20. Rachowicz W., Pardo D., and Demkowicz L. Fully automatic h p-adaptivity in 3D. Computer Methods in Applied Mechanics and Engineering 195 37-40 (2006) 4816-4842
21. Scott J.A. Parallel frontal solvers for large sparse linear systems. ACM Transactions on Mathematical Software 29 4 (2003) 395-417
22. Smith B.F., Bjørstad P., and Gropp W. Domain Decomposition, Parallel Multi-level Methods for Elliptic Partial Differential Equations. 1st ed. (1996), Cambridge University Press, New York
23. Zoltan: Data-management services for parallel applications. http://www.cs.sandia.gov/Zoltan/, 2007