eBook ISBN:  9780821877715 
Product Code:  CONM/180.E 
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AMS Member Price:  $100.00 
eBook ISBN:  9780821877715 
Product Code:  CONM/180.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 180; 1994; 546 ppMSC: Primary 65;
This book contains proceedings from the Seventh International Conference on Domain Decomposition Methods, held at Pennsylvania State University in October 1993. The term “domain decomposition” has for nearly a decade been associated with the partly iterative, partly direct algorithms explored in the proceedings of this conference. Noteworthy trends in the current volume include progress in dealing with socalled “bad parameters” in elliptic partial differential equation problems, as well as developments in partial differential equations outside of the ellipticallydominated framework. Also described here are convergence and complexity results for novel discretizations, which bring with them new challenges in the derivation of appropriate operators for coarsened spaces. Implementations and architectural considerations are discussed, as well as partitioning tools and environments. In addition, the book describes a wide array of applications, from semiconductor device simulation to structural mechanics to aerodynamics. Presenting many of the latest results in the field, this book offers readers an uptodate guide to the many facets of the theory and practice of domain decomposition.
ReadershipResearch mathematicians.

Table of Contents

Part I. Theory [ MR 1312370 ]

Folkmar A. Bornemann — Interpolation spaces and optimal multilevel preconditioners [ MR 1312371 ]

Susanne C. Brenner — Twolevel additive Schwarz preconditioners for nonconforming finite elements [ MR 1312372 ]

H.J. Bungartz, M. Griebel, D. Röschke and C. Zenger — Two proofs of convergence for the combination technique for the efficient solution of sparse grid problems [ MR 1312373 ]

XiaoChuan Cai and Maksymilian Dryja — Domain decomposition methods for monotone nonlinear elliptic problems [ MR 1312374 ]

Peter Deuflhard — Cascadic conjugate gradient methods for elliptic partial differential equations: algorithm and numerical results [ MR 1312375 ]

Maksymilian Dryja — Multilevel methods for elliptic problems with discontinuous coefficients in three dimensions [ MR 1312376 ]

Ralf Kornhuber and Harry Yserentant — Multilevel methods for elliptic problems on domains not resolved by the coarse grid [ MR 1312377 ]

P. Le Tallec, T. Sassi and M. Vidrascu — Threedimensional domain decomposition methods with nonmatching grids and unstructured coarse solvers [ MR 1312378 ]

S. V. Nepomnyaschikh — Domain decomposition for elliptic problems with large condition numbers [ MR 1312379 ]

P. Oswald — Stable subspace splittings for Sobolev spaces and domain decomposition algorithms [ MR 1312380 ]

Luca F. Pavarino — A wire basket based method for spectral elements in three dimensions [ MR 1312381 ]

Alex Pothen — An analysis of spectral graph partitioning via quadratic assignment problems [ MR 1312382 ]

U. Rüde — Error estimates based on stable splittings [ MR 1312383 ]

Marcus Sarkis — Multilevel methods for $P_1$ nonconforming finite elements and discontinuous coefficients in three dimensions [ MR 1312384 ]

K. H. Tan and M. J. A. Borsboom — On generalized Schwarz coupling applied to advectiondominated problems [ MR 1312385 ]

Olof B. Widlund — Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements [ MR 1312386 ]

Part II. Algorithms [ MR 1312370 ]

S. F. Ashby, C. T. Kelley, P. E. Saylor and J. S. Scroggs — Preconditioning via asymptoticallydefined domain decomposition [ MR 1312387 ]

M. Azaïez and A. Quarteroni — A spectral Stokes solver in domain decomposition methods [ MR 1312388 ]

Nikolai S. Bakhvalov and Andrew V. Knyazev — Preconditioned iterative methods in a subspace for linear algebraic equations with large jumps in the coefficients [ MR 1312389 ]

Randolph E. Bank and Jinchao Xu — The hierarchical basis multigrid method and incomplete LU decomposition

Tony F. Chan and Barry F. Smith — Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes

