Multi-Model Multi-Domain Computational Methods: Papers & Software

Our group research is motivated by and spans several application regimes in aerodynamics and acoustics. It also includes foci in algorithmic technique, algorithmic theory, and software with applications beyond these areas. We sort the publication of papers and codes sponsored (at least in part) under this project according to the dominant category.

Full Potential

X.-C. Cai, W. D. Gropp, D. E. Keyes, R. G. Melvin and D. P. Young, 1998, "Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation", SIAM J. Sci. Comput. 19:246-265.

Steady Euler and Navier-Stokes

D. K. Kaushik, D. E. Keyes and B. F. Smith, 1998, "Newton-Krylov-Schwarz Methods for Aerodynamics Problems: Compressible and Incompressible Flows on Unstructured Grids" , submitted to Proceedings of the 11th Intl. Conf. on Domain Decomposition Methods, C.-H. Lai et al., eds., pp. 514-520.

W. D. Gropp, D. E. Keyes, L. C. McInnes and M. D. Tidriri, 1998, "Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD", ICASE TR 98-24 (to appear in Int. J. Supercomputer Applications). Also available in abridged form in Proceedings of Parallel CFD'97, A. Ecer et al., eds., Elsevier, pp. 333-344.

D. K. Kaushik, D. E. Keyes and B. F. Smith, 1998, "On the Interaction of Architecture and Algorithm in the Domain-Based Parallelization of an Unstructured Grid Incompressible Flow Code" , in Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel et al., eds., AMS, pp. 311-319.

D. E. Keyes, D. K. Kaushik and B. F. Smith, 1998, "Prospects for CFD on Petaflops Systems", in CFD Review 1998, M. Hafez and K. Oshima, eds., World Scientific, pp. 1079-1096.

P. R. McHugh, D. A. Knoll and D. E. Keyes, 1998, "Application of a Schwarz-Preconditioned Newton-Krylov Algorithm to a Low-Speed Reacting Flow Problem", AIAA J. 36:290-292.

Unsteady Euler and Navier Stokes

X.-C. Cai, C. Farhat and M. Sarkis, 1998, "A Minimum Overlap Restricted Additive Schwarz Preconditioner and Applications in 3D Flow Simulations", in Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel et al., eds., AMS, pp. 238-244.

X.-C. Cai, C. Farhat and M. Sarkis, 1997, "Schwarz methods for the unsteady compressible Navier-Stokes equations on unstructured meshes", in Domain Decomposition Methods in Sciences and Engineering, R. Glowinski, J. Periaux, Z. Shi and O. Widlund, eds., Wiley.

X.-C. Cai, C. Farhat and M. Sarkis, 1996, "Variable degree Schwarz methods for the implicit solution of unsteady compressible Navier-Stokes equations on two-dimensional unstructured meshes", ICASE Report No. 96-48, NASA Langley Research Center.

Helmholtz

M. A. Casarin, Jr. and O. B. Widlund, 1999, "Overlapping Schwarz Methods for Helmholtz's Equation", in Proceedings of the 11th Intl. Conf. on Domain Decomposition Methods, C. H. Lai et al., eds., Domain Decomposition Press, pp. 178-189.

X.-C. Cai, M. A. Casarin, Jr., F. W. Elliott, Jr., and O. B. Widlund, 1998, "Overlapping Schwarz Algorithms for Solving Helmholtz's Equation", in Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel et al., eds., AMS, pp. 391-399.

L. C. McInnes, R. Susan-Resiga, D. E. Keyes and H. M. Atassi, 1998, "Additive Schwarz Methods with Nonreflecting Boundary Conditions for the Parallel Computation of Helmholtz Problems", in Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel et al., eds., AMS, pp. 349-357.

R. Susan-Resiga and H. M. Atassi, 1998, "A Domain Decomposition Method for the Exterior Helmholtz Problem", J. Comput. Phys. 147:388-401.

L. C. McInnes, R. Susan-Resiga, H. M. Atassi, and D. E. Keyes, 1998, "Parallel Solution of Helmholtz Problems using Additive Schwarz Methods", Mathematical and Numerical Aspects of Wave Propagation., J. A. DeSanto, ed., SIAM, pp. 623-625.

R. Susan-Resiga and H. M. Atassi, 1998, "Parallel Computing Using Schwarz Domain Decomposition Method for Aeroacoustic Problems", AIAA Paper 98-2218, in Proceedings of the 4th AIAA/CEAS Aeroacoustics Conference, pp. 86-96.

