Domain Decomposition Methods in Science and Engineering XXVI / / Susanne C. Brenner [and five others], editors

• Pubblicazione: Cham, Switzerland : , : Springer Nature Switzerland AG, , [2022]; ©2022
• Edizione: First edition.
• Descrizione fisica: 1 online resource (777 pages)
• Disciplina: 515.353
• Soggetto topico: Decomposition method; Differential equations, Partial; Descomposició (Matemàtica); Processament de dades; Equacions en derivades parcials
• Soggetto genere / forma: Congressos; Llibres electrònics
• Persona (resp. second.): BrennerSusanne C.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Background of the Conference Series -- About the 26th Conference -- Acknowledgments -- Contents -- List of Contributors -- Part I Plenary Talks (PT) -- Multiscale Model Reduction for a Class of Optimal Control Problems with Highly Oscillating Coefficients -- 1 Introduction -- 2 Method description -- 2.1 Multiscale basis functions -- 2.2 The proposed method -- 2.3 Outline of error analysis -- 3 Numerical results -- References -- SeveralWays to Achieve Robustness When SolvingWave Propagation Problems -- 1 Motivation and challenges -- 1.1 Why the time-harmonic problem in mid and high frequency is hard -- 2 What is the best coarse space for Helmholtz? -- 2.1 Spectral coarse spaces for Helmholtz -- 2.2 Comparison of coarse spaces -- 3 Can we improve on the auxiliary subspace preconditioner? -- 4 General conclusions -- References -- Scalable Hybrid TFETI-DP Methods for Large Boundary Variational Inequalities -- 1 Introduction -- 2 Model problem -- 3 Domain decomposition and discretization -- 4 TFETI problem -- 5 Connecting subdomains into clusters -- 6 Bounds on the spectrum of H and optimality -- 7 Numerical experiments -- 7.1 Comparing estimate and experiments -- 7.2 Comparing linear unpreconditioned H-TFETI-DP and TFETI -- 7.3 Model variational inequality and elastic body on rigid obstacle -- References -- Fundamental Coarse Space Components for Schwarz Methods with Crosspoints -- 1 Introduction -- 2 Modal analysis of the Schwarz iteration map -- 3 The special case of 2 × 2 subdomains -- 4 A new coarse space for parallel Schwarz methods -- 5 Numerical experiments -- 6 A note on the optimized Robin parameter -- 7 Conclusion -- References -- Nonoverlapping Domain Decomposition Methods for Time HarmonicWave Problems -- 1 Elliptic equations versus the Helmholtz equation -- 2 Impedance-based transmission conditions and related DDM. ; 3 Convergence analysis -- 4 Construction of appropriate impedance operators -- 5 The problem of cross points -- References -- Quantitative Analysis of Nonlinear Multifidelity Optimization for Inverse Electrophysiology -- 1 Introduction -- 2 Electrophysiological models -- 3 Inverse problem of Conductivity Identification -- 4 Multilevel Quasi-Newton Trust-region Method -- Quasi-Newton trust-region method -- Recursive multilevel trust-region method -- 5 Numerical results -- 5.1 Patient-specific geometry -- 5.2 Convergence study -- 6 Conclusion -- References -- Adaptive Space-Time Finite Element and Isogeometric Analysis -- 1 Introduction -- 2 Space-time variational formulations -- 3 Space-time isogeometric analysis -- 4 Space-time finite element analysis -- 5 Space-time optimal control -- References -- Nonoverlapping Domain Decomposition Methods for Saddle Point Problems -- 1 Introduction -- 2 Problem setting -- 3 Domain decomposition -- 4 Positive definite formulations -- 4.1 The primal system (6) -- 4.2 The dual system (12) -- 5 Condition number estimates -- 6 Connections and differences -- References -- Local Residual Minimization Smoothing for Improving Convergence Behavior of a Space-Time Domain Decomposition Method -- 1 Introduction -- 2 Flow model problem -- 3 Local residual minimization -- 4 Numerical results -- 5 Conclusions -- References -- Part II Talks in Minisymposia -- GenEO Coarse Spaces for Heterogeneous Indefinite Elliptic Problems -- 1 Introduction and motivations -- 2 Discretisation and domain decomposition solver -- 3 Theoretical results -- 4 Numerical results -- 5 Conclusions -- References -- Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems -- 1 Introduction -- 2 Model problem, discretisation and preconditioning strategies -- 3 Numerical results -- 3.1 Direct subdomain solves -- 3.2 Inexact subdomain solves. ; 4 Conclusions -- References -- Non-Overlapping Domain Decomposition Methods with Cross-Points and Padé Approximants for the Helmholtz Equation -- 1 Introduction -- 2 Model problem -- 3 Non-overlapping domain decomposition algorithm -- 4 Nodal FEM-NDDM and the cross-points problem -- 5 Numerical results -- References -- OSDS: A Sweeping Preconditioner for the Helmholtz Equation -- 1 Statement of the problem and some algorithms -- 2 Overlapping splitting double sweep -- 2.1 Substructuring -- 2.2 Overlapping Splitting Double Sweep preconditioner (OSDS) -- 3 Numerical results -- 3.1 Wedge test -- 3.2 Influence of the overlap -- 4 Conclusion -- References -- Decomposition and Preconditioning of Deep Convolutional Neural Networks for Training Acceleration -- 1 Introduction -- 2 Proposed approaches -- 2.1 Decomposing a DCNN into sub-networks -- 2.2 Preconditioning of DCNNs -- 3 Experiments -- 4 Conclusion -- References -- Numerical Calculation