Clint N. Dawson and Mary F. Wheeler — Twogrid methods for mixed finite element approximations of nonlinear parabolic equations [ MR 1312392 ]

Luc Giraud and Ray S. Tuminaro — Domain decomposition algorithms for PDE problems with large scale variations

Roland Glowinski, TsorngWhay Pan and Jacques Périaux — A one shot domain decomposition/fictitious domain method for the NavierStokes equations [ MR 1312393 ]

M. Griebel — Domainoriented multilevel methods [ MR 1312394 ]

Michael Holst and Faisal Saied — Multigrid and domain decomposition methods for electrostatics problems [ MR 1312395 ]

Edgar Katzer — A parallel subspace decomposition method for hyperbolic equations [ MR 1312396 ]

Seongjai Kim — Numerical treatments for the Helmholtz problem by domain decomposition techniques [ MR 1312397 ]

Yu. A. Kuznetsov, P. Neittaanmäki and P. Tarvainen — Schwarz methods for obstacle problems with convectiondiffusion operators [ MR 1312398 ]

C.H. Lai — On domain decomposition and shooting methods for twopoint boundary value problems [ MR 1312399 ]

W. Layton, J. Maubach and P. Rabier — Robust methods for highly nonsymmetric problems

Nancy J. Lybeck and Kenneth L. Bowers — Domain decomposition via the SincGalerkin method for second order differential equations

Petr Mejzlík — A bisection method to find all solutions of a system of nonlinear equations [ MR 1312402 ]

Ilya D. Mishev — Preconditioning cellcentered finite difference equations on grids with local refinement [ MR 1312403 ]

F. Nataf and F. Rogier — Outflow boundary conditions and domain decomposition method [ MR 1312404 ]

J. Tinsley Oden, Abani Patra and Yusheng Feng — Domain decomposition for adaptive $hp$ finite element methods

Michael Pernice — Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers

L. Ridgway Scott — Elliptic preconditioners using fast summation techniques [ MR 1312405 ]

Jian Ping Shao — The modified vertex space domain decomposition method for Neumann boundary value problems [ MR 1312406 ]

Tsi Min Shih, Chin Bo Liem, Tao Lü and Ai Hui Zhou — A multicolor splitting method and convergence analysis for local grid refinement [ MR 1312407 ]

Olaf Steinbach — Boundary elements in domain decomposition methods [ MR 1312408 ]

Victor H. Sun and WeiPai Tang — An overdetermined Schwarz alternating method [ MR 1312409 ]

Xue Cheng Tai — Domain decomposition for linear and nonlinear elliptic problems via function or space decomposition [ MR 1312410 ]

H. Wang, H. K. Dahle, R. E. Ewing, T. Lin and J. E. Våg — ELLAMbased domain decomposition and local refinement techniques for advectiondiffusion equations with interfaces

Part III. Parallelism [ MR 1312370 ]

Petter E. Bjørstad, W. M. Coughran, Jr. and Eric Grosse — Parallel domain decomposition applied to coupled transport equations

Nikos Chrisochoides, Geoffrey Fox and Joe Thompson — MENUSPGG: A mapping environment for unstructured and structured numerical parallel grid generation

Patrick Ciarlet Jr — A comparison of three iterative algorithms based on domain decomposition methods

E. De Sturler — IBLU preconditioners for massively parallel computers

Charbel Farhat and PoShu Chen — Tailoring domain decomposition methods for efficient parallel coarse grid solution and for systems with many righthand sides [ MR 1312411 ]

Hai Xiang Lin — Analysis and Implementation of DD methods for parallel FE Computations

M. Reza Mehrabi and Robert A. Brown — Finiteelement/Newton method for solution of nonlinear problems in transport processes using domain decomposition and nested dissection on MIMD parallel computers [ MR 1312412 ]

Mo Mu and John R. Rice — Modeling with collaborating PDE solvers: theory and practice [ MR 1312413 ]

FrancoisXavier Roux and Damien TromeurDervout — Parallelization of a multigrid solver via a domain decomposition method

