Ebook: Domain Decomposition Methods in Science and Engineering

Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

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Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

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Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

Content:
Front Matter....Pages i-xviii
Non-matching Grids and Lagrange Multipliers....Pages 3-18
A FETI Method for a Class of Indefinite or Complex Second- or Fourth-Order Problems....Pages 19-34
Hybrid Schwarz-Multigrid Methods for the Spectral Element Method: Extensions to Navier-Stokes....Pages 35-49
Numerical Approximation of Dirichlet-to-Neumann Mapping and its Application to Voice Generation Problem....Pages 51-65
Selecting Constraints in Dual-Primal FETI Methods for Elasticity in Three Dimensions....Pages 67-81
Coupled Boundary and Finite Element Tearing and Interconnecting Methods....Pages 83-97
Parallel Simulation of Multiphase/Multicomponent Flow Models....Pages 99-113
Uncoupling-Coupling Techniques for Metastable Dynamical Systems....Pages 115-129
On the Construction of Approximate Boundary Conditions for Solving the Interior Problem of the Acoustic Scattering Transmission Problem....Pages 133-140
Approximation and Fast Calculation of Non-local Boundary Conditions for the Time-dependent Schr?dinger Equation....Pages 141-148
Domain Decomposition and Additive Schwarz Techniques in the Solution of a TE Model of the Scattering by an Electrically Deep Cavity....Pages 149-156
A Model for Parallel Adaptive Finite Element Software....Pages 159-166
Towards a Unified Framework for Scientific Computing....Pages 167-174
Distributed Point Objects. A New Concept for Parallel Finite Elements....Pages 175-182
Local Defect Correction Techniques Applied to a Combustion Problem....Pages 185-192
Electronic Packaging and Reduction in Modelling Time Using Domain Decomposition....Pages 193-200
Improving Robustness and Parallel Scalability of Newton Method Through Nonlinear Preconditioning....Pages 201-208
Iterative Substructuring Methods for Indoor Air Flow Simulation....Pages 209-216
Fluid-Structure Interaction Using Nonconforming Finite Element Methods....Pages 217-224
Interaction Laws in Viscous-Inviscid Coupling....Pages 225-232
Comparison of the Dirichlet-Neumann and Optimal Schwarz Method on the Sphere....Pages 235-242
Finite Volume Methods on Non-Matching Grids with Arbitrary Interface Conditions and Highly Heterogeneous Media....Pages 243-250
Nonlinear Advection Problems and Overlapping Schwarz Waveform Relaxation....Pages 251-258
A New Cement to Glue Nonconforming Grids with Robin Interface Conditions: The Finite Element Case....Pages 259-266
Acceleration of a Domain Decomposition Method for Advection-Diffusion Problems....Pages 267-274
A Stabilized Three-Field Formulation and its Decoupling for Advection-Diffusion Problems....Pages 275-282
Approximation of Optimal Interface Boundary Conditions for Two-Lagrange Multiplier FETI Method....Pages 283-290
Optimized Overlapping Schwarz Methods for Parabolic PDEs with Time-Delay....Pages 291-298
A More General Version of the Hybrid-Trefftz Finite Element Model by Application of TH-Domain Decomposition....Pages 301-308
Mixed Finite Element Methods for Diffusion Equations on Nonmatching Grids....Pages 311-318
Mortar Finite Elements with Dual Lagrange Multipliers: Some Applications....Pages 319-326
Non-Conforming Finite Element Methods for Nonmatching Grids in Three Dimensions....Pages 327-334
On an Additive Schwarz Preconditioner for the Crouzeix-Raviart Mortar Finite Element....Pages 335-342
A FETI-DP Method for the Mortar Discretization of Elliptic Problems with Discontinuous Coefficients....Pages 345-352
A FETI-DP Formulation for Two-dimensional Stokes Problem on Nonmatching Grids....Pages 353-360
Some Computational Results for Dual-Primal FETI Methods for Elliptic Problems in 3D....Pages 361-368
The FETI Based Domain Decomposition Method for Solving 3D-Multibody Contact Problems with Coulomb Friction....Pages 369-376
Choosing Nonmortars: Does it Influence the Performance of FETI-DP Algorithms?....Pages 377-384
Domain Decomposition Methods in Electrothermomechanical Coupling Problems....Pages 387-394
A Multiphysics Strategy for Free Surface Flows....Pages 395-402
Weighted Norm-Equivalences for Preconditioning....Pages 405-412
Preconditioning for Heterogeneous Problems....Pages 415-422
On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations....Pages 425-432
A Parareal in Time Semi-implicit Approximation of the Navier-Stokes Equations....Pages 433-440
The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation....Pages 441-448
Stability of the Parareal Algorithm....Pages 449-456
Multilevel Homotopic Adaptive Finite Element Methods for Convection Dominated Problems....Pages 459-468
A Convergent Algorithm for Time Parallelization Applied to Reservoir Simulation....Pages 469-476
Nonlinear Positive Interpolation Operators for Analysis with Multilevel Grids....Pages 477-484
On Scalable Algorithms for Numerical Solution of Variational Inequalities Based on FETI and Semi-monotonic Augmented Lagrangians....Pages 487-494
Fast Solving of Contact Problems on Complicated Geometries....Pages 495-502
Generalized Aitken-like Acceleration of the Schwarz Method....Pages 505-512
The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical Experiments....Pages 513-520
Modelling of an Underground Waste Disposal Site by Upscaling and Simulation with Domain Decomposition Method....Pages 521-528
Non-Overlapping DDMs to Solve Flow in Heterogeneous Porous Media....Pages 529-536
Domain Embedding/Controllability Methods for the Conjugate Gradient Solution of Wave Propagation Problems....Pages 537-546
An Accelerated Block-Parallel Newton Method via Overlapped Partitioning....Pages 547-554
Generation of Balanced Subdomain Clusters with Minimum Interface for Distributed Domain Decomposition Applications....Pages 555-562
Iterative Methods for Stokes/Darcy Coupling....Pages 563-570
Preconditioning Techniques for the Bidomain Equations....Pages 571-580
Direct Schur Complement Method by Hierarchical Matrix Techniques....Pages 581-588
Balancing Neumann-Neumann Methods for Elliptic Optimal Control Problems....Pages 589-596
Domain Decomposition Preconditioners for Spectral N?d?lec Elements in Two and Three Dimensions....Pages 597-604
Parallel Distributed Object-Oriented Framework for Domain Decomposition....Pages 605-614
A Domain Decomposition Based Two-Level Newton Scheme for Nonlinear Problems....Pages 615-622
Domain Decomposition for Discontinuous Galerkin Method with Application to Stokes Flow....Pages 623-630
Hierarchical Matrices for Convection-Dominated Problems....Pages 631-638
Parallel Performance of Some Two-Level ASPIN Algorithms....Pages 639-646
Algebraic Analysis of Schwarz Methods for Singular Systems....Pages 647-652
Schwarz Waveform Relaxation Method for the Viscous Shallow Water Equations....Pages 653-660
A Two-Grid Alternate Strip-Based Domain Decomposition Strategy in Two-Dimensions....Pages 661-668
Parallel Solution of Cardiac Reaction-Diffusion Models....Pages 669-676
Predictor-Corrector Methods for Solving Continuous Casting Problem....Pages 677-684
Back Matter....Pages 685-690