H. M. Atassi and R. Susan-Resiga, 1998, "Parallel Computation of Harmonic Waves using Domain Decomposition, Part I: General Formulation", in Proceedings of the ASME Noise Control and Acoustics Division, NCA-25, pp. 375-379.

R. Susan-Resiga and H. M. Atassi, 1998, "Parallel Computation of Harmonic Waves using Domain Decomposition, Part II: Numerical Implementation and Applications", in Proceedings of the ASME Noise Control and Acoustics Division, NCA-25, pp. 381-388.

Multi-Model Methods

M. Paraschivoiu and X.-C. Cai, 1999, "A unigrid multi-model full potential and Euler formulation for transonic flows", in Proceedings of the Copper Mountain Conference on Multigrid Methods.

X.-C. Cai, M. Paraschivoiu, and M. Sarkis, 1999, "An explicit multi-model compressible flow formulation based on the full potential equation and the Euler equations on 3D unstructured meshes", in Proceedings of the 11th Intl. Conf. on Domain Decomposition Methods, C-H. Lai et al., eds., pp. 159-177.

M. Paraschivoiu, X.-C. Cai, M. Sarkis, D. P. Young, and D. E. Keyes, 1999, "Multi-Domain Multi-Model Formulation for Compressible Flows: Conservative Interface Coupling and Parallel Implicit Solvers for 3D Unstructured Meshes", AIAA Paper 99-0784.

Algorithms for Numerical Linear Algebra, PDEs and Optimization

X.-C. Cai and M. Sarkis, 1999, "A restricted additive Schwarz preconditioner for general sparse linear systems", SIAM J. Sci. Comput., 21, pp. 792-797.

R. Aitbayev, X.-C. Cai, and M. Paraschivoiu, 1999, " Parallel two-level methods for three-dimensional transonic compressible flow simulations on unstructured meshes", in Proceedings of Parallel CFD'99, A. Ecer et al., eds., Elsevier (to appear).

D. Hysom and A. Pothen, Efficient Parallel Computation of ILU(k) Preconditioners (postscript file), In Proceedings of Supercomputing '99, to appear.

F. Dobrian, G. Kumfert and A. Pothen, 1999, The design of a sparse direct solver library using object-oriented techniques, in Modern Software Tools in Scientific Computing, A. M. Bruaset, et al., eds., Springer.

G. Kumfert and A. Pothen, 1998, An object-oriented collection of minimum degree algorithms: design, implementation, and experiences, in Computing in Object-oriented Parallel Environments, Lecture Notes in Computer Science 1505, D. Caromel et al., eds., pp. 95--106, Springer.

Florin Dobrian, Gary Kumfert, and Alex Pothen, 1998, Object-oriented design of a sparse symmetric solver, in Computing in Object-oriented Parallel Environments, Lecture Notes in Computer Science 1505, D. Caromel et al., eds., pp. 207--214, Springer.

X.-C. Cai and M. Sarkis, 1998, "Local multiplicative Schwarz algorithms for convection-diffusion equations," East-West J. Numer. Math., 6.

D. E. Keyes, 1998, "Trends in Algorithms for Nonuniform Applications on Hierarchical Distributed Architectures" (ps) in Proceedings of the Workshop on Computational Aerosciences for the 21st Century, M. D. Salas and W. K. Anderson, eds., Elsevier.

D. E. Keyes, 1998, "How Scalable is Domain Decomposition in Practice?" , in Proceedings of the 11th Intl. Conf. on Domain Decomposition Methods, C.-H. Lai et al., eds. Domain Decomposition Press, pp. 286-297.

X.-C. Cai, D. E. Keyes and V. Venkatakrishnan, 1997, "Newton-Krylov-Schwarz: An implicit solver for CFD", in Domain Decomposition Methods in Sciences and Engineering, R. Glowinski, J. Periaux, Z. Shi and O. Widlund, eds., Wiley.

G. Kumfert and A. Pothen, 1997, "Two improved algorithms for reducing the envelope and wavefront", BIT, 37(3):559--590.

R. G. Melvin, W. P. Huffman, D. P. Young, F. T. Johnson, C. T. Hilmes and M. B. Bieterman, 1997, Recent Progress in Aerodynamic Design Optimization", ISSTECH-96-024, The Boeing Company.