Jonathan Richard Shewchuk and Omar Ghattas — A compiler for parallel finite element methods with domaindecomposed unstructured meshes

Part IV. Applications [ MR 1312370 ]

Renzo Arina and Claudio Canuto — A $\chi $formulation of the viscousinviscid domain decomposition for the Euler/NavierStokes equations

Wei Cai — Domain decomposition and computation of two dimensional detonation waves

X.C. Cai, W. D. Gropp, D. E. Keyes and M. D. Tidriri — Parallel implicit methods for aerodynamics [ MR 1611307 ]

Y. Cai and I. M. Navon — Parallel domaindecomposed preconditioners in finite element shallow water flow modeling

F. Camilli, M. Falcone, P. Lanucara and A. Seghini — A domain decomposition method for Bellman equations [ MR 1312414 ]

J. G. Chefter, C. K. Chu and D. E. Keyes — Domain decomposition for the shallow water equations

R. K. Coomer and I. G. Graham — Domain decomposition methods for device modelling [ MR 1312415 ]

George C. Hsiao, Michael D. Marcozzi and Shangyou Zhang — An efficient computational method for the flow past an airfoil [ MR 1312416 ]

P. G. Jacobs, V. A. Mousseau, P. R. McHugh and D. A. Knoll — NewtonKrylovSchwarz techniques applied to the twodimensional incompressible NavierStokes and energy equations

H. C. Ku, H. E. Gilreath, R. Paul and J. C. Sommerer — Direct numerical simulation of jet flow via a multiblock technique

Patrick Le Tallec, Jan Mandel and Marina Vidrascu — Balancing domain decomposition for plates [ MR 1312417 ]

S. Micheletti, A. Quarteroni and R. Sacco — Nonlinear block iterative solution of semiconductor device equations by a domain decomposition method

I. Raspo, J. Ouazzani and R. Peyret — A direct Chebyshev multidomain method for flow computation with application to rotating systems

L. Vozovoi, M. Israeli and A. Averbuch — Multidomain Fourier algorithms for parallel solution of the NavierStokes equations [ MR 1312418 ]


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This book contains proceedings from the Seventh International Conference on Domain Decomposition Methods, held at Pennsylvania State University in October 1993. The term “domain decomposition” has for nearly a decade been associated with the partly iterative, partly direct algorithms explored in the proceedings of this conference. Noteworthy trends in the current volume include progress in dealing with socalled “bad parameters” in elliptic partial differential equation problems, as well as developments in partial differential equations outside of the ellipticallydominated framework. Also described here are convergence and complexity results for novel discretizations, which bring with them new challenges in the derivation of appropriate operators for coarsened spaces. Implementations and architectural considerations are discussed, as well as partitioning tools and environments. In addition, the book describes a wide array of applications, from semiconductor device simulation to structural mechanics to aerodynamics. Presenting many of the latest results in the field, this book offers readers an uptodate guide to the many facets of the theory and practice of domain decomposition.
Research mathematicians.

Part I. Theory [ MR 1312370 ]

Folkmar A. Bornemann — Interpolation spaces and optimal multilevel preconditioners [ MR 1312371 ]

Susanne C. Brenner — Twolevel additive Schwarz preconditioners for nonconforming finite elements [ MR 1312372 ]

H.J. Bungartz, M. Griebel, D. Röschke and C. Zenger — Two proofs of convergence for the combination technique for the efficient solution of sparse grid problems [ MR 1312373 ]

XiaoChuan Cai and Maksymilian Dryja — Domain decomposition methods for monotone nonlinear elliptic problems [ MR 1312374 ]

Peter Deuflhard — Cascadic conjugate gradient methods for elliptic partial differential equations: algorithm and numerical results [ MR 1312375 ]

Maksymilian Dryja — Multilevel methods for elliptic problems with discontinuous coefficients in three dimensions [ MR 1312376 ]

Ralf Kornhuber and Harry Yserentant — Multilevel methods for elliptic problems on domains not resolved by the coarse grid [ MR 1312377 ]

