Domain Decomposition Methods in Science and Engineering XXVII (Lecture Notes in Computational Science and Engineering, 149)

✍ Scribed by Zdeněk Dostál (editor), Tomáš Kozubek (editor), Axel Klawonn (editor), Ulrich Langer (editor), Luca F. Pavarino (editor), Jakub Šístek (editor), Olof B. Widlund (editor)

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 546
• Category: Library

✦ Synopsis

These are the proceedings of the 27th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Prague, Czech Republic, in July 2022.

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 2022.

✦ Table of Contents

Preface
Contents
List of Contributors
Part I
Plenary Talks (PT)
A Short Note on Solving Partial Differential Equations Using Convolutional Neural Networks
1 Introduction
2 Model problem and discretization
3 Solving the finite difference problem using classical methods versus using convolutional neural networks
4 Network architecture and hyper parameters
5 Numerical results
6 Conclusion
References
Optimized Robin Transmission Conditions for Anisotropic Diffusion on Arbitrary Meshes
Domain Decomposition Algorithms for Neural Network Approximation of Partial Differential Equations
Convergence Bounds for One-Dimensional ASH and RAS
Part II Talks in Minisymposia
Weak Scalability of Domain Decomposition Methods for Discrete Fracture Networks
How Does the Partition of Unity Influence SORAS Preconditioner?
Convergence of the Micro-Macro Parareal Method for a Linear Scale-Separated Ornstein-Uhlenbeck SDE
A Trefftz-Like Coarse Space for the Two-Level Schwarz Method on Perforated Domains
On Global and Monotone Convergence of the Preconditioned Newton’s Method for Some Mildly Nonlinear Systems
Optimized Schwarz Method in Time for Transport Control
An Overlapping Preconditioner for 2D Virtual Problems Posed in H(rot) with Irregular Subdomains
A Two-Level Restricted Additive Schwarz Method for Asynchronous Computations
Cross-Points in the Neumann-Neumann Method
A Preconditioner for Free-Surface Hydrodynamics BEM
A Performance Comparison of Classical Volume and New Substructured One- and Two-Level Schwarz Methods in PETSc
Semi-Discrete Analysis of a Simplified Air-Sea Coupling Problem with Nonlinear Coupling Conditions
A Block Jacobi Sweeping Preconditioner for the Helmholtz Equation
Optimized Neumann-Neumann Method for the Stokes-Darcy Problem
Finite Basis Physics-Informed Neural Networks as a Schwarz Domain Decomposition Method
Multigrid Interpretation of a Three-Level Parareal Algorithm
Coupling Dispersive Shallow Water Models by Deriving Asymptotic Interface Operators
Piece-wise Constant, Linear and Oscillatory: a Historical Introduction to Spectral Coarse Spaces with Focus on Schwarz Methods
A New Nodal Integration Method for Helmholtz Problems Based on Domain Decomposition Techniques
Dirichlet-Neumann and Neumann-Neumann Methods for Elliptic Control Problems
An Introduction to Heterogeneous Domain Decomposition Methods for Multi-Physics Problems
Substructuring of Arbitrary Domain Decomposition Methods
Spectral Q1-Based Coarse Spaces for Schwarz Methods
Optimized Schwarz Methods for Stokes-Darcy Flows: the Brinkman Equations
Parareal Algorithms for the Cahn-Hilliard Equation
A Parallel Space-Time Finite Element Method for the Simulation of an Electric Motor
Reynolds-BlendedWeights for BDDC in Applications to Incompressible Flows
Neural Network Interface Condition Approximation in a Domain Decomposition Method Applied to Maxwell’s Equations
Learning Adaptive FETI-DP Constraints for Irregular Domain Decompositions
Adaptive Three-Level BDDC Using Frugal Constraints
Efficient Adaptive Elimination Strategies in Nonlinear FETI-DP Methods in Combination with Adaptive Spectral Coarse Spaces
On the Use of Hybrid Coarse-Level Models in Multilevel Minimization Methods
Nonlinear Schwarz Preconditioning for Quasi-Newton Methods
Nonlinear Schwarz Preconditioning for Nonlinear Optimization Problems with Bound Constraints
Domain Decomposition Solvers for Operators with Fractional Interface Perturbations
Optimized Schwarz Methods for Isogeometric Analysis
An Alternating Approach for Optimizing Transmission Conditions in Algebraic Schwarz Methods
FETI-DP Algorithms for 2D Biot Model with Discontinuous Galerkin Discretization
Linear, Super-Linear and Combined Fourier Heat Kernel Convergence Estimates for Schwarz Waveform Relaxation
Cyclic and Chaotic Examples in Schwarz-Preconditioned Newton Methods
Global-Local Forward Models within Bayesian Inversion for Large Strain Fracturing in Porous Media
On Algebraic Bounds for POSM and MRAS
Hierarchical LU Preconditioning for the Time-Harmonic Maxwell Equations
Convergence Bounds for Parareal with Spatial Coarsening
Three-Level NOSAS Preconditioners
Optimized Schwarz Method for Coupled Direct-Adjoint Problems Applied to Parameter Identification in Advection-Diffusion Equation
Three-Level BDDC for Virtual Elements
An Adaptive Overlapping Schwarz Algorithm for Isogeometric Analysis
Part III Contributed Talks
Numerical Assessment of PML Transmission Conditions in a Domain Decomposition Method for the Helmholtz Equation
Unmapped Tent Pitching Schemes by Waveform Relaxation
A 2-Level Domain Decomposition Preconditioner for KKT Systems with Heat-Equation Constraints
Auxiliary Space Preconditioning with a Symmetric Gauss-Seidel Smoothing Scheme for IsoGeometric Discretization of H0¹curlº-elliptic Problem
Composing Two Different Nonlinear FETI–DP Methods
Biot Model with Generalized Eigenvalue Problems for Scalability and Robustness to Parameters
Adaptive Schwarz Method for a Non-Conforming Crouzeix-Raviart Discretization of a Multiscale Elliptic Problem
A Variational-Based Multirate Time-Integrator for FETI and Structural Dynamics: Lagrange-Multiplier with Micro-Discretization
Accelerated Convergence of the Pipelined Dynamic Iteration Method for RLC Circuits
GPU Optimizations for the Hierarchical Poincaré-Steklov Scheme