M. A. Casarin and O. B. Widlund, 1996, "A Hierarchical Preconditioner for the Mortar Finite Element Method", Electronic Transactions on Numerical Analysis (ETNA) 4:75-88.

D. P. Young and D. E. Keyes, 1996, "Newton's Method and Design Optimization", ISSTECH-96-011, The Boeing Company.

Algorithmic Theory

L. Pavarino and O. B. Widlund, 2000, "Iterative Substructuring Methods for Spectral Element Discretizations of Elliptic Systems in Three Dimensions", in Parallel Solution of Partial Differential Equations, P. Bjorstad and M. Luskin, eds., Springer, pp. 1-30.

L. Pavarino and O. B. Widlund, 1999, "Iterative Substructuring Methods for Spectral Element Discretizations of Elliptic Systems. I: Compressible Linear Elasticity", SIAM J. Numer. Anal. 37:353-374.

L. Pavarino and O. B. Widlund, 1999, "Iterative Substructuring Methods for Spectral Element Discretizations of Elliptic Systems. II: Mixed Methods for Linear Elasticity and Stokes Flow", SIAM J. Numer. Anal. 37:375-402.

Y. Achdou, Y. Maday and O. B. Widlund, 1999, "Iterative Substructuring Preconditioners for Mortar Element Methods in Two Dimensions", SIAM J. Numer. Anal., 2: 551-580.

X.-C. Cai, T. Mathew, and M. Sarkis, 1999, "Maximum norm analysis of overlapping non-matching grid discretizations of elliptic equations", SIAM J. Numer. Anal. (to appear).

X.-C. Cai, M. Dryja and M. Sarkis, 1999, "Overlapping non-matching grid mortar element methods for elliptic problems",SIAM J. Numer. Anal., 36, pp. 581-606.

A. Toselli, 1999, "Domain decomposition methods for vector field problems", Courant Institute Tech Report 785.

A. Toselli, 1999, "Neumann-Neumann methods for vector field problems", Courant Institute Tech Report 786 (submitted to ETNA).

A. Toselli, 1999, "Overlapping methods with Perfectly Matched Layers for the solution of the Helmholtz equation", in Proceedings of the 11th Intl. Conf. on Domain Decomposition Methods, Domain Decomposition Press, pp. 551-557.

O. B. Widlund, 1999, "Error Control and Adaptivity in Scientific Computing", in NATO Science Series C: Mathematics and Physical Sciences, H. Bulgak and C. Zenger, eds., Volume 536, Kluwer, pp. 325-354.

A. Toselli, O. B. Widlund and B. I. Wohlmuth, 1998, "An Iterative Substructuring Method for Maxwell's Equations in Two Dimensions", Courant Institute Tech Report 768 (to appear in Math. Comp.).

B. I. Wohlmuth, A. Toselli and O. B. Widlund, 1998, "An Iterative Substructuring Method for Raviart--Thomas vector fields in three dimensions", Courant Institute Tech Report 775 (to appear in SIAM J. Numer. Anal.).

R. Hiptmair and A. Toselli, 1998, "Overlapping and multilevel Schwarz methods for vector valued elliptic problems in three dimensions", in "Parallel Solution of PDEs, IMA Volumes in Mathematics and its Applications", Springer.

A. Toselli, 1998, "Overlapping Schwarz methods for time-dependent Maxwell's equations in conductive media", in Mathematical and Numerical Aspects of Wave Propagation, John A. DeSanto, ed., SIAM,

O. B. Widlund, 1998, "Schwarz Methods for Helmholtz's Equation", in Mathematical and Numerical Aspects of Wave Propagation, John A. DeSanto, ed., SIAM, pp. 620--623.

C. T. Kelley and D. E. Keyes, 1998, "Convergence Analysis of Pseudo-Transient Continuation", SIAM J. Num. Anal. 35:508-523.

A. Toselli, 1998, "Some Results on Overlapping Schwarz Methods for the Helmholtz Equation Employing Perfectly Matched Layers", Courant Institute Tech Report 765, NYU.

X.-C. Cai, M. Dryja and M. Sarkis, 1997, Overlapping non-matching grid mortar element methods for elliptic problems", Tech Report CU-CS-842-97, Dept. of Comp. Sci., Univ. of Colorado at Boulder.

