Multi-Model Multi-Domain Computational Methods: Papers

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.

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 (submitted to 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, 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.

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, 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.

Helmholtz

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. 437-445.

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, 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

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

W. D. Gropp, D. E. Keyes, L. C. McInnes and M. D. Tidriri, 1998,

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.

X.-C. Cai and M. Sarkis, 1997, "A restricted additive Schwarz preconditioner for general sparse linear systems", Tech Report CU-CS-843-97, Dept. of Comp. Sci., Univ. of Colorado at Boulder.

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.

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

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

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.

Algorithmic Theory

Y. Achdou, Y. Maday and O. B. Widlund, 1997, "Iterative Substructuring Preconditioners for Mortar Element Methods in Two Dimensions", Courant Institute Tech Report 735, 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.

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

F. Ben Belgacem, A. Toselli, O. B. Widlund and B. I. Wolmuth, 1998, "An Iterative Substructuring Method for Maxwell's Equations in Two Dimensions", Courant Institute Tech Report 768, NYU.

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

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.

High-Performance Software Engineering

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" , in Proceedings of the 4th National Symposium on Large-Scale Analysis and Design on High Performance Computers and Workstations, O. Storaasli, ed., Williamsburg, VA, October 15-17, 1997 (to appear).

Freely Available Software

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/)

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.