P. Le Tallec, T. Sassi and M. Vidrascu — Threedimensional domain decomposition methods with nonmatching grids and unstructured coarse solvers [ MR 1312378 ]

S. V. Nepomnyaschikh — Domain decomposition for elliptic problems with large condition numbers [ MR 1312379 ]

P. Oswald — Stable subspace splittings for Sobolev spaces and domain decomposition algorithms [ MR 1312380 ]

Luca F. Pavarino — A wire basket based method for spectral elements in three dimensions [ MR 1312381 ]

Alex Pothen — An analysis of spectral graph partitioning via quadratic assignment problems [ MR 1312382 ]

U. Rüde — Error estimates based on stable splittings [ MR 1312383 ]

Marcus Sarkis — Multilevel methods for $P_1$ nonconforming finite elements and discontinuous coefficients in three dimensions [ MR 1312384 ]

K. H. Tan and M. J. A. Borsboom — On generalized Schwarz coupling applied to advectiondominated problems [ MR 1312385 ]

Olof B. Widlund — Exotic coarse spaces for Schwarz methods for lower order and spectral finite elements [ MR 1312386 ]

Part II. Algorithms [ MR 1312370 ]

S. F. Ashby, C. T. Kelley, P. E. Saylor and J. S. Scroggs — Preconditioning via asymptoticallydefined domain decomposition [ MR 1312387 ]

M. Azaïez and A. Quarteroni — A spectral Stokes solver in domain decomposition methods [ MR 1312388 ]

Nikolai S. Bakhvalov and Andrew V. Knyazev — Preconditioned iterative methods in a subspace for linear algebraic equations with large jumps in the coefficients [ MR 1312389 ]

Randolph E. Bank and Jinchao Xu — The hierarchical basis multigrid method and incomplete LU decomposition

Tony F. Chan and Barry F. Smith — Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes

Clint N. Dawson and Mary F. Wheeler — Twogrid methods for mixed finite element approximations of nonlinear parabolic equations [ MR 1312392 ]

Luc Giraud and Ray S. Tuminaro — Domain decomposition algorithms for PDE problems with large scale variations

Roland Glowinski, TsorngWhay Pan and Jacques Périaux — A one shot domain decomposition/fictitious domain method for the NavierStokes equations [ MR 1312393 ]

M. Griebel — Domainoriented multilevel methods [ MR 1312394 ]

Michael Holst and Faisal Saied — Multigrid and domain decomposition methods for electrostatics problems [ MR 1312395 ]

Edgar Katzer — A parallel subspace decomposition method for hyperbolic equations [ MR 1312396 ]

Seongjai Kim — Numerical treatments for the Helmholtz problem by domain decomposition techniques [ MR 1312397 ]

Yu. A. Kuznetsov, P. Neittaanmäki and P. Tarvainen — Schwarz methods for obstacle problems with convectiondiffusion operators [ MR 1312398 ]

C.H. Lai — On domain decomposition and shooting methods for twopoint boundary value problems [ MR 1312399 ]

W. Layton, J. Maubach and P. Rabier — Robust methods for highly nonsymmetric problems

Nancy J. Lybeck and Kenneth L. Bowers — Domain decomposition via the SincGalerkin method for second order differential equations

Petr Mejzlík — A bisection method to find all solutions of a system of nonlinear equations [ MR 1312402 ]

Ilya D. Mishev — Preconditioning cellcentered finite difference equations on grids with local refinement [ MR 1312403 ]

F. Nataf and F. Rogier — Outflow boundary conditions and domain decomposition method [ MR 1312404 ]

J. Tinsley Oden, Abani Patra and Yusheng Feng — Domain decomposition for adaptive $hp$ finite element methods

Michael Pernice — Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers

L. Ridgway Scott — Elliptic preconditioners using fast summation techniques [ MR 1312405 ]

Jian Ping Shao — The modified vertex space domain decomposition method for Neumann boundary value problems [ MR 1312406 ]