A. Toselli, 1997, "Overlapping Schwarz Methods for Maxwell's Equations in Three Dimensions", Courant Institute Tech Report 736, NYU.

A. Toselli, 1997, "Some Results on Schwarz Methods for a Low-Frequency Approximation of Time-Dependent Maxwell's Equations in Conductive Media", in Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel et al., eds., AMS, pp. 388-395.

Y. Wu, X.-C. Cai and D. E. Keyes, 1997, "Additive Schwarz Methods for Hyperbolic Equations", in Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel et al., eds., AMS, pp. 513--521.

Y. Achdou, Y. Maday and O. B. Widlund, 1996, "Methode iterative de sous-structuration pout les elements avec joints", Comptes Rendues Aca. Sci. Paris, I, 322:185-190.

High-Performance Software Engineering

Kyle Anderson, William Gropp, Dinesh Kaushik, David Keyes and Barry Smith, 1999, "Achieving High Sustained Performance in an Unstructured Mesh CFD Application" (ps) Bell Prize award paper, Special Category, in the Proceedings of SC'99.

William Gropp, Dinesh Kaushik, David Keyes and Barry Smith, 1999, "Towards Realistic Performance Bounds for Implicit CFD Codes", (ps) in Proceedings of Parallel CFD'99, A. Ecer et al., eds., Elsevier (to appear).

M. E. Hayder, C. Ierotheou and D. E. Keyes, 1999, Three Parallel Programming Paradigms: Comparisons on an Archetypal PDE Computation, Parallel and Distributed Computing Practices (to appear).

Dinesh Kaushik and David Keyes, 1999, "Efficient Parallelization of an Unstructured Grid Solver: A Memory-centric Approach" (ps) submitted to the Proceedings of the International Conference on Parallel CFD (Istanbul, June 1999).

S. Balay, W. D. Gropp. L. C. McInnes and B. F. Smith, 1997, "Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries", in Modern Software Tools in Scientific Computing, E. Arge, A. M. Bruaset and H. P. Langtangen, eds., Birkhauser.

M. E. Hayder, D. E. Keyes and P. Mehrotra, 1997, "A Comparison of PETSc Library and HPF Implementations of an Archetypal PDE Computation" , Advances in Engineering Software 29:415-424.

Freely Available Software

This project has provided partial support for the software PETSc (the dominant support for which came from the U.S. Department of Energy) and for the sparse linear algebra software, SLOAN, gkOrder, and Spindle (shared support for which came from the U.S. Department of Education), as well as other software still in the polishing process in doctoral dissertations and intended for public release.

S. Balay, W. D. Gropp. L. C. McInnes and B. F. Smith, 1996, "PETSc 2.0 Users Manual", Argonne National Laboratory Tech Report 95-11, Revision 2.0.17. (software downloadable at http://info.mcs.anl.gov/petsc/)

F. Dobrian, G. Kumfert, and A. Pothen, 1996--2000, linear algebra software collection

Edited Proceedings in Domain Decomposition

Our group is active in the international conferences on domain decomposition methods, and three co-PIs have, during this project, assumed editorial responsibilities for these proceedings, as listed chronologically below. The annual domain decomposition proceedings have become a prime archive for work related to this project. As an example of the scale of this activity, the proceedings of DD-9 contains exactly 100 invited and contributed papers.

R. Glowinski, J. Periaux, Z.-C. Shi, and O. Widlund, eds., 1997, Domain Decomposition Methods in Sciences and Engineering: Proceedings of the 8th International Conference on Domain Decomposition (Beijing, China, May 1995), Wiley.

P. E. Bjorstad, M. Espedal and D. E. Keyes, eds., 1998, Domain Decomposition Methods in Computational Science and Engineering: Proceedings of the 9th International Conference on Domain Decomposition (Bergen, Norway, June 1996), Domain Decomposition Press.

X. C. Cai, C. Farhat and J. Mandel, eds., 1998, Domain Decomposition Methods in Computational Science and Engineering: Proceedings of the 10th International Conference on Domain Decomposition (Boulder, USA, August 1997), AMS.

C.-H. Lai, P. E. Bjorstad, M. Cross, and O. B. Widlund, eds., 2000, Domain Decomposition Methods in Computational Science and Engineering: Proceedings of the 11th International Conference on Domain Decomposition (Greenwich, UK, July 1998), Domain Decomposition Press.