Domain decomposition methods
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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations Open
Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework,…
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A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods Open
Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades an important research effort has gone into developing preconditioners for the simplest representative of such wave prop…
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D3M: A Deep Domain Decomposition Method for Partial Differential Equations Open
A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization proble…
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Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology Open
Physics-Informed Neural Networks (PINNs) and extended PINNs (XPINNs) have emerged as a promising approach in computational science and engineering for solving partial differential equations (PDEs) by combining the power of artificial intel…
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Spectral Tensor-Train Decomposition Open
The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomp…
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An analysis of a class of variational multiscale methods based on subspace decomposition Open
Numerical homogenization tries to approximate the solutions of elliptic\npartial differential equations with strongly oscillating coefficients by\nfunctions from modified finite element spaces. We present in this paper a class\nof such met…
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Forward and inverse modeling of water flow in unsaturated soils with discontinuous hydraulic conductivities using physics-informed neural networks with domain decomposition Open
Modeling water flow in unsaturated soils is vital for describing various hydrological and ecological phenomena. Soil water dynamics is described by well-established physical laws (Richardson–Richards equation – RRE). Solving the RRE is dif…
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Nonlinear Preconditioning: How to Use a Nonlinear Schwarz Method to Precondition Newton's Method Open
For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much bette…
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Multilevel Balancing Domain Decomposition at Extreme Scales Open
© 2016 Society for Industrial and Applied Mathematics. In this paper we present a fully distributed, communicator-aware, recursive, and interlevel-overlapped message-passing implementation of the multilevel balancing domain decomposition b…
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Adaptive aggregation-based domain decomposition multigrid for twisted mass fermions Open
The Adaptive Aggregation-based Domain Decomposition Multigrid method (arXiv:1303.1377) is extended for two degenerate flavors of twisted mass fermions. By fine-tuning the parameters we achieve a speed-up of the order of hundred times compa…
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<span> <b>Swift</b> </span>: a modern highly parallel gravity and smoothed particle hydrodynamics solver for astrophysical and cosmological applications Open
Numerical simulations have become one of the key tools used by theorists in all the fields of astrophysics and cosmology. The development of modern tools that target the largest existing computing systems and exploit state-of-the-art numer…
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An Approximate Schur Decomposition-Based Spatial Domain Color Image Watermarking Method Open
In this paper, an approximate Schur decomposition-based spatial domain blind color image watermarking method is proposed to protect the copyright of color images, which has low computation complexity similiar to the watermarking technique …
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Time domain room acoustic simulations using the spectral element method Open
This paper presents a wave-based numerical scheme based on a spectral element method, coupled with an implicit-explicit Runge-Kutta time stepping method, for simulating room acoustics in the time domain. The scheme has certain features whi…
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RASCAS: RAdiation SCattering in Astrophysical Simulations Open
Context. Resonant lines are powerful probes of the interstellar and circumgalactic medium of galaxies. Their transfer in gas being a complex process, the interpretation of their observational signatures, either in absorption or in emission…
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Computational electro‐elasticity and magneto‐elasticity for quasi‐incompressible media immersed in free space Open
Summary In this work, a mixed variational formulation to simulate quasi‐incompressible electro‐active or magneto‐active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the pr…
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New massively parallel scheme for Incompressible Smoothed Particle Hydrodynamics (ISPH) for highly nonlinear and distorted flow Open
A new massively parallel scheme is developed to simulate free-surface flows with the meshless method incompressible smoothed particle hydrodynamics (ISPH) for simulations involving more than 100 million particles. As a pressure-projection …
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Universal time-domain Prony fitting decomposition for optimized hierarchical quantum master equations Open
In this Communication, we propose the time-domain Prony fitting decomposition (t-PFD) as an accurate and efficient exponential series method, applicable to arbitrary bath correlation functions. The resulting numerical efficiency of hierarc…
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Optimal Interface Conditions for Domain Decomposition Methods Open
We define optimal interface conditions for the additive Schwarz method (ASM) in the sense that convergence is achieved in a number of steps equals to the number of subdomains. Since these boundary conditions are difficult to use, we approx…
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Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review Open
Scientific machine learning (SciML), an area of research where techniques from machine learning and scientific computing are combined, has become of increasing importance and receives growing attention. Here, our focus is on a very specifi…
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Multilevel domain decomposition-based architectures for physics-informed neural networks Open
Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequency and/or multi-scale solutions. Finite basis physics-inform…
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Some Schwarz methods for symmetric and nonsymmetric elliptic problems. Open
Evaluating and understanding biodiversity in marine ecosystems are both necessary and challenging for conservation. This paper compiles and summarizes current knowledge of the diversity of marine taxa in Canada's three oceans while recogni…
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BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields Open
A BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local …
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Adaptive Selection of Primal Constraints for Isogeometric BDDC Deluxe Preconditioners Open
Isogeometric analysis has been introduced as an alternative to finite element methods in order to simplify the integration of computer-aided design (CAD) software and the discretization of variational problems of continuum mechanics. In co…
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On the application of the spectral element method in electromagnetic problems involving domain decomposition Open
One of the challenges in electromagnetics is to solve electromagnetic fields originated from a radiating source or a scattering object in distances that largely exceed the dimensions of the source or scatterer. In this paper, domain decomp…
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SWIFT Open
We present a new open-source cosmological code, called SWIFT, designed to solve the equations of hydrodynamics using a particle-based approach (Smooth Particle Hydrodynamics) on hybrid shared / distributed-memory architectures. SWIFT was d…
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Scalability of an Eulerian-Lagrangian large-eddy simulation solver with hybrid MPI/OpenMP parallelisation Open
Eulerian-Lagrangian approaches capable of accurately reproducing complex fluid flows are becoming more and more popular due to the increasing availability and capacity of High Performance Computing facilities. However, the parallelisation …
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Parallel computing in railway research Open
Available computing power for researchers has been increasing exponentially over the last decade. Parallel computing is possibly the best way to harness computing power provided by multiple computing units. This paper reviews parallel comp…
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Mesh moving techniques in fluid-structure interaction: robustness, accumulated distortion and computational efficiency Open
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh moving technique (MMT) used to adapt the computational mesh in the moving fluid domain. An ideal MMT is computationally inexpensiv…
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Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption Open
This paper rigorously analyses preconditioners for the time-harmonic Maxwell\nequations with absorption, where the PDE is discretised using curl-conforming\nfinite-element methods of fixed, arbitrary order and the preconditioner is\nconstr…
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Robust and parallel scalable iterative solutions for large-scale finite cell analyses Open
The finite cell method is a flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a wide …