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Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

Content:
Front Matter....Pages i-xviii
Non-matching Grids and Lagrange Multipliers....Pages 3-18
A FETI Method for a Class of Indefinite or Complex Second- or Fourth-Order Problems....Pages 19-34
Hybrid Schwarz-Multigrid Methods for the Spectral Element Method: Extensions to Navier-Stokes....Pages 35-49
Numerical Approximation of Dirichlet-to-Neumann Mapping and its Application to Voice Generation Problem....Pages 51-65
Selecting Constraints in Dual-Primal FETI Methods for Elasticity in Three Dimensions....Pages 67-81
Coupled Boundary and Finite Element Tearing and Interconnecting Methods....Pages 83-97
Parallel Simulation of Multiphase/Multicomponent Flow Models....Pages 99-113
Uncoupling-Coupling Techniques for Metastable Dynamical Systems....Pages 115-129
On the Construction of Approximate Boundary Conditions for Solving the Interior Problem of the Acoustic Scattering Transmission Problem....Pages 133-140
Approximation and Fast Calculation of Non-local Boundary Conditions for the Time-dependent Schr?dinger Equation....Pages 141-148
Domain Decomposition and Additive Schwarz Techniques in the Solution of a TE Model of the Scattering by an Electrically Deep Cavity....Pages 149-156
A Model for Parallel Adaptive Finite Element Software....Pages 159-166
Towards a Unified Framework for Scientific Computing....Pages 167-174
Distributed Point Objects. A New Concept for Parallel Finite Elements....Pages 175-182
Local Defect Correction Techniques Applied to a Combustion Problem....Pages 185-192
Electronic Packaging and Reduction in Modelling Time Using Domain Decomposition....Pages 193-200
Improving Robustness and Parallel Scalability of Newton Method Through Nonlinear Preconditioning....Pages 201-208
Iterative Substructuring Methods for Indoor Air Flow Simulation....Pages 209-216
Fluid-Structure Interaction Using Nonconforming Finite Element Methods....Pages 217-224
Interaction Laws in Viscous-Inviscid Coupling....Pages 225-232
Comparison of the Dirichlet-Neumann and Optimal Schwarz Method on the Sphere....Pages 235-242
Finite Volume Methods on Non-Matching Grids with Arbitrary Interface Conditions and Highly Heterogeneous Media....Pages 243-250
Nonlinear Advection Problems and Overlapping Schwarz Waveform Relaxation....Pages 251-258
A New Cement to Glue Nonconforming Grids with Robin Interface Conditions: The Finite Element Case....Pages 259-266
Acceleration of a Domain Decomposition Method for Advection-Diffusion Problems....Pages 267-274
A Stabilized Three-Field Formulation and its Decoupling for Advection-Diffusion Problems....Pages 275-282
Approximation of Optimal Interface Boundary Conditions for Two-Lagrange Multiplier FETI Method....Pages 283-290
Optimized Overlapping Schwarz Methods for Parabolic PDEs with Time-Delay....Pages 291-298
A More General Version of the Hybrid-Trefftz Finite Element Model by Application of TH-Domain Decomposition....Pages 301-308
Mixed Finite Element Methods for Diffusion Equations on Nonmatching Grids....Pages 311-318
Mortar Finite Elements with Dual Lagrange Multipliers: Some Applications....Pages 319-326
Non-Conforming Finite Element Methods for Nonmatching Grids in Three Dimensions....Pages 327-334
On an Additive Schwarz Preconditioner for the Crouzeix-Raviart Mortar Finite Element....Pages 335-342
A FETI-DP Method for the Mortar Discretization of Elliptic Problems with Discontinuous Coefficients....Pages 345-352
A FETI-DP Formulation for Two-dimensional Stokes Problem on Nonmatching Grids....Pages 353-360