Tsi Min Shih, Chin Bo Liem, Tao Lü and Ai Hui Zhou — A multicolor splitting method and convergence analysis for local grid refinement [ MR 1312407 ]

Olaf Steinbach — Boundary elements in domain decomposition methods [ MR 1312408 ]

Victor H. Sun and WeiPai Tang — An overdetermined Schwarz alternating method [ MR 1312409 ]

Xue Cheng Tai — Domain decomposition for linear and nonlinear elliptic problems via function or space decomposition [ MR 1312410 ]

H. Wang, H. K. Dahle, R. E. Ewing, T. Lin and J. E. Våg — ELLAMbased domain decomposition and local refinement techniques for advectiondiffusion equations with interfaces

Part III. Parallelism [ MR 1312370 ]

Petter E. Bjørstad, W. M. Coughran, Jr. and Eric Grosse — Parallel domain decomposition applied to coupled transport equations

Nikos Chrisochoides, Geoffrey Fox and Joe Thompson — MENUSPGG: A mapping environment for unstructured and structured numerical parallel grid generation

Patrick Ciarlet Jr — A comparison of three iterative algorithms based on domain decomposition methods

E. De Sturler — IBLU preconditioners for massively parallel computers

Charbel Farhat and PoShu Chen — Tailoring domain decomposition methods for efficient parallel coarse grid solution and for systems with many righthand sides [ MR 1312411 ]

Hai Xiang Lin — Analysis and Implementation of DD methods for parallel FE Computations

M. Reza Mehrabi and Robert A. Brown — Finiteelement/Newton method for solution of nonlinear problems in transport processes using domain decomposition and nested dissection on MIMD parallel computers [ MR 1312412 ]

Mo Mu and John R. Rice — Modeling with collaborating PDE solvers: theory and practice [ MR 1312413 ]

FrancoisXavier Roux and Damien TromeurDervout — Parallelization of a multigrid solver via a domain decomposition method

Jonathan Richard Shewchuk and Omar Ghattas — A compiler for parallel finite element methods with domaindecomposed unstructured meshes

Part IV. Applications [ MR 1312370 ]

Renzo Arina and Claudio Canuto — A $\chi $formulation of the viscousinviscid domain decomposition for the Euler/NavierStokes equations

Wei Cai — Domain decomposition and computation of two dimensional detonation waves

X.C. Cai, W. D. Gropp, D. E. Keyes and M. D. Tidriri — Parallel implicit methods for aerodynamics [ MR 1611307 ]

Y. Cai and I. M. Navon — Parallel domaindecomposed preconditioners in finite element shallow water flow modeling

F. Camilli, M. Falcone, P. Lanucara and A. Seghini — A domain decomposition method for Bellman equations [ MR 1312414 ]

J. G. Chefter, C. K. Chu and D. E. Keyes — Domain decomposition for the shallow water equations

R. K. Coomer and I. G. Graham — Domain decomposition methods for device modelling [ MR 1312415 ]

George C. Hsiao, Michael D. Marcozzi and Shangyou Zhang — An efficient computational method for the flow past an airfoil [ MR 1312416 ]

P. G. Jacobs, V. A. Mousseau, P. R. McHugh and D. A. Knoll — NewtonKrylovSchwarz techniques applied to the twodimensional incompressible NavierStokes and energy equations

H. C. Ku, H. E. Gilreath, R. Paul and J. C. Sommerer — Direct numerical simulation of jet flow via a multiblock technique

Patrick Le Tallec, Jan Mandel and Marina Vidrascu — Balancing domain decomposition for plates [ MR 1312417 ]

S. Micheletti, A. Quarteroni and R. Sacco — Nonlinear block iterative solution of semiconductor device equations by a domain decomposition method

I. Raspo, J. Ouazzani and R. Peyret — A direct Chebyshev multidomain method for flow computation with application to rotating systems

L. Vozovoi, M. Israeli and A. Averbuch — Multidomain Fourier algorithms for parallel solution of the NavierStokes equations [ MR 1312418 ]