of the Portal Pressure Gradient of the Human Liver With a Domain Decomposition Method -- 1 Introduction -- 2 Numerical method -- 3 Numerical experiments -- References -- A Parallel Adaptive Finite Element Method for Modeling a Deformable Droplet Travelling in Air -- 1 Introduction -- 2 A mathematical model based on the Cahn-Hilliard-Navier-Stokes equations -- 3 A parallel, semi-implicit solution algorithm based on an adaptive finite element discretization, and an overlapping Schwarz pr -- 4 Numerical experiments -- 5 Conclusions -- References -- On the Effect of Boundary Conditions on the Scalability of Schwarz Methods -- 1 Introduction -- 2 Laplace eigenpairs for mixed external conditions -- 3 Convergence and scalability -- 4 Numerical experiments -- References -- On the Asymptotic Optimality of Spectral Coarse Spaces -- 1 Introduction -- 2 A perturbation approach -- 3 Optimizing the coarse-space functions. ; References -- Discrete Analysis of SchwarzWaveform Relaxation for a Simplified Air-Sea Coupling Problem with Nonlinear Transmission Conditions -- 1 Introduction -- 2 Model problem for ocean-atmosphere coupling -- 3 Discretized coupled problem -- 3.1 Implementation of the surface layer -- 3.2 SchwarzWaveform Relaxation -- 4 Convergence analysis -- 5 Numerical experiments -- 6 Conclusion -- References -- A Posteriori Error Estimates in Maximum Norm for Interior Penalty Discontinuous Galerkin Approximation of the Obstacle Problem -- 1 Introduction -- 2 The elliptic obstacle problem -- 3 The Symmetric Interior Penalty method -- 4 Reliable a posteriori error estimates in the maximum norm -- 5 Numerical results -- 5.1 Numerical experiments -- References -- Spectral Equivalence Properties of Higher-Order Tensor Product Finite Elements -- 1 Introduction -- 2 Shape functions -- 2.1 Edge shape functions -- 2.2 Face shape functions -- 2.3 Interior shape functions -- 2.4 Lowest-order shape functions -- 3 Spectral equivalence results -- 3.1 Mass matrix equivalence -- 3.2 Stiffness matrix equivalence -- 4 Numerical results -- References -- Optimizing Transmission Conditions for Multiple Subdomains in the Magnetotelluric Approximation of Maxwell's Equations -- 1 Optimized Schwarz for the Magnetotelluric Approximation -- 2 Optimization for 2, 3, 4, 5 and 6 subdomains -- 3 Optimization for many subdomains -- References -- Non-overlapping Spectral Additive Schwarz Methods for HDG and Multiscale Discretizations -- 1 Introduction -- 2 Domain decomposition setting -- 3 NOSAS with exact and inexact solvers -- 4 Multiscale discretization methods -- 5 Numerical experiments -- References -- Robust BPX Solver for Cahn-Hilliard Equations -- 1 Introduction -- 2 Numerical approximation -- 3 Newton's method -- 4 Preconditioned iterative solver -- 5 Conclusions -- References. ; Natural Factor Based Solvers -- 1 Summary -- 2 Introduction -- 3 Crouzeix-Raviart nonconforming finite elements -- 4 Conforming finite elements -- 5 The null space method -- 6 Range null-space hybrid -- 7 An auxiliary problem and 2 × 2 systems -- 8 PCG for the block system and numerical experiments -- References -- A Simple Finite Difference Discretization for Ventcell Transmission Conditions at Cross Points -- 1 Introduction -- 2 Optimized Schwarz with Ventcell transmission conditions -- 3 Numerical experiments -- 4 Conclusions -- References -- Cycles in Newton-Raphson Preconditioned by Schwarz (ASPIN and Its Cousins) -- 1 Introduction -- 2 Convergence of generic fixed point iterations and Newton-Raphson -- 3 The fixed point iteration of alternating Schwarz -- 4 Accelerated alternating Schwarz with guaranteed convergence -- References -- Should Multilevel Methods for Discontinuous Galerkin Discretizations Use Discontinuous Interpolation Operators? -- 1 Discontinuous interpolation for a model problem -- 2 Study of optimal parameters by Local Fourier Analysis -- 3 Numerical results -- 4 Conclusion -- References -- Domain Decomposition in Shallow Water Modelling of Dutch Lakes for Multiple Applications -- 1 Introduction -- 1.1 Area of interest -- 1.2 Previous approaches -- 1.3 New approach -- 2 Computational grids -- 3 Domain decomposition for parallel computing in Delft3D FM -- 4 Conclusions and outlook -- References -- A Variational Interpretation of Restricted Additive SchwarzWith Impedance Transmission Condition for the Helmholtz Problem -- 1 The Helmholtz problem -- 2 Parallel iterative Schwarz method -- 3 Variational formulation of RAS with impedance transmission condition (ORAS) -- 4 Connecting the parallel iterative method with ORAS -- 5 Numerical results -- References. ; Application of Multilevel BDDC to the Problem of Pressure in Simulations of Incompressible Flow.
• Sommario/riassunto: These are the proceedings of the 26th International Conference on Domain Decomposition Methods in Science and Engineering, which was hosted by the Chinese University of Hong Kong and held online in December 2020. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2020.
• Titolo autorizzato: Domain Decomposition Methods in Science and Engineering XXVI
• ISBN: 3-030-95025-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996518464203316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture notes in computational science and engineering ; ; Volume 145.