Some Computational Results for Dual-Primal FETI Methods for Elliptic Problems in 3D....Pages 361-368
The FETI Based Domain Decomposition Method for Solving 3D-Multibody Contact Problems with Coulomb Friction....Pages 369-376
Choosing Nonmortars: Does it Influence the Performance of FETI-DP Algorithms?....Pages 377-384
Domain Decomposition Methods in Electrothermomechanical Coupling Problems....Pages 387-394
A Multiphysics Strategy for Free Surface Flows....Pages 395-402
Weighted Norm-Equivalences for Preconditioning....Pages 405-412
Preconditioning for Heterogeneous Problems....Pages 415-422
On the Convergence and the Stability of the Parareal Algorithm to Solve Partial Differential Equations....Pages 425-432
A Parareal in Time Semi-implicit Approximation of the Navier-Stokes Equations....Pages 433-440
The Parareal in Time Iterative Solver: a Further Direction to Parallel Implementation....Pages 441-448
Stability of the Parareal Algorithm....Pages 449-456
Multilevel Homotopic Adaptive Finite Element Methods for Convection Dominated Problems....Pages 459-468
A Convergent Algorithm for Time Parallelization Applied to Reservoir Simulation....Pages 469-476
Nonlinear Positive Interpolation Operators for Analysis with Multilevel Grids....Pages 477-484
On Scalable Algorithms for Numerical Solution of Variational Inequalities Based on FETI and Semi-monotonic Augmented Lagrangians....Pages 487-494
Fast Solving of Contact Problems on Complicated Geometries....Pages 495-502
Generalized Aitken-like Acceleration of the Schwarz Method....Pages 505-512
The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical Experiments....Pages 513-520
Modelling of an Underground Waste Disposal Site by Upscaling and Simulation with Domain Decomposition Method....Pages 521-528
Non-Overlapping DDMs to Solve Flow in Heterogeneous Porous Media....Pages 529-536
Domain Embedding/Controllability Methods for the Conjugate Gradient Solution of Wave Propagation Problems....Pages 537-546
An Accelerated Block-Parallel Newton Method via Overlapped Partitioning....Pages 547-554
Generation of Balanced Subdomain Clusters with Minimum Interface for Distributed Domain Decomposition Applications....Pages 555-562
Iterative Methods for Stokes/Darcy Coupling....Pages 563-570
Preconditioning Techniques for the Bidomain Equations....Pages 571-580
Direct Schur Complement Method by Hierarchical Matrix Techniques....Pages 581-588
Balancing Neumann-Neumann Methods for Elliptic Optimal Control Problems....Pages 589-596
Domain Decomposition Preconditioners for Spectral N?d?lec Elements in Two and Three Dimensions....Pages 597-604
Parallel Distributed Object-Oriented Framework for Domain Decomposition....Pages 605-614
A Domain Decomposition Based Two-Level Newton Scheme for Nonlinear Problems....Pages 615-622
Domain Decomposition for Discontinuous Galerkin Method with Application to Stokes Flow....Pages 623-630
Hierarchical Matrices for Convection-Dominated Problems....Pages 631-638
Parallel Performance of Some Two-Level ASPIN Algorithms....Pages 639-646
Algebraic Analysis of Schwarz Methods for Singular Systems....Pages 647-652
Schwarz Waveform Relaxation Method for the Viscous Shallow Water Equations....Pages 653-660
A Two-Grid Alternate Strip-Based Domain Decomposition Strategy in Two-Dimensions....Pages 661-668
Parallel Solution of Cardiac Reaction-Diffusion Models....Pages 669-676
Predictor-Corrector Methods for Solving Continuous Casting Problem....Pages 677-684
Back Matter....Pages